Constraints on global mean sea level during Pliocene warmth


Reconstructing the evolution of sea level during past warmer epochs such as the Pliocene provides insight into the response of sea level and ice sheets to prolonged warming1. Although estimates of the global mean sea level (GMSL) during this time do exist, they vary by several tens of metres2,3,4, hindering the assessment of past and future ice-sheet stability. Here we show that during the mid-Piacenzian Warm Period, which was on average two to three degrees Celsius warmer than the pre-industrial period5, the GMSL was about 16.2 metres higher than today owing to global ice-volume changes, and around 17.4 metres when thermal expansion of the oceans is included. During the even warmer Pliocene Climatic Optimum (about four degrees Celsius warmer than pre-industrial levels)6, our results show that the GMSL was 23.5 metres above the present level, with an additional 1.6 metres from thermal expansion. We provide six GMSL data points, ranging from 4.39 to 3.27 million years ago, that are based on phreatic overgrowths on speleothems from the western Mediterranean (Mallorca, Spain). This record is unique owing to its clear relationship to sea level, its reliable U–Pb ages and its long timespan, which allows us to quantify uncertainties on potential uplift. Our data indicate that ice sheets are very sensitive to warming and provide important calibration targets for future ice-sheet models7.

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Fig. 1: POS in Coves d’Artà.
Fig. 2: GIA and other corrections.
Fig. 3: Pliocene sea-level and CO2 concentration changes.

Data availability

The data produced in this study are available at the NOAA ( and Pangaea ( data repositories.

Code availability

The computer code used to do the sea-level (GIA) calculation, written in MATLAB, is available on github:


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We thank the owner and personnel of Coves d’Artà for granting permission and offering logistic support during the field research conducted for this study. We thank F. L. Forray and G. Lucia for helping with the coring process. B.P.O. and V.J.P. are funded by a collaborative NSF grant (AGS 1602670). Additional research costs were covered by a NSF grant (EAR 0326902 to Y.A. and V.J.P.) and MINECO grants (CGL2013-48441-P and CGL2016-79246-P to J.J.F.). O.A.D. received student research grants from the Cave Research Foundation, the Geological Society of America, and the Fred L. and Helen M. Tharp Endowed Scholarship (School of Geosciences, University of South Florida). J.A. thanks the PALSEA working group and the NSF (grant OCE-0825293 “PLIOMAX”) for facilitating discussions at regular meetings, and the Vetlesen Foundation for support.

Author information




B.P.O., J.J.F. and O.A.D. designed the research. A.G. and J.G. first documented the presence of POS in the cave studied. B.P.O., J.J.F., J.G., A.G. and O.A.D. measured POS elevations and collected samples. V.J.P., O.A.D. and Y.A. measured U–Pb ages of POS samples. J.A. produced the GIA and long-term deformation corrections. O.A.D., J.A. and B.P.O. drafted and wrote the majority of the manuscript with input from all authors.

Corresponding author

Correspondence to Bogdan P. Onac.

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The authors declare no competing interests.

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Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Peer review information Nature thanks Eelco Rohling, Jon Woodhead and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Extended data figures and tables

Extended Data Fig. 1 Schematic profile of a coastal cave in Mallorca hosting POS at different levels.

a, b, Standalone (a) and cave-wall (b) POS structures. The asterisked POS is an example of an asymmetric knob-like carbonate encrustation that forms when only the tip of the stalactite is submerged.

Extended Data Fig. 2 U–Pb isochrons and calculated age estimates for the six POS samples.

a, 235U–207Pb two-dimensional isochron for sample AR-02; bf, Concordia-constrained linear three-dimensional isochron for samples AR-05 (b), AR-11 (c), AR-15 (d), AR-09 (e) and AR-03 (f). Error ellipses on individual ages are 2σ.

Extended Data Fig. 3 GIA contribution due to ongoing adjustment.

This GIA contribution is caused by the incomplete present-day adjustment to the late Pleistocene ice and ocean loading cycles. a, Model simulation using a viscosity structure of 5 × 1020 Pa s viscosity in the upper mantle, 5 × 1021 Pa s viscosity in the lower mantle, and an elastic lithospheric thickness of 96 km. b, Standard deviation of model predictions obtained using 36 different radial viscosity profiles, including varying the lithospheric thickness. The square marks the position of Coves d’Artà. The figures were produced using Matlab 2015b and the m_map plotting package (

Extended Data Fig. 4 GIA contribution due to Pliocene ice age cycles.

The model simulation uses a viscosity structure of 5 × 1020 Pa s viscosity in the upper mantle, 5 × 1021 Pa s viscosity in the lower mantle, and an elastic lithospheric thickness of 96 km. a, Snapshot of sea level at 3.244 Ma (grey vertical line in b) assuming a GMSL curve based on the LR04 benthic record10. The colour scale is chosen to diverge around the GMSL value of 13 m. The red square marks the position of Coves d’Artà. The figure was produced using Matlab 2015b and the m_map plotting package ( b, Local sea level at Coves d’Artà based on Rohling et al.2 (blue), de Boer et al.4 (yellow), and the LR04 benthic record10 (red). Respective GMSL curves are shown in black and mostly coincide with local sea level at Coves d’Artà (note that for the estimates based on Rohling et al.2 the black GMSL curve is mostly behind the local sea-level curve in blue). Sea level is relative to the beginning of this run (4.9 Ma).

Extended Data Fig. 5 Total GIA correction.

ac, Local sea-level change at Coves d’Artà, as calculated from the GIA model based on the GMSL curves by Rohling et al.2 (a), the LR04 benthic record10 (b) and de Boer et al.4 (c). Uncertainties due to Earth’s viscoelastic structure are denoted by grey bands. df, GIA correction colour coded by the GMSL value; standard deviations are shown as grey bands. Black markers indicate the GIA correction and its uncertainty for each POS. Results are for the GMSL curves by Rohling et al.2 (d), the LR04 benthic record10 (e) and de Boer et al.4 (f).

Extended Data Fig. 6 Uplift rate estimation.

Determining the amount of uplift based on the best fit of observed relative sea-level changes across the POS to other GMSL reconstructions over the same time interval. ac, GMSL curves2,4,10; grey bars are 1σ uncertainties. Boxes indicate the age uncertainty for each POS and the 50th and 99th percentiles of the GMSL values that fall within this age range. We calculate synthetic sea-level changes relative to the youngest POS and compare them to the observed sea-level changes, assuming a range of uplift rates. df, Histograms of uplift rates in which we find a good fit between the observed and the synthetic data. Percentiles (16th, 50th and 84th) are shown by vertical lines (solid line is the median, dashed lines are uncertainty bounds). We conducted ten million iterations for this Monte Carlo search. g, Histogram combining all uplift rates that resulted in a good fit.

Extended Data Fig. 7 Joint uplift rate estimation from varying the upper and lower cutoff.

ai, Joint histograms for a variety of lower and upper percentile cutoffs. The lower cutoff was varied between the 40th, 50th and 60th percentiles (different rows), whereas the upper cutoff was varied between the 90th, 95th and 99th percentiles (different columns). Percentiles in the histograms (16th, 50th and 84th) are shown by vertical lines (solid line is the median, dashed lines are uncertainty bounds). Panel f is identical to Extended Data Fig. 6g. j, Combination of all joint histograms to obtain our best-estimate uplift rate used for Table 1, Fig. 2c and Fig. 3.

Extended Data Fig. 8 Reconstructed elevation of the GMSL for each POS after all corrections have been applied.

af, PDFs for the GMSL estimate for AR-02, AR-05, AR-11, AR-15, AR-09 and AR-03, respectively. PDFs are constructed assuming Gaussian uncertainties for the measured elevation of POS, the respective indicative range, the GIA correction, thermal expansion and POS age (Table 1); a non-Gaussian distribution is obtained for the uplift correction (Table 1, Extended Data Figs. 6, 7). The mode (thick black line) and lower and upper uncertainty bounds (16th and 84th percentiles, thick dashed lines) are shown by vertical lines and correspond to the GMSL estimates reported in Table 1. We used a kernel with 1-m bandwidth to calculate the mode and PDF (thin black line).

Extended Data Table 1 GMSL estimates for different percentiles (10th, 33th, 50th, 66th and 90th) following IPCC’s likelihood scale

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Dumitru, O.A., Austermann, J., Polyak, V.J. et al. Constraints on global mean sea level during Pliocene warmth. Nature 574, 233–236 (2019).

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