Abstract On 103- to 106-year timescales, global sea level is determined largely by the volume of ice stored on land, which in turn largely reflects the thermal state of the Earth system. Here we use observations from five well-studied time slices covering the last 40 My to identify a well-defined and clearly sigmoidal relationship between atmospheric CO 2 and sea level on geological (near-equilibrium) timescales. This strongly supports the dominant role of CO 2 in determining Earth’s climate on these timescales and suggests that other variables that influence long-term global climate (e.g., topography, ocean circulation) play a secondary role. The relationship between CO 2 and sea level we describe portrays the “likely” (68% probability) long-term sea-level response after Earth system adjustment over many centuries. Because it appears largely independent of other boundary condition changes, it also may provide useful long-range predictions of future sea level. For instance, with CO 2 stabilized at 400–450 ppm (as required for the frequently quoted “acceptable warming” of 2 °C), or even at AD 2011 levels of 392 ppm, we infer a likely (68% confidence) long-term sea-level rise of more than 9 m above the present. Therefore, our results imply that to avoid significantly elevated sea level in the long term, atmospheric CO 2 should be reduced to levels similar to those of preindustrial times.

Sea-level change is one of the most significant and long-lasting consequences of anthropogenic climate change (1). However, accurate forecasting of the future magnitude of sea-level change is difficult because current numerical climate models lack the capacity to accurately resolve the dynamical processes that govern size changes of continental ice sheets [e.g., total disappearance of the current continental ice sheets would raise mean sea level by about 70 m (1)]. This complicates long-range sea-level projections because the retreat of continental ice sheets will increasingly contribute to sea-level rise as the 21st century progresses (2), and because this rise will continue long into the future, even if temperatures were stabilized, according to different mitigation scenarios for greenhouse gas emissions (1). Because of the absence of adequate ice-dynamical processes in models, even the most recent estimates have to rely on assumed (linear) relationships between ice-volume reduction and global mean temperature increase (1), which as yet remain largely untested. Therefore, here we provide a natural context to projections of future long-term (multicentury) sea-level rise, by assessing key relationships in the Earth’s climate system using recent high-quality data from the geological past. Because global mean temperature is hard to measure in the geological past without applying (often problematic) assumptions about polar amplification or deep-sea temperature relationships (3, 4), we instead concentrate on quantifying the “likely” [68% probability (5)] long-term relationship between two entities that can be measured more directly, namely ice-volume/sea-level and CO 2 levels.

Data from gas bubbles in ice-core samples provide a high-fidelity CO 2 record for the last 800,000 y (6⇓–8) that, when coupled with sea-level records of similar resolution (9), illustrates that CO 2 and sea level are intimately related on these timescales (Fig. 1). This relationship arises because CO 2 is the principal greenhouse gas that amplifies orbital forcing and to a large extent determines the thermal state of the Earth system across glacial–interglacial cycles and thus the amount of ice stored on land (3). In detail, there are short leads and lags between Earth system components because of different timescales of inertia, but the overall relationship is strong (R2 = 0.68; n = 2051; Fig. 1).

Fig. 1. The relationship between the partial pressure of atmospheric CO 2 (ppmv) and global sea level (m). (A) The record of CO 2 and sea level over the past 550,000 y (6⇓⇓–9). The dotted horizontal line denotes preindustrial values for each variable. (B) Cross-plot of pCO 2 [and ln(CO 2 /C 0 )] against sea level (m) for the same data shown in A. A linear best-fit line is shown with an R2 (correlation coefficient) = 0.68.

Radiative forcing of climate by CO 2 changes is logarithmic in nature (10), and the relationship between ln(CO 2 /C 0 ) (where C 0 = 278 ppm = preindustrial CO 2 ) and sea level over the past 550,000 y can be well approximated by a linear fit (Fig. 1B). However, this linear relationship cannot be simply extended beyond the data—for instance, to predict changes for increasing CO 2 forcing—because the sea-level response to CO 2 forcing below 280 ppm relates to the growth and retreat of large ice sheets that extended to relatively low latitudes in the Northern Hemisphere, and which today no longer exist [the Laurentide and Fennoscandian ice sheets (11)]. Sea-level change in the future instead will be dominated by changes in the ice sheets that have remained, mostly at higher latitudes: the Greenland Ice Sheet (GrIS), Western Antarctic Ice Sheet (WAIS), and Eastern Antarctic Ice Sheet (EAIS). The threshold CO 2 required for the retreat of these ice sheets is clearly higher than the preindustrial level of 280 ppm; otherwise, they would have been in retreat during the current interglacial before the anthropogenic CO 2 increase [sea-level data show that ice volume has been stable for at least the last 3,000–5,000 years (12)]. To assess the equilibrium response of these ice sheets to CO 2 forcing, we must examine the geological record well beyond 550,000 y ago, to include times when the Earth’s climate was significantly warmer than today. The Cenozoic Era (0–65 Ma) contains several time periods when the Earth was warmer, CO 2 was higher, and continental ice volume was reduced, relative to the present. Here, we compile reconstructions of atmospheric CO 2 concentrations and sea level from a variety of proxies and archives (ice cores and sediment cores) from the last 40 My, to better determine the nature of the relationship between these two variables on geological timescales.

Our atmospheric CO 2 data, displayed as a number of time series in Fig. 2, come from three methods: (i) gas bubbles trapped in ice cores [0–550 kya (6⇓–8)]; (ii) the carbon isotopic composition of sedimentary alkenones recovered from deep-sea sediments—the fractionation between alkenones and total dissolved carbon in seawater is largely a function of [CO 2 ] aq [20–38 Ma (13)]; and (iii) the boron isotopic composition of planktic foraminifera from deep-sea sediments, which depends on pH (e.g., ref. 14), from which [CO 2 ] aq and atmospheric CO 2 can be calculated [2.7–3.2 Ma, 11–17 Ma, and 33–36 Ma (15⇓⇓–18)]. Those methods, based on deep ocean sediments, can reproduce the ice-core CO 2 record accurately (19⇓⇓–22), but each has several inherent uncertainties. However, over recent years there has been a trend toward increasing agreement between pre–ice-core CO 2 estimates (23), and for our chosen time intervals, there is, on the whole, a good agreement among the δ11B-based, δ13C-based, and stomatal index-based estimates (Fig. S1). The notable exception is the Miocene (11–17 Ma) time slice, in which in parts, only stomatal and δ11B-based estimates agree (see discussion in SI CO2 and Sea-Level Estimates and ref. 18). Nonetheless, overall agreement among multiple proxies provides confidence in the higher-resolution marine-based records we have chosen to use here.

The sea-level records we use also derive from several methods and sources, and also are displayed in time series in Figs. 1 and 2: (i) changes in the oxygen isotopic composition of foraminifera and bulk carbonate from Red Sea sediments, which predominantly record sea level [Pleistocene, 0–550 kya (24–25)]; (ii) backstripping of marginal sediments combined with estimates of paleo-water depth based on detailed lithofacies, ichnological, and benthic foraminiferal analyses [Pliocene (2.7–3.2 Ma) and Eocene–Oligocene (20–38 Ma) (26, 27)]; and (iii) sea-level change reconstructed using Mg/Ca of foraminifera to isolate the ice-volume signal from foraminiferal δ18O. Because of uncertainties in the Mg/Ca of seawater (see ref. 27 and references therein), we calculate only relative sea-level records using this approach and pin them to either a highstand from backstripping [Miocene (11–17 Ma) (28)] or an estimate of an ice-free world [+64 m; Eocene–Oligocene (33–36 Ma)]. Other sea-level records are available for these time periods, and there generally is a good agreement among different methodologies for the same time period, which provides a high degree of confidence in the reconstructions (Fig S2 and ref. 26). Again, a notable exception is the Miocene (11–17 Ma), when sea level from backstripping from the New Jersey margin (NJM) is particularly problematic (29). However, the record we use here, based on δ18O (SI CO2 and Sea-Level Estimates), agrees well with backstripping from the Marion Plateau, Australia (29). We have been conservative in our assignment of uncertainty for all data used; beyond 550 kya, typical uncertainty at 95% confidence is ±15–30% for CO 2 and ±25–30 m for sea level. More extensive details about these methods and the approaches we have followed may be found in SI CO2 and Sea-Level Estimates.

The compiled CO 2 and sea-level records cover about two thirds of the last 40 My, but not in a continuous fashion (Fig. 2), and we restrict our selection to the time periods with the highest density of data for both sea-level and CO 2 . Although other variables and boundary conditions that influence ice growth/retreat also may have changed between the time intervals (e.g., ocean gateway configurations, continental positions, and orography), we focus here on establishing the first-order relationships and accept that these may be refined further by future studies.

Acknowledgments The authors thank Damon Teagle for comments on an early draft of this manuscript and Edward Gasson for sharing his data for Fig. 3. This work contributes to Natural Environment Research Council (London) (NERC) Grants NE/D00876X/2 and NE/I005596/1 (to G.L.F.), NERC consortium iGlass Grant NE/I009906/1 (to E.J.R.), and 2012 Australian Laureate Fellowship FL120100050 (to E.J.R.). The authors also acknowledge a Royal Society Wolfson Research Merit Award (to E.J.R.).