Earth is heading towards a climate that last existed more than three million years ago (Ma) during the ‘mid-Pliocene warm period’1, when atmospheric carbon dioxide concentrations were about 400 parts per million, global sea level oscillated in response to orbital forcing2,3 and peak global-mean sea level (GMSL) may have reached about 20 metres above the present-day value4,5. For sea-level rise of this magnitude, extensive retreat or collapse of the Greenland, West Antarctic and marine-based sectors of the East Antarctic ice sheets is required. Yet the relative amplitude of sea-level variations within glacial–interglacial cycles remains poorly constrained. To address this, we calibrate a theoretical relationship between modern sediment transport by waves and water depth, and then apply the technique to grain size in a continuous 800-metre-thick Pliocene sequence of shallow-marine sediments from Whanganui Basin, New Zealand. Water-depth variations obtained in this way, after corrections for tectonic subsidence, yield cyclic relative sea-level (RSL) variations. Here we show that sea level varied on average by 13 ± 5 metres over glacial–interglacial cycles during the middle-to-late Pliocene (about 3.3–2.5 Ma). The resulting record is independent of the global ice volume proxy3 (as derived from the deep-ocean oxygen isotope record) and sea-level cycles are in phase with 20-thousand-year (kyr) periodic changes in insolation over Antarctica, paced by eccentricity-modulated orbital precession6 between 3.3 and 2.7 Ma. Thereafter, sea-level fluctuations are paced by the 41-kyr period of cycles in Earth’s axial tilt as ice sheets stabilize on Antarctica and intensify in the Northern Hemisphere3,6. Strictly, we provide the amplitude of RSL change, rather than absolute GMSL change. However, simulations of RSL change based on glacio-isostatic adjustment show that our record approximates eustatic sea level, defined here as GMSL unregistered to the centre of the Earth. Nonetheless, under conservative assumptions, our estimates limit maximum Pliocene sea-level rise to less than 25 metres and provide new constraints on polar ice-volume variability under the climate conditions predicted for this century.
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The code for the palaeobathymetry-grain size method is available from https://doi.org/10.1594/PANGAEA.902701.
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We thank L. van Rijn for comments on the grain size–water depth methodology. This research was primarily funded by The Royal Society of New Zealand, Marsden Grant 13 VUW 112, with additional support from the New Zealand Ministry of Business Innovation and Employment contract C05X1001. Technical drilling expertise was provided by D. Mandeno and A. Pyne of the Science Drilling Office, Antarctic Research Centre, Victoria University of Wellington and Webster Drilling and Exploration Ltd.
The authors declare no competing interests.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Peer review information Nature thanks Natasha Barlow and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Extended data figures and tables
a, Observations (dots) and model values (shaded bands represent the maximum and minimum ranges from the average bold lines) for sand (∑V>63) and water depth for three different modern shelf transects (Manawatu, NZ, green36; Monterey Bay, USA, blue39; Whanganui Bight, NZ, grey40). Wave parameters used are as follows: for Manawatu, Hs = 1.2 m and Tp = 20 s (ref. 41); for Monterey, Hs = 1.8 m and Tp = 20 s (ref. 42); and for Whanganui Bight, Hs = 2.2 m and Tp = 20 s (ref. 43). See Methods for nomenclature. Model error is described by equation (8). The red shaded band for ∑V>63 = 95%–100% represents the limit of the method, where all water depths contain 100% ∑V>63. The modern Whanganui Bight is selected as the most appropriate modern analogue to determine water depth from ∑V>63 recorded in both core and outcrop in this study. b, Derivatives of water depth–grain size models, for an average sediment cycle amplitude of 30% ∑V>63, for peak wave period Tp = 20 s and significant wave height Hs = 2.0 m (dark grey) and Hs = 2.5 m (light grey) and the difference (dashed light grey). c, Calibration of ΣV>63 from maximum grain size in distribution and measured D90 from core samples (blue circles) described by a linear relationship (dotted dark blue line; equation (5)) and the deviation (grey) of the model from observations. d, Calibration of peak wave period (Tp) exponent for the critical required velocity (Ucr,w; equation (1))14. Observations for Manawatu (most extensively sampled; green circles) are used for comparison between peak wave period exponents 0.33 (solid dark green line), 0.43 (dashed dark green line) and 0.5 (dotted light green line), with the deviations between models and observations shown by the respective patterned thinner black lines.
The figure shows a semi-enclosed broad embayment open to the dominant westerly wind, with an arcuate shoreline and a westward-deepening shelf15. The location of the Siberia-1 core (red circle) and the Rangitikei River Section (dotted red line) are noted.
Southern and Northern hemisphere high-latitude summer insolation18 (65° S, 1 January, solid line; 65° N, 1 July, dashed line) Pearson correlation coefficient with the PlioSeaNZ record between 3.3 and 3.0 Ma, using the ‘slideCor’ function from the R – Astrochron package47. Here a 0-kyr lag period denotes no temporal shift in the untuned PlioSeaNZ age model, and ±10-kyr lag periods signify correlation with a positive or negative shift of the PlioSeaNZ age model with respect to the astronomical record.
Extended Data Fig. 4 Assessment of RSL predicted at Whanganui, New Zealand, for pre-determined ESL scenarios.
a–c, RSL calculated for 20-kyr glacial–interglacial polar ice-sheet variability for three values of ESL (a, 15 m; b, 20 m; and c, 25 m) and three scenarios of polar ice-sheet contribution. Scenario 1 represents an Antarctic-only contribution, scenario 2 represents a Greenland Ice Sheet (GIS) contribution (of 5 m) in phase with a 15-m Antarctic contribution, and scenario 3 has a 30-m AIS contribution in anti-phase with 5 m of GIS accumulation. For each ESL value, all scenarios are indistinguishable as RSL at the Whanganui, New Zealand, site. d–f, RSL calculated for 20-kyr Antarctic variability and 40-kyr Northern Hemisphere variability, with 10 m from AIS and three different contributions from Northern Hemisphere ice sheets (NHIS); d, 10 m; e, 20 m; and f, 30 m.
Modelled RSL at Whanganui, New Zealand, for comparison of symmetrical glacial–interglacial cyclicity (bold lines) and extended glacials and interglacials (dashed lines) using the ANICE-SELEN ice-sheet model. a, Modelled RSL for a 15-m ESL fluctuation as a symmetrical waveform (bold black line) and with extended glacials and interglacials (dashed grey line); b, the residuals of RSL curves from a with respect to ESL (symmetrical, bold black; and extended, dashed grey). c, As a but for a 10-m ESL fluctuation of a linear 20-kyr chronology (bold dark blue line) and a longer period cyclicity from cumulative extended glacial and interglacials (dashed blue line); d, as b showing the residuals from c but repeated using the ICE-5G model54 (symmetrical bold, yellow; and extended, dashed yellow). The differences between the ANICE-SELEN and ICE-5G models in d are evident but are of the order of tens of centimetres. Interestingly, longer periodicity and extended glacials/interglacials yield larger RSL excursions with respect to ESL (positive values).
Shown is the predicted RSL rise for a 15-m ESL change, after 10 kyr of linear melting between glacial and interglacial for scenarios described in Extended Data Fig 4 (namely, scenarios 1 (short-dashed line), 2 (dashed line) and 3 (solid grey line)), for the four Earth models (a, b, c, d; Extended Data Table 2). Higher contrast between lower and upper mantle results in lower values for the predicted RSL rise. A thicker lithosphere (120 km) results in a slightly higher than eustatic peak for scenario 1.
Extended Data Fig. 7 Calculated global RSL change produced by instantaneous ice-sheet melting of 15-m ESL.
Shown is RSL (normalized with respect to ESL) according to scenario 1 (AIS only) after 10 kyr of viscous relaxation (mantle viscosity profile a; Extended Data Table 2) following an instantaneous melting. The white band denotes RSL from 0.8 to 1.2 of the ESL signal. The GIA-driven RSL fingerprints are more evident if compared to Fig. 4a (10-kyr-long linear melting). The Whanganui site is highlighted by the red and white bullseye.
This file contains geological data (Supplementary Figs 1 & 2) that provides the basis for environmental interpretation of the stratigraphy. Location figures of the modern grain size transects and wave data referred to in the manuscript are shown in Supplementary Figs 3 & 4. The sample sites are correlated and backstripped using stratigraphic thicknesses shown in the cross-section (Supplementary Fig. 5).