Relationship between sea level and climate forcing by CO₂ on geological timescales

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 CO₂ and sea level on geological (near-equilibrium) timescales. This strongly supports the dominant role of CO₂ 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 CO₂ 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 CO₂ 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 CO₂ 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 CO₂ levels.

Data from gas bubbles in ice-core samples provide a high-fidelity CO₂ record for the last 800,000 y (6–8) that, when coupled with sea-level records of similar resolution (9), illustrates that CO₂ and sea level are intimately related on these timescales (Fig. 1). This relationship arises because CO₂ 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 CO₂ (ppmv) and global sea level (m). (A) The record of CO₂ 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 pCO₂ [and ln(CO₂/C₀)] 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 CO₂ changes is logarithmic in nature (10), and the relationship between ln(CO₂/C₀) (where C₀ = 278 ppm = preindustrial CO₂) 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 CO₂ forcing—because the sea-level response to CO₂ 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 CO₂ 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 CO₂ 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 CO₂ 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, CO₂ was higher, and continental ice volume was reduced, relative to the present. Here, we compile reconstructions of atmospheric CO₂ 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 CO₂ 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 [CO₂]_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 [CO₂]_aq and atmospheric CO₂ 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 CO₂ 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 CO₂ 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.

Fig. 2.

Time series of sea-level and CO₂ data used to construct Fig. 3. (A) Alkenone δ¹³C based CO₂ (13) and sea level based on sequence stratigraphy of the NJM (27). (B) Boron isotope-based CO₂ record (15) with sea level based on the oxygen isotope composition of planktic foraminifera fixed at ice-free (e.g., pre-Eocene–Oligocene boundary) = + 65 m (SI CO2 and Sea-Level Estimates). (C) Boron isotope-based CO₂ record (18) with sea level from the benthic foraminiferal δ¹⁸O (45) fixed to the Miocene highstand of the NJM sequence stratigraphic record (28) (SI CO2 and Sea-Level Estimates). (D) Boron isotope-based CO₂ records (gray diamonds) (17) and (black triangles) (16). Sea-level record from a compilation (26) using several methodologies, including sequence stratigraphy and benthic foraminiferal δ¹⁸O corrected for temperature (see ref. 26 for details). Note CO₂ and highstands do not correlate exactly in time, but in each case sea-level estimate and CO₂ are within 10,000 y. (E) Benthic oxygen isotope stack (30) with the locations of the time slices shown in A–D (and Fig. 1), shown as appropriately colored and labeled band. All data displayed in (A–D) can be found in Dataset S1.

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 CO₂ 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 CO₂ 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 CO₂. 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.

Results and Discussion

A combination of data from all five time slices (Fig. 3A) reveals that on these longer timescales, there is a clearly sigmoidal relationship between sea level and climate forcing by CO₂. Moreover, there is a striking similarity between data from different time periods and those generated by different techniques (e.g., Fig. 3A). This overall agreement implies that this relationship is robust and reflects the fundamental behavior of the Cenozoic climate system, despite some significant changes in boundary conditions (e.g., closing of the Panama Gateway since the Pliocene, closure of Tethys since the Miocene). In detail, it is evident that for CO₂ between ∼200 and ∼300 ppm (data from the Pleistocene, Pliocene, and Miocene), the relationship is similar to that defined by the ice-core data alone (Fig. 1), whereas the sea-level estimates remain rather “flat” within the range −10 ± 10 to +20 ± 10 m (68% confidence, see below) for CO₂ values between ∼400 and ∼650 ppm (Fig. 3A; defined by data from the Pliocene, Miocene, and Oligocene). At CO₂ > 650 ppm, CO₂ changes again are associated with sustained changes in sea level (Fig. 3A; defined by data from the Eocene and Oligocene).

Fig. 3.

Cross-plot of estimates of atmospheric CO₂ and coinciding sea level. (A) Data are split according to time period and technique used. Symbols as in Fig. 2. Note for the Eocene–Oligocene from δ¹¹B and δ¹⁸O, only data that form a decreasing CO₂ trend are plotted for clarity. (B) Results from our probabilistic analysis of the data that fully accounts for uncertainty in both X and Y parameters (see text; Dataset S2). (C) Data shown in Fig. 3A along with EAIS ice-sheet model output (37) for declining CO₂ with orbital variation (red) and the results of inverse modeling of δ¹⁸O (blue) (39). (D) Relative deep-sea temperature change (ΔDST; second x-axis) and sea-level compilation (blue) (40). ΔDST has been scaled by assuming (i) for ΔDST > 0, ΔDST = global temperature change (ΔT_global), when ΔDST < 0, ΔDST = ΔT_global/1.5 (following ref. 46); and (ii) for a ΔDST > 0 climate sensitivity of 2.96 K per CO₂ doubling (4), for a ΔDST < 0 a climate sensitivity of 11.5 K per CO₂ doubling (4). The last glacial maximum (LGM) datapoint from ref. 40 lies outside this plot at −0.1 ± 0.1, −130 ± 10 m (indicated by arrow). On all panels, dotted lines denote the preindustrial conditions of 0 m and 280 ppm CO₂. The horizontal orange line shows +14 m, which is the sea-level rise associated with the total melting of WAIS and GrIS (31). For C and D, the least-squares spline fit through the data (thick gray lines) is shown only as a probability maximum and 84 and 16 percentiles for clarity.

Because of the nature of Cenozoic climate change, many of the data points derive from periods of global cooling and declining CO₂ (30). However, for the Miocene, Pleistocene, and Eocene–Oligocene, there also are data from warming intervals in which CO₂ is increasing (Figs. 1 and 2). In the Pleistocene (CO₂ < 280 ppm), there is no evidence of hysteresis beyond a few thousand years; intervals with increasing and decreasing CO₂ give a similar sea-level response (Fig. 1), as also was elaborated for the relationship between sea level and temperature in that period (9). Similarly, for the Miocene (CO₂ < 450 ppm), there is no evidence of hysteresis within a temporal resolution of ∼300,000 y (Fig. 2). Conversely, the Eocene–Oligocene data show some suggestion of hysteresis (SI CO2 and Sea-Level Estimates and Fig. S3). As yet, this remains insufficiently defined, but it concerns only times with CO₂ > 800 ppm (Fig. S3).

To facilitate a quantitative comparison between ln(CO₂/C₀) and sea level, we have performed a probabilistic analysis. For this analysis, we randomly perturbed all data points within normal distributions characterized by their mean and SDs (recalculated so as to be symmetrical), then applied a statistical B-spline smoothing fit with automated node detection. This procedure was repeated 300 times, followed by an assessment of the distributions of sea-level values per CO₂ step, where we determined the probability maximum (distribution peak) as well as the 68% and 95% probability intervals (using the 16% and 84% percentiles, and the 2.5% and 97.5% percentiles). Removal of any one particular dataset does not result in a significantly different geometry to the distribution of the probability maximum. This assessment (Fig. 3B) clearly reveals a sea-level “plateau” at around 22 m between CO₂ levels of about 400 and 650 ppm, with average 68% confidence limits for this interval of ⁺¹³/₋₁₂ m, which covers sea-level values that might be expected in the absence of GrIS and WAIS [+14 m (31)], although within the bounds of uncertainty, we cannot rule out that there was an additional component of mass reduction in the EAIS at these midlevel CO₂ values (18, 32). Based on the probability maximum and full contributions from GrIS and WAIS, this may have been equivalent to about 10 m of sea-level rise.

Our observed long-term relationship between sea level and CO₂ forcing reaffirms the importance of CO₂ as a main driver of changes in the Earth’s climate over the past 40 My. The exact nature of the relationship can be understood in the context of the ice sheets involved. During the Eocene, when CO₂ levels were higher than 1,000 ppm, sea level was 60–70 m higher than today, reflecting the absence of any of the major ice sheets that currently reside at high latitudes (30). Sea-level change during the Eocene–Oligocene, with CO₂ in general decline from 1,000 ppm to 650 ppm (13, 15), was driven largely by buildup of the EAIS (33). Our ln(CO₂/C₀)–sea-level (SL) [ln(CO₂/C₀):SL] relationship indeed suggests there was strong ice-sheet (EAIS) expansion with CO₂ decline during those times (Fig. 3A). Next, we observe a lack of long-term sea-level response for CO₂ levels between about 650 and 400 ppm. This suggests that during these times, very little continental ice grew (or retreated); presumably CO₂ was too high, hence the climate too warm to grow more continental ice after the “carrying capacity” of the EAIS had been reached (Fig. 3A). It also suggests that 300–400 ppm is the approximate threshold CO₂ value for retreat and growth, respectively, of WAIS and GrIS (and possibly a more mobile portion of EAIS). Sea levels of 20–30 m above the present during the Pliocene and Miocene, when CO₂ was largely between 400 and 280 ppm, are thought to predominantly reflect mass changes in the GrIS and WAIS (26, 31). However, recent records proximal to the Antarctic ice sheet indicate that some portion [maybe as much as 10 m sea-level equivalent (26, 34)] of the EAIS also retreated during these warm periods (26, 35). Finally, sea levels lower than those of the present, as observed during the last 550,000 y and during the Miocene, were caused largely by growth of the Laurentide and Fennoscandian ice sheets (11, 18). As also argued before, the threshold CO₂ value for the growth of these ice sheets must be below 280 ppm (6); a recent assessment suggests that with our current orbital configuration, a threshold of 240 ± 5 ppm is appropriate (36).

This study directly determines the relationship between CO₂ and sea level from data covering the entire range of climates experienced by the Earth over the past 40 My. We find a strong similarity to nonlinear relationships that have been proposed by ice-sheet modeling (37, 38), theoretical studies (39), and a recent synthesis of deep-sea temperature and sea level for the past 10–40 My (40). A comparison between our work and these earlier studies is shown in Fig. 3 C and D. Our data compilation and probabilistic analysis are in good agreement with the deep-sea temperature:sea-level compilation (40) (Fig. 3D) and ice-sheet modeling output (37) (Fig. 3C). However, although the overall shape of our ln(CO₂/C₀):SL relationship is similar to that inferred using inverse modeling of the benthic foraminiferal δ¹⁸O record (39), our compilation places the transition from a nonglaciated to fully glaciated EAIS at considerably higher CO₂ (650–1,000 ppm CO₂ vs. their 380–480 ppm CO₂; Fig. 3C).

Our quantitative ln(CO₂/C₀):SL relationship reflects the long-term (greater than orbital timescales) near-equilibrium relationship between these variables. Because it is constrained by real-world observations of the Earth system, our relationship inherently includes all feedbacks and processes that contribute to sea-level change. It also appears to be largely independent of other boundary condition changes and therefore may be used with confidence to determine a likely estimate for sea level if the Earth system were to reach equilibrium with modern or future CO₂ forcing. Given the present-day (AD 2011) atmospheric CO₂ concentration of 392 ppm, we estimate that the long-term sea level will reach +24 ⁺⁷/₋₁₅ m (at 68% confidence) relative to the present. This estimate is an order of magnitude larger than current projections for the end of this century [up to 2 m; best estimate, 0.8 m (41)] and seems closer to the worst-case long-term sea-level projection portrayed by Meehl et al. (1). Using terminology of the Intergovernmental Panel on Climate Change Fourth Assessment Report IPCC AR4 (5), we find it very likely (i.e., at 90% confidence) that long-term sea-level rise for sustained present-day CO₂ forcing will be >6 m, and likely (68% confidence) that it will be >9 m. Through analogy with the geological record, this rise likely will be achieved through melting of the GrIS and WAIS and possibly some portion of the EAIS (if sea level were to rise >14 m). However, it will take many centuries to get to these high levels. Given the typical mean rates of natural sea-level rises on multicentury timescales [1.0–1.5 cm⋅yr⁻¹, with extremes during deglaciation of 5 cm⋅yr⁻¹ (41–43)], our projection suggests an expected equilibration time of the Earth system to modern CO₂ forcing of 5–25 centuries. Notably, however, this is likely still faster than the rates at which CO₂ is removed from the atmosphere via natural processes (deep-sea sediment dissolution and silicate weathering), which operate on 10,000–100,000-y timescales (44).

Clearly our relationship has limited relevance to short-term sea-level projections for the next century. However, accurately determining the long-term response of sea level to CO₂ forcing has significant implications for the long-term stabilization of greenhouse gas emissions (by natural processes or human activity) and for decisions about the “acceptable” long-term level of CO₂/warming. For instance, our results imply that acceptance of a long-term 2 °C warming [CO₂ between 400 and 450 ppm (46)] would mean acceptance of likely (68% confidence) long-term sea-level rise by more than 9 m above the present. Future studies may improve this estimate, notably by better populating the interval between CO₂ concentrations of 500–280 ppm (i.e., the Pliocene/middle Miocene). Regardless, the current relationship is sufficiently refined to imply that CO₂ would need to be reduced significantly toward 280 ppm before any lost ice volume might be regrown (similarly over many centuries).