Globally correlated, negative excursions in carbon isotope (δ13C) values measured in marine and terrestrial substrates throughout the Phanerozoic indicate episodic, massive additions of isotopically depleted carbon to the ocean–atmosphere system1,2,3,4,5,6,7,8,9,10. These events not only changed the carbon isotope composition of atmospheric carbon dioxide (δ13CCO2), but also raised pCO2 concentrations (for example, ref. 11). The magnitude of the carbon isotope excursion (CIE) and the amount of pCO2 rise (ΔpCO2) calculated for such events should relate to one another, and the source of the carbon input and changes in the global carbon cycle have been reconstructed upon this premise (for example, refs 5,9,11,12). Determination of the ‘true’ magnitude of a CIE (that is, the amount of the CIE caused only by the change in δ13CCO2) is fundamental to calculating the amount of carbon added to the atmosphere at the event and improving our understanding of feedbacks in the climate system13,14.

One complicating factor is that the magnitude of the CIE is characteristically larger when measured in terrestrial versus marine substrates by up to several per mil6,7,8,9,11,15. Workers have argued that larger-magnitude negative excursions recorded in terrestrial substrates reflect increased humidity or precipitation6,7 based on the increased carbon isotope fractionation that modern land plants demonstrate in response to these environmental factors. Others have attributed this difference to an increased abundance of angiosperm flora, which are characteristically isotopically depleted in comparison with gymnosperm flora16,17. Both of these mechanisms are problematic as general explanations for any global discrepancy between terrestrial and marine CIEs because their influences are most likely to be locally and heterogeneously expressed15,18 (Supplementary Information). Moreover, changes in angiosperm abundance cannot explain larger terrestrial versus marine CIEs in pre-Cretaceous substrates (for example, ref. 7). The reconciliation of terrestrial versus marine CIEs requires a mechanism fundamental to all C3 photosynthesis, and thus globally applicable (we note that classical C4 photosynthesis is a recent evolutionary innovation, relegated to no more than the last ~13 million years of Earth’s history19,20, and that CAM photosynthesis is largely limited to aqueous and desert environments).

Previous experiments have shown that the carbon isotope value of plant tissues (δ13Cp) is affected by changes in pCO2 concentration, independent of changes in δ13CCO2, and identified a positive relationship between pCO2 concentration and carbon isotope fractionation (Δδ13Cp≈δ13CCO2−δ13Cp) in both angiosperm and gymnosperm taxa (for example, refs 21,22; Supplementary Information). More recently, time-series correlations between climate variables and tree-ring Δδ13Cp values have been shown to improve when a correction proportional to the increase in pCO2 is applied (for example, refs 23,24,25). However, a wide range of corrections for the effect of changing pCO2 on Δδ13Cp (S; ‰/p.p.m.v.) have been reported and applied, typically ranging from S=0.73 to 2.0‰ per 100 p.p.m.v. increase in pCO2 (for example, refs 23,24; Supplementary Information).

Our recent work growing plants under controlled environmental conditions across a wide range of pCO2 levels (up to 4,200 p.p.m.v.) provided a unifying relationship for the effect of pCO2 on C3 plant tissue, showing that S decreases systematically with increasing pCO2 across a wide range of C3 plants (R=0.96, n=33) (Fig. 1) (26). This relationship suggests that for any large release of isotopically depleted carbon to the ocean or atmosphere, the land-plant-derived substrates of the terrestrial record (CIEterrestrial; that is, terrestrial organic matter, soil carbonate, plant lipids and tooth enamel) will record a larger-amplitude CIE than marine substrates (CIEmarine; that is, benthic foraminifera, planktic foraminifera and bulk marine carbonate). Thus, we propose that the difference in magnitude between these two substrates (ΔCIE=CIEterrestrial−CIEmarine) results from the additional fractionation by land plants due to rising pCO2 levels, which is then propagated within the terrestrial record. We apply this to the particularly well-studied and globally widespread CIE at the Palaeocene–Eocene Thermal Maximum (PETM), for which analysis of >150 CIEs shows a significant, 2.1‰ greater amplitude CIE recorded in terrestrial versus marine substrates11, in order to calculate absolute pCO2 levels during the Late Palaeocene and at the height of the CIE for the range of sources (and thus, ΔpCO2 values) postulated for the carbon release.

Figure 1: The effect of pCO2 concentration on C3 land-plant carbon isotope fractionation.
figure 1

Across field and chamber experiments on a wide range of C3 land-plant species, the amount of carbon-isotope fractionation per change in pCO2 (S, ‰ per p.p.m.v.) decreases within increasing pCO2 level according to the following equation: S=(B)(A2)/[A+B(pCO2+C)]2 with R=0.96 (n=33) (black curve), where A=28.26, B=0.21 and C=25. Purple closed circles reflect data from our experiments26; open black circles represent data compiled from published studies (Supplementary Table S2). Horizontal bars encompass the range of pCO2 levels used within each experiment; the circle is plotted at the midpoint of the range. The grey curve (inset) represents the integral of the black curve, and follows the general hyperbolic relationship: Δδ13Cp=[(A)(B)(pCO2+C)]/[A+(B)(pCO2+C)] (see Supplementary Information). As the relationship between pCO2 and Δδ13Cp is nonlinear, absolute estimates of pCO2(initial) (blue) and pCO2(excursion) (red) can be calculated by solving equations (1) and (2) provided ΔpCO2 and ΔCIE are known (dashed lines); for a given magnitude CIE, the ΔpCO2 estimate is dependent on the δ13C value of the source. Figure is modified from 26 with new data reported in Lomax et al.59 (Supplementary Information; Supplementary Table S1).


Reconciliation of ΔCIE via the pCO2 effect

The larger-magnitude CIE recorded in terrestrial versus marine substrates can be described by the following equation relating ΔCIE to the effect of changing pCO2 levels on carbon isotope fractionation by C3 land plants:

where pCO2(initial) and pCO2(excursion) are the pCO2 levels immediately before and at the height of the CIE, respectively, and A, B and C are constants produced by the best-fit curve through the experimental data and published values (Fig. 1 inset and Supplementary Information). For CIE events where the magnitude of both CIEterrestrial and CIEmarine are well-documented globally, knowledge of ΔCIE can be used towards the determination of both pCO2(initial) and pCO2(excursion) provided the change in pCO2pCO2) is known (Fig. 1 inset):

Estimates of ΔpCO2, which are dependent on the true magnitude of the CIE and the δ13C value of the source (δ13Csource), are commonly calculated using methods ranging from mass balance equations (for example, refs 5,11) to numerical models (for example, refs 12,27). Therefore, provided independent estimates of ΔCIE and ΔpCO2, equations (1) and (2) can be solved simultaneously for absolute estimates of pCO2(initial) and pCO2(excursion) (Fig. 2), allowing for a wholly new quantitative reconstruction of changes in the global carbon cycle. Although determination of pCO2(initial) and pCO2(excursion) requires precise estimates of ΔCIE and ΔpCO2, Fig. 2 shows that the value for pCO2(initial) is more sensitive to ΔCIE than to ΔpCO2, while pCO2(excursion) is more sensitive to ΔpCO2 than to ΔCIE.

Figure 2: Determination of pCO2 levels as a function of ΔCIE and ΔpCO2.
figure 2

For any hypothetical CIE, pCO2(initial) (left) and pCO2(excursion) (right) are a function of the difference between the terrestrial and marine CIE (ΔCIE; ΔCIE=CIEterrestrial−CIEmarine) and the rise in pCO2pCO2; ΔpCO2=pCO2(excursion)pCO2(initial)). Values for pCO2(initial) and pCO2(excursion) were calculated by solving equations (1) and (2) simultaneously.

Determination of pCO2 levels across the CIE at the PETM

The highly studied, globally widespread CIE that marks the PETM represents an ideal event upon which to first apply our methods to quantify pCO2(initial) and pCO2(excursion) because of the large number of CIEterrestrial and CIEmarine records that can be used to provide a robust estimate of ΔCIE globally. More than 150 total CIEmarine and CIEterrestrial records have been measured across the PETM (reviewed by McInerney and Wing11); the average CIE measured in terrestrial substrates that include soil carbonate, plant lipids, bulk soil organic matter and tooth enamel (CIEterrestrial±1σ=−4.7±1.5‰, n=48) is 2.1‰ more negative than that measured in benthic foraminifera, planktic foraminifera and bulk marine carbonate from marine environments (CIEmarine ±1σ=−2.6±1.1‰, n=105) (ΔCIE=−2.1‰). Bulk marine organic matter was not included in our determination of CIEmarine because it can include mixed pools of carbon from photosynthetic and non-photosynthetic organisms from terrestrial and marine environments15,28,29,30. By averaging across the large number of diverse sites and substrates available for the PETM, biasing effects of local and regional changes in climate6,8,31,32,33,34,35,36,37,38,39, vegetation16,17,38, sediment transport40,41, salinity15,42 and dissolution43,44 on ΔCIE are limited. Using this ΔCIE value (−2.1‰), Late Palaeocene (pCO2(initial)) and PETM (pCO2(excursion)) pCO2 levels can be determined across a range of ΔpCO2 estimates by simultaneously solving equations (1) and (2) (Fig. 3).

Figure 3: Reconstruction of pCO2 levels during the Late Palaeocene and PETM.
figure 3

Across a range of possible pCO2 increases (ΔpCO2), pCO2 levels for the Late Palaeocene (blue curve; pCO2(initial)) and PETM (red curve; pCO2(excursion)) were calculated by simultaneously solving equations (1) and (2) for ΔpCO2=0–3,600 p.p.m.v. and ΔCIE=−2.1‰ (thick curves). Blue and red shaded regions show solutions for ΔCIE=−1.6 to −2.6‰ to illustrate the effect of ΔCIE on pCO2 estimates (for a given ΔpCO2, lower ΔCIE values yield higher pCO2 estimates and vice versa). ΔCIE=−2.5‰ assumes that n-alkanes (CIE=−5.1‰; 11) best represent CIEterrestrial; ΔCIE=−1.6‰ suggests a smaller offset between CIEterrestrial and CIEmarine owing to an underestimation of the magnitude of CIEmarine (CIEmarine=−3.1‰ versus −2.6‰). Vertical lines mark ΔpCO2 estimates for specific proposed sources of the event (green=methane hydrate14, δ13Csource=−60‰; purple=thermogenic methane54 or permafrost thawing50, δ13Csource=−30‰; and orange=wildfire burning55 or oxidation of organic matter from drying of epicontinental seas56, δ13Csource=−22‰) based on a mass balance equation (equation (3) and the parameters used by McInerney and Wing11 (0.3 p.p.m.v. increase in pCO2 per Pg C added, δ13Cinitial=−2.5‰, and Minitial=50,000 Pg C); horizontal arrows mark the range of ΔpCO2 estimates calculated for each source (equation (3)), provided a range of estimates for the pCO2 increase per Pg C added (0.23 to 0.39) and estimates of δ13Cinitial (−2.5 to −0.1‰) (Methods). The range of average Late Palaeocene (60–55Ma) pCO2 estimates from other proxies (blue bars) are indicated; a single pCO2 estimate from stomata provides a lower bound on pCO2 during the PETM (red point and arrow) (references are provided in the Supplementary Information). Dashed lines mark pre-industrial (280 p.p.m.v.) and present-day (393 p.p.m.v.) pCO2 levels, as well as a model-based projection of pCO2 in the year 2300 if fossil fuel burning continues unabated (1,900 p.p.m.v.) (46). Grey-shaded region represents the range of pCO2 projections for the year 2100 from the IPCC (566–821 p.p.m.v.) (60).

Reconstructed estimates of pCO2(initial) and pCO2(excursion) increase as ΔpCO2 increases (Fig. 3); thus the solution based on a methane hydrate source (δ13Csource =−60‰, ΔpCO2=710 p.p.m.v.) yielded the lowest Late Palaeocene pCO2 estimate (pCO2(initial)=674 p.p.m.v.), followed by thermogenic methane or permafrost thawing (δ13Csource=−30‰, ΔpCO2=1,566 p.p.m.v.) that yielded pCO2(initial)=915 p.p.m.v., and then wildfire or drying of epicontinental seas (δ13Csource=−22‰, ΔpCO2=2,308 p.p.m.v.) having the highest Late Palaeocene pCO2 estimate (pCO2(initial)=1,034 p.p.m.v.). If these sources can be thought to exhaust the carbon isotope range of potential sources, we calculate that Late Palaeocene pCO2 levels may have been as low as ~280 p.p.m.v. higher than present, and were much lower than the recent pCO2 estimates for the year 2300 (45,46; Fig. 3). pCO2 levels at the peak of the PETM were calculated to be 1,384, 2,481 and 3,342 p.p.m.v. for methane hydrate, thermogenic methane or permafrost thawing, and drying of epicontinental seas or wildfire sources (ΔpCO2=710, 1,566 and 2,308 p.p.m.v.), respectively (Fig. 3).


Determination of Late Palaeocene and PETM pCO2 levels is important for quantifying climate sensitivity to CO2 for this greenhouse period (for example, ref. 47); however, previous proxy estimates for the Late Palaeocene are highly varied, ranging from 100 to 2,400 p.p.m.v., and robust PETM pCO2 estimates are lacking (Supplementary Information; Fig. 3). Across a wide range of increases in pCO2 at the PETM (ΔpCO2 ≤ 3,000 p.p.m.v.), our results indicate that Late Palaeocene pCO2 levels were≤1,112 p.p.m.v. (Fig. 3). If we consider a relatively small increase in pCO2 levels (ΔpCO2<1,000 p.p.m.v.), as would be attributed to a methane hydrate source, our Late Palaeocene pCO2 estimates are consistent with values determined from liverwort, phytoplankton and stomatal proxies (Fig. 3). The boron isotope proxy, in contrast, is more consistent with our results assuming that the amount of pCO2 increase was larger (>1,000 p.p.m.v.), as would be required for the thawing permafrost model, for example (Fig. 3).

Although our reconciliation does not allow for the determination of the carbon source of the CIE at the PETM, recent work indicates significant warming before the onset of the CIE (33,48), and suggests an orbitally forced mechanism for the release of carbon at the event49,50,51. If we consider the two hypotheses suggesting that orbital forcing triggered the release of carbon through a methane hydrate release (49) (ΔpCO2=710 p.p.m.v.) or large-scale thawing of permafrost (50) (ΔpCO2=1,566 p.p.m.v.), we calculate Late Palaeocene pCO2 levels=674 (+159−109) or 915 (+225−153) p.p.m.v., respectively (error based on ΔCIE=−1.6 to −2.6‰; Fig. 3). Notably, these calculated values for Late Palaeocene pCO2 are consistent with the pCO2 levels required by Lunt et al.49 (~560 p.p.m.v.) and DeConto et al.50 (~900 p.p.m.v.) for each of their respective models.

Many arguments have been made to explain the larger CIE measured in terrestrial versus marine substrates at the PETM6,8,15,16,17,18,42,43, but each requires additional phenomena secondary to the carbon release (Supplementary Information). Based on the fundamental observation of increased carbon isotope fractionation in C3 land plants in response to elevated pCO2 levels (Fig. 1), we propose that the larger amplitude CIE recorded in terrestrial substrates results from the primary phenomenon of rising pCO2 levels. We attribute deviations from the average size of the CIE measured on the same substrate at different sites to local or regional changes in water availability6,8,18,36, plant composition16,17,38,52, dissolution43 and salinity42. For these reasons, the average of many CIEs measured across the planet should be used to determine the average magnitude of the marine and terrestrial signals for the purpose of reconciling the magnitude of the event and reconstructing pCO2 levels.

We further note systematic differences in the magnitude of the CIE within the marine and terrestrial substrates as compiled by McInerney and Wing11 in their Table 1. Within the marine record, foraminifera (benthic and planktonic) and bulk marine carbonate record the smallest CIE (−2.5 to −2.7‰), while algal lipids and bulk marine organic matter record a greater CIE (−3.5 to −4.1‰). In terrestrial systems, the smallest CIE is measured in bulk soil organic matter (−3.5‰), followed by tooth enamel and plant lipids (−4.8 to −5.1‰), with the largest CIE measured in soil carbonate (−5.5‰). The greater CIE measured in algal lipids compared with foraminifera is likely caused by elevated pCO2 levels, as photosynthetic algae are also known to show increasing carbon isotope fractionation with increasing concentrations of CO2 dissolved in water although these relationships vary widely (reviewed within ref. 53) and differ from that of higher land plants. Bulk organic matter in terrestrial and marine environments show the same median magnitude CIE (−3.5‰); the CIE measured in terrestrial bulk organic matter may be dampened relative to other terrestrial substrates by mixing of organic matter of a different age15, while the marine bulk organic matter CIE is likely augmented compared with other marine substrates by photosynthetic inputs from terrestrial and marine environments15,28,29,30. Variability in the degree of these inputs may explain why bulk marine organic matter shows the greatest variability among all substrates (1σ=±2.2‰). Within purely terrestrial systems, the median CIE recorded in plant lipids (−5.0‰) reflects the full effects of elevated pCO2 levels on plant isotope fractionation (as shown here and in 26); the similar median CIE recorded in fossil tooth enamel (−4.9‰) is not surprising considering that it reflects the δ13C value of the plants the herbivore consumes. The very large CIE measured in paleosol carbonate (average=−5.5‰, median=−6.3‰) may reflect a combination of the enhanced fractionation by plants under high pCO2, diffusion of increased pCO2 levels into the soil and increased productivity. Based on measurements of enamel carbonate, Secord et al.33 attribute 1.5‰ of the CIE measured in soil carbonate to increased rates of carbon turnover, driven by warmer climate.

Our results illustrate the need to account for changes in pCO2 concentration when interpreting changes in the carbon isotope composition of substrates derived at least in part from C3 land plants, which dominate the terrestrial carbon record. Although our analysis was applied specifically to the PETM, the fundamental pCO2 effect and equations presented here can be applied similarly to other global CIE events recorded in marine and terrestrial sediments (for example, Aptian–Albian, Early Toarcian, Triassic–Jurassic, Permian–Triassic and many others) in order to quantitatively reconstruct levels of pCO2 before and during the CIE event.


Quantifying ΔpCO2

We used the following mass balance equation modified from McInerney and Wing11 to quantify ΔpCO2 for each of the proposed sources (vertical, coloured lines in Fig. 3: green=methane hydrate14, δ13Csource=−60‰; purple=thermogenic methane54 or permafrost thawing50, δ13Csource=−30‰; and orange=wildfire burning55 or oxidation of organic matter from drying of epicontinental seas56, δ13Csource=−22‰):

where Minital is the mass of the Palaeocene surface reservoir, δ13Cfinal is the δ13C value at the PETM (δ13Cfinal13Cinitial+CIEmarine), δ13Cinitial is the δ13C value of the Late Palaeocene carbon pool and δ13Csource is the δ13C value of the source responsible for the CIE. We used CIEmarine (and not CIEterrestrial) because it does not incorporate any land-plant-derived components and thus only represents changes in δ13CCO2. The constant 0.3 indicates that for every 1 Pg C added pCO2 increases 0.3 p.p.m.v. (11); this value is within the range of values suggested from models of the carbon release at the PETM (for example, 0.23–0.39; 12,27,57). We calculated the value for CIEmarine (−2.6‰) as the average of the CIEs measured in benthic forams (−2.5±1.0‰, n=36), planktic forams (−2.7±1.0‰, n=36) and bulk marine carbonate (−2.7±1.1‰, n=33) as listed in Table 1 of McInerney and Wing11. Bulk marine organic matter (CIE=−4.1±2.2‰, n=11) was not included in the average because it may contain a mix of marine and terrestrial inputs28,29,30; the single CIE measured on algal lipids (CIE=−3.5‰) was also excluded. Our values for Minitial=50,000 Pg C and δ13Cinitial=−2.5‰ were based on the values used by McInerney and Wing11. We note, however, that the value for δ13Cinitial=−2.5‰ may be too low; we estimate δ13Cinitial as high as −0.1‰ assuming a pre-industrial value of −2.1 to −2.6‰ (14) offset by +2.0‰ based on the secular change in δ13C (58).

Additional information

How to cite this article: Schubert, B. A. & Jahren, A. H. Reconciliation of marine and terrestrial carbon isotope excursions based on changing atmospheric CO2 levels. Nat. Commun. 4:1653 doi: 10.1038/ncomms2659 (2013).