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• Review Article
• Published: 17 April 2011

Enigmatic origin of the largest-known carbon isotope excursion in Earth's history

• John P. Grotzinger 1 ,
• David A. Fike 2 &
• Woodward W. Fischer 1  

Nature Geoscience volume  4 ,  pages 285–292 ( 2011 ) Cite this article

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• Biogeochemistry
• Palaeontology

Carbonate rocks from the Middle Ediacaran period in locations all over the globe record the largest excursion in carbon isotopic compositions in Earth history. This finding suggests a dramatic reorganization of Earth's carbon cycle. Named the Shuram excursion for its original discovery in the Shuram Formation, Oman, the anomaly closely precedes impressive events in evolution, including the rise of large metazoans and the origin of biomineralization in animals. Instead of a true record of the carbon cycle at the time of sedimentation, the carbon isotope signature recorded in the Shuram excursion could be caused by alteration following deposition of the carbonate sediments, a scenario supported by several geochemical indicators. However, such secondary processes are intrinsically local, which makes it difficult to explain the coincident occurrence of carbon isotope anomalies in numerous records around the globe. Both possibilities are intriguing: if the Shuram excursion preserves a genuine record of ancient seawater chemistry, it reflects a perturbation to the carbon cycle that is stronger than any known perturbations of the modern Earth. If, however, it represents secondary alteration during burial of sediments, then marine sediments must have been globally preconditioned in a unique way, to allow ordinary and local processes to produce an extraordinary and widespread response.

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Acknowledgements

We thank the Agouron Institute and the NASA Astrobiology Institute for support. T. Raub helped with construction of Fig. 2 . K. Bergmann supplied the image in Fig. 4b . M. Saltzman is acknowledged for sharing pre-publication composite carbon isotope data used to construct Fig. 1 , and C. Verdel and B. Wernicke are thanked for sharing pre-publication data for the Johnnie Formation shown in Fig. 3 . L.

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Grotzinger, J., Fike, D. & Fischer, W. Enigmatic origin of the largest-known carbon isotope excursion in Earth's history. Nature Geosci 4 , 285–292 (2011). https://doi.org/10.1038/ngeo1138

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Negative carbon isotope excursions: an interpretive framework

P Vervoort 1 , M Adloff 2 , S E Greene 3 and S Kirtland Turner 4,1

Published 14 August 2019 • © 2019 The Author(s). Published by IOP Publishing Ltd Environmental Research Letters , Volume 14 , Number 8 Focus on Carbon Cycle Dynamics During Episodes of Rapid Climate Change Citation P Vervoort et al 2019 Environ. Res. Lett. 14 085014 DOI 10.1088/1748-9326/ab3318

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1 Department of Earth and Planetary Science, University of California Riverside, Riverside, CA 92521, United States of America

2 School of Geographical Sciences, University of Bristol, Bristol, BS1 1SS, United Kingdom

3 School of Geography, Earth and Environmental Sciences, University of Birmingham, Birmingham, B15 2TT, United Kingdom

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P Vervoort https://orcid.org/0000-0001-9800-6723

M Adloff https://orcid.org/0000-0001-7515-6702

S E Greene https://orcid.org/0000-0002-3025-9043

S Kirtland Turner https://orcid.org/0000-0002-3606-5071

• Received 31 December 2018
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Numerous negative carbon isotope excursions (nCIEs) in the geologic record occurring over 10 4 –10 5 years are interpreted as episodes of massive carbon release. nCIEs help to illuminate the connection between past carbon cycling and climate variability. Theoretically, the size of a nCIE can be used to determine the mass of carbon released, provided that the carbon source is known or other environmental changes such as temperature or ocean pH can be constrained. A simple isotopic mass balance equation often serves as a first order estimate for the mass of carbon input, but this approach ignores the effects of negative carbon cycle-climate feedbacks. Here we show, using 432 earth system model simulations, that the mass of carbon release and associated environmental impacts for a nCIE of a given size and carbon source depend on the onset duration of that nCIE: the longer the nCIE onset duration, the greater the required carbon input in order to counterbalance the input of 13 C-enriched carbon through carbonate compensation and weathering feedbacks. On timescales >10 3 years, these feedbacks remove carbon from the atmosphere so that the relative rise in atmospheric CO 2 decreases with the nCIE onset duration. Consequently, the impacts on global temperature, surface ocean pH and saturation state are reduced if the nCIE has a long onset duration. The framework provided here demonstrates how constraints on the total nCIE duration and relative shape—together determining the onset duration—affect the interpretation of sedimentary nCIEs. Finally, we evaluate selected well-studied nCIEs, including the Eocene Thermal Maximum 2 (∼54 Ma), the Paleocene–Eocene Thermal Maximum (∼56 Ma), and the Aptian Oceanic Anoxic Event (∼120 Ma), in the context of our model-based framework and show how modeled environmental changes can be used to narrow down the most likely carbon emissions scenarios.

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Introduction

Transient negative carbon isotope excursions (nCIEs) in the geologic record have garnered increasing attention because of the parallels with the modern climate experiment. As anthropogenic emissions of fossil fuel carbon accumulate in the atmosphere, the carbon isotopic composition of atmospheric carbon dioxide ( δ 13 C CO2 ) has declined by ∼1.5‰ (the Suess effect) (Suess 1955 , Keeling et al 1979 , Keeling et al 1980 , Mook 1986 ). Ultimately, the Suess effect will be recorded as a nCIE in the sedimentological record of the future (Norris et al 2013 ). Numerous nCIEs in the geological record are coeval with evidence for increasing global temperature and/or ocean acidification—a combination of impacts that are the hallmark of atmospheric greenhouse gas loading (Hönisch et al 2012 ). Investigating rates and masses of carbon release for past nCIEs in combination with environmental impacts informs us about climate sensitivity under various carbon emission scenarios and background climate states. Comparison of these events with the modern provides essential insight into the long-term response of the Earth system to fossil fuel emissions. An increasing number of nCIEs have emerged from the geological record as high-resolution measurements on marine sediment cores become more abundant, leading to hypotheses that these events may represent threshold or tipping point processes rather than independent, stand-alone events (Lunt et al 2011 , DeConto et al 2012 , Armstrong McKay and Lenton 2018 ). Hence, geological nCIEs may also provide an opportunity to investigate the sensitivity and role of carbon cycle feedbacks in amplifying or diminishing the consequences of massive carbon release.

The carbon stored in the exchangeable reservoir, consisting of atmospheric carbon (CO 2 ), dissolved inorganic (DIC) and organic carbon (DOC) in the oceans, and carbon stored in land biota and soils, has a residence time of ∼10 5 years (figure 1 ). For nCIEs that are represented globally in both deep and shallow marine and terrestrial settings and occur on timescales shorter than 10 5 years, the presumption is these originate from the release of isotopically light carbon to the exchangeable carbon reservoir (Dickens et al 1995 ). Fluxes of carbon required to generate a given nCIE are often calculated by a simple isotopic mass balance approach (equation ( 1 )).

Figure 1.  Carbon cycle schematic indicating pre-industrial carbon reservoirs (black) and associated isotopic values (red). Atmospheric carbon dioxide (CO 2 ), marine dissolved inorganic carbon (DIC), marine dissolved organic carbon (DOC), and terrestrial biomass and soil carbon make up the total exchangeable carbon reservoir (triangular arrow symbols). Figure adapted from Andy Ridgwell, personal communication, with reservoir sizes from Sundquist and Visser 2005 except for methane hydrates (from Archer et al 2009b ). Isotopic compositions from Dunkley Jones et al 2013 . cGENIE experiments in this study have slightly different reservoir sizes and isotopic compositions to better match conditions of the early Cenozoic and Mesozoic. The cGENIE exchangeable carbon reservoir in all our experiments includes 1770 Pg C atmospheric CO 2 with δ 13 C CO2 of −4.9‰, 30 300 Pg C DIC with δ 13 C DIC of 1.7‰, 7 Pg C of marine dissolved organic carbon with a δ 13 C of −27.4‰. Note that the version of cGENIE used here does not include a representation of terrestrial biomass or soil carbon and there is no explicit standing stock of marine biomass.

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The mass of carbon required ( M a ) to generate a nCIE of a particular magnitude ( δ f – δ i ) in the exchangeable carbon reservoir ( M i ) with an initial carbon isotopic composition ( δ i ) depends on the source of the added carbon and hence its isotopic signature ( δ a ). Volcanic activity, for instance, emits CO 2 with a δ 13 C that approximates the mantle value of −5 to −8‰ (Javoy et al 1986 ), while photosynthetic fractionation leaves marine and terrestrial organic matter more depleted in 13 C, with δ 13 C signatures ranging from −20 to −30‰ (Boutton 1991 ). Organic carbon reservoirs occurring in the form of coal, oil or gas may reach isotopic values lower than −40‰ (Boutton 1991 ) while microbial breakdown of organic matter drives the δ 13 C of the resulting methane even lower (more negative than −50‰) (Kvenvolden 1993 ). A particular-sized nCIE can be generated by the input of either a relatively large mass of carbon with higher δ 13 C or a small mass of carbon with lower δ 13 C. Hence, a well-known issue interpreting nCIEs is that the carbon isotopic record alone does not provide sufficient information to estimate the mass of carbon input responsible or the magnitude of change in atmospheric CO 2 associated with a nCIE. A greater mass of carbon added to the exchangeable reservoir should equate to a greater rise in atmospheric CO 2 on 10 3 -year timescales, with different implications for radiative forcing and temperature response.

A less often considered difficulty with the isotopic mass balance approach is that it assumes that the total mass of released carbon is instantaneously distributed through the exchangeable reservoir to produce a globally uniform nCIE. This assumption is problematic both for very rapid or very slow release of carbon. If carbon is released more rapidly than the mixing times between the various pools in the exchangeable reservoir (10 3 years), some of these carbon pools will record an amplified nCIE (e.g. Kirtland Turner and Ridgwell 2016 ). For carbon release over longer timescales that approach the residence time of carbon in the exchangeable reservoir, it becomes crucial to account for feedbacks such as carbonate compensation and rock weathering. More recently, modeling approaches have been utilized that explicitly consider the timing of a nCIE derived from sedimentary age models (Cui et al 2011 , Cui et al 2013 , Gutjahr et al 2017 , Dunkley Jones et al 2018 ) in calculating the mass of carbon required to generate a particular nCIE.

However, even constraining the size of a nCIE to use in isotope mass balance calculations or more sophisticated modeling for a single event is not straightforward. Marine carbonates are often used as targets for reconstructing nCIEs because they are presumed to reflect the isotopic composition of the DIC pool, by far the largest pool in the exchangeable surface reservoir (figure 1 ). However, marine carbonate nCIEs may vary between locations for the same event due to many factors, including spatial variations in bioturbation and dissolution intensity (Sluijs and Dickens 2012 ) and whether the carbonate originated from a benthic (seafloor) or planktonic (surface) source. Water depth (for benthic carbonates) may also lead to variations between records. It is possible to identify nCIEs from organic matter as well, although these records must be interpreted with the further caveat that changes in atmospheric CO 2 may lead to changes in the fractionation between DIC and organic matter or changes in organic matter composition that overprint the record of the nCIE as seen by the global exchangeable reservoir (Corsetti et al 2005 ).

When considering multiple nCIEs in the geologic record, there is wide variation not only in magnitude, but also in shape and duration, all of which complicate the calculation of required carbon input. This nuance is not captured in a simple isotopic mass balance approach. Importantly, the goal in using isotopic mass balance to infer the magnitude of carbon released is often to constrain past climate sensitivity (or the global temperature increase due to a doubling of atmospheric CO 2 ) by relating this carbon release to a change in atmospheric CO 2 and combining this with estimates of temperature change. Uncertainty in carbon source and nCIE size will result in the misinterpretation of carbon input required to explain δ 13 C excursions (equation (1)) but assumed duration and relative timing of an event will also influence (1) the carbon input required, as various reservoir exchanges and feedbacks act on different timescales and (2) the proportional increase in atmospheric CO 2 by determining the fraction of the total emitted carbon that remains in the atmosphere following its release. Hence, uncertainty in age models translates into uncertainty in reconstructed climate sensitivity because for a given mass of carbon release to the exchangeable reservoir, one cannot infer the increase in atmospheric CO 2 without constraining the timing of that carbon input. Instantaneous carbon release will lead to the maximum change in atmospheric CO 2 while slower release of the same mass of carbon will dampen the atmospheric CO 2 rise.

The many nCIEs across the geological record demonstrate that the carbon cycle has been disrupted frequently throughout Earth's history (Saltzman and Thomas 2012 ). Perhaps the most well studied nCIE, the Paleocene–Eocene Thermal Maximum (PETM, ∼56 Ma) (figure 2 (b)), is characterized by a rapid onset of several thousand years, a negative δ 13 C excursion of ∼3–4‰ and complete isotopic recovery on timescales of 10 5 years (Röhl et al 2007 , Zachos et al 2008 , McInerney and Wing 2011 , Westerhold et al 2018a ). Another well-known nCIE is the Eocene Thermal Maximum 2 (ETM-2) (figure 2 (c)), which is characterized by a nCIE that is half the magnitude of the PETM and more symmetrical in shape, i.e. the onset duration is equal to the duration of the recovery phase (Lourens et al 2005 , Stap et al 2009 ). The PETM, ETM-2, and other smaller nCIEs of the early Cenozoic are known collectively as hyperthermals (Thomas and Zachos 1999 ). Many of these purported hyperthermals are more similar to the magnitude and shape of the ETM-2, i.e. nCIEs of 1–2‰ occurring over 40–100 kyr (Sexton et al 2011 , Kirtland Turner et al 2014 , Westerhold et al 2018b ). Though a precise definition of 'hyperthermal' is lacking, these events are typified by simultaneous deep-sea warming and carbonate dissolution in addition to a negative δ 13 C excursion.

Figure 2.  Three examples of geologic negative carbon isotope excursions. (a) Bulk δ 13 C record for the Aptian Ocean Anoxic Event (OAE-1a) from Resolution Guyot (Jenkyns 1995 ) with linear interpolation between nCIE onset, peak and end, based on the age model from Malinverno et al ( 2010 ) (black line). (b) Bulk δ 13 C record for the Paleocene–Eocene Thermal maximum (PETM) from ODP Site 1001 (Bralower et al 1997 ) (black line). (c) Bulk record for the Eocene Thermal Maximum 2 (ETM-2) from Site 1258 (Kirtland Turner et al 2014 ). The red lines indicate simulated nCIEs from this study that most closely resemble the bulk δ 13 C records.

While not always described in the 'hyperthermal' terminology, a number of Mesozoic events share similar characteristics. For instance, the Toarcian Oceanic Anoxic Event (T-OAE, ∼183 Ma) is characterized by a nCIE of ∼6‰ between two positive δ 13 C excursions (Jenkyns 1988 , Hermoso et al 2012 , Müller et al 2017 ). Similarly, nCIEs have been reconstructed in association with the end-Permian mass extinction (∼252 Ma) (Meyer et al 2011 ), the end-Triassic mass extinction (∼201 Ma) (Pálfy et al 2001 ), and preceding multiple Cretaceous OAEs (particularly Aptian OAE-1a (∼120 Ma) (Menegatti et al 1998 ) (figure 2 (a)), and OAE-1b (∼111 Ma) (Wilson and Norris 2001 ). One complication in comparing these older events to the Cenozoic hyperthermals is that deep-sea records are scarce, and nCIEs are often reconstructed from shallow marine settings using carbonate that may have an unclear diagenetic history or using organic matter that may reflect a combination of sources (e.g. Corsetti et al 2005 ). However, carbon isotope records of these events have been previously evaluated as reflecting changes in the exchangeable carbon reservoir as a result of massive carbon input similar to the Cenozoic hyperthermals.

Given the range of nCIEs observed in the geologic record in terms of size, duration, and shape, as well as varying confidence regarding age control, we herein present an ensemble of modeled nCIEs using the Earth system model 'cGENIE' to reproduce variable nCIEs assuming various carbon sources. We generate 432 experiments (figure 3 ) and calculate the associated fluxes of carbon and impacts on marine and atmospheric chemistry and temperature for each. Advancing beyond a simple isotope mass balance approach, our modeling utilizes a 3D dynamical ocean model and incorporates carbon cycle feedbacks such as changes in ocean solubility and carbon speciation, carbonate compensation, and temperature-dependent rock weathering. Our framework facilitates assessment of individual nCIEs throughout the geologic record by providing an interpretive template for relating nCIEs of a given size, duration, and shape in the marine DIC reservoir to particular carbon cycle drivers and climatic and environmental consequences.

Figure 3.  Experimental design. Ensemble of 4  ×  3  ×  4  ×  9 = 432 inversions of surface ocean DIC δ 13 C varying nCIE size (4), duration (3), carbon isotopic composition of the carbon source (4) and shape (9).

cGENIE model and set-up

In this study, we use the intermediate complexity carbon-Grid ENabled Integrated Earth system model (cGENIE). cGENIE comprises a 3D frictional geostrophic ocean model and a simple energy-moisture balance atmosphere (Edwards and Marsh 2005 ). We include a CO 2 —climate feedback: radiative forcing due to CO 2 doubling in cGENIE is ∼4 W m −2 . We also include temperature-dependent continental weathering (Colbourn et al 2013 ) with a 1:1 carbonate to silicate weathering ratio and allow transport of alkaline species from the terrestrial into the marine environment. To balance terrestrial input, we couple a sediment model that calculates the sedimentary preservation of inorganic carbon in the form of calcium carbonate (CaCO 3 ) in deep sea sediments (Ridgwell and Hargreaves 2007 ). Biogeochemical cycling of elements and isotopes is represented throughout these four model components (Ridgwell et al 2007 ). A detailed description and evaluation of the carbon isotope ( δ 13 C) cycle in cGENIE is provided in Ridgwell et al ( 2007 ) and Kirtland Turner and Ridgwell ( 2016 ). Marine (export) productivity is calculated by the local availability of phosphate with modifiers for light limitation and sea ice extent (Ridgwell et al 2007 ). Phosphate is modeled as a closed system, with no input or burial fluxes, so its oceanic distribution is controlled by a combination of modeled patterns in export production and physical ocean circulation (which returns nutrients from the deep ocean to the surface). Calcium carbonate (CaCO 3 ) export is calculated using a fixed ratio of calcium carbonate to particulate organic carbon (POC) of 0.2. Both POC and CaCO 3 are remineralized in the water column using fixed depth-dependent profiles. Any POC reaching the seafloor is remineralized there (hence we do not account for sedimentary organic carbon burial). Importantly, our model also excludes any representation of land biota or soils, so that the exchangeable carbon reservoir is approximated as atmospheric carbon and marine dissolved inorganic and organic carbon only, which make up about 95% of the pre-industrial exchangeable reservoir (figure 1 ).

Because our goal is to provide a general interpretative framework for nCIEs applicable throughout the geological record, we use a simplified low-resolution (18  ×  18) continental configuration with a single symmetric pole-to-pole continent and 16 ocean depth levels. Still, the model ocean circulation is comparable to that in a higher resolution configuration run for the late Paleocene (figure S1, tables S1–S2 is available online at stacks.iop.org/ERL/14/085014/mmedia ). Both configurations show a dominant Southern Ocean overturning circulation, though the configuration used here shows overall weaker overturning strength and more symmetrical circulation between hemispheres. Due to differences in the overturning circulation and hence differences in nutrient distribution, the symmetric configuration yields slight increases in fluxes of particulate organic and inorganic carbon and a slight increase in the size of the marine dissolved organic carbon reservoir. However, due to the highly idealized continental configuration and its influence on the modeled circulation pattern, we cannot make explicit comparisons to the behavior of ocean circulation in previous Paleocene cGENIE experiments (e.g. Kirtland Turner and Ridgwell 2016 ).

The model is equilibrated to greenhouse climate conditions, with atmospheric CO 2 concentrations of three times preindustrial values (834 ppm), to approximate Mesozoic and Cenozoic greenhouse conditions (Fletcher et al 2008 ). We use the same initial carbon cycle conditions as the published cGENIE Paleocene configuration including: atmospheric δ 13 C of −4.9‰, adjusted major ion concentrations (Ca 2+ 18.2 mmol kg −1 , Mg 2+ 29.9 mmol kg −1 ), and lower alkalinity (1975 μ mol kg −1 ) along with modern (pre-industrial) inventories for phosphate (2.16 μ mol kg −1 ) and sulfate (15.0 mmol kg −1 ) (Ridgwell and Schmidt 2010 ). The model is run to steady state with carbon input from volcanic outgassing and alkaline run-off from the continent balanced by carbon removal through burial of CaCO 3 . The resulting modeled global average sea surface temperature is ∼26 °C, sea ice is absent and mean sedimentary wt% CaCO 3 is 42%.

Experimental methodology

Our ensemble tests various combinations of nCIE duration (3), size (4), and carbon source (4) and applies 9 different δ 13 C profiles that vary the shape of the nCIE for a total of 3  ×  4  ×  4  ×  9 = 432 experiments (figure 3 ).

We employ an inverse modeling technique to produce nCIEs wherein the isotopic signature of the surface ocean dissolved inorganic carbon pool ( δ 13 C DIC) is forced to follow a prescribed δ 13 C evolution, while an internal algorithm determines how much atmospheric CO 2 input with a specified isotopic signature is necessary to match this profile (Cui et al 2011 , Cui et al 2013 , Kirtland Turner and Ridgwell 2013 , Dunkley Jones et al 2018 ). We choose to force surface DIC δ 13 C rather than atmospheric CO 2 δ 13 C because the former is a closer approximation to data from marine carbonates. When modeled surface DIC δ 13 C values are higher than prescribed, a pulse of isotopically light CO 2 is released into the atmosphere. CO 2 with the same isotopic signature is removed from the atmosphere when modeled surface DIC δ 13 C drops below the prescribed value. Hence, CO 2 is artificially removed when carbonate compensation and weathering feedbacks are unable to sufficiently restore surface DIC δ 13 C values, but this carbon removal does not represent any particular physical process.

We impose carbon input (and removal) with isotopic signatures of −6‰, −12‰, −22‰ and −60‰, conceptually corresponding to carbon input from volcanism, a mixture of volcanism and organic carbon, organic carbon, and biogenic methane, respectively. The modeled nCIEs vary in size (0.5‰, 1.0‰, 3.0‰ and 6.0‰) and duration (50, 100 and 300 kyr) to represent the wide range of nCIEs recorded in the geological record. Furthermore, we define nine nCIE shapes (figure 3 ). We identify three dimensions of symmetry in duration: events can be (1) symmetrical in duration with equal duration onset and recovery phases ( δ 13 C minimum occurs halfway through the event duration) or asymmetrical with either (2) a relatively rapid onset and slow recovery ( δ 13 C minimum occurs at ¼ of event duration) or (3) relatively slow onset and rapid recovery ( δ 13 C minimum occurs at ¾ of event duration). We also identify three dimensions of symmetry in size: (1) δ 13 C values at the onset and recovery are identical, (2) final δ 13 C values are 50% higher than initial (overshoot) and (3) final δ 13 C values are 50% lower than initial (undershoot). Hence, the most rapid modeled nCIE onset is 12.5 kyr in experiments with a total duration of 50 kyr. The slowest nCIE onset of 225 kyr occurs in experiments with a total duration of 300 kyr. A 1‰ nCIE with an overshoot will end with DIC δ 13 C values 0.5‰ higher than initial while a 1‰ nCIE with an undershoot will end with DIC δ 13 C values 0.5‰ lower than initial.

Our large ensemble of nCIE experiments allows us to compare both the required carbon input and removal in terms of total mass and fluxes for particular nCIEs and relate the range of these values to uncertainty in carbon source, event duration, and event shape. We calculate 1000-year-binned average values of input and removal fluxes and sum net masses of carbon input/removal over the onset/recovery phases. We also compare the resulting carbon cycle and climate changes in the context of these same nCIE characteristics. In particular, we evaluate modeled changes in atmospheric CO 2 , sea surface temperature (SST), surface ocean pH, surface ocean saturation state, weathering rates and wt% CaCO 3 at the nCIE peak.

Diagnosed carbon forcing

All modeled nCIEs require an input of isotopically light carbon during the onset phase, while carbon needs to be removed during nCIE recovery to restore surface DIC δ 13 C to higher values. The total mass of carbon necessary to produce a nCIE of specific size depends to a first order on the isotopic signature of the source carbon. Total masses of carbon input diagnosed in our experiments vary by three orders of magnitude (figures 4 , S2). On the high end, to generate the largest size (6‰) nCIE from volcanic carbon with a δ 13 C of −6‰ requires a carbon input mass that is an order of magnitude larger than the entire mass of ∼32 000 Pg C in the modeled exchangeable reservoir at the start of the experiment. This contrasts with just a few thousand Pg C necessary to generate the same nCIE with carbon derived from methane with δ 13 C signature of −60‰ (figures 4 (a), S2). Significant variability in the required carbon input is also generated by variations in the duration and shape of the nCIE alone. Our results generally show that increasing assumed nCIE duration leads to an increase in the total carbon input on the 10 4 -year input timescales modeled here. Increases greater than 50% occur for some combinations of nCIE size and carbon source (figure 4 (a)—left panel and figure S2— moving left to right within each of subplots e–h) . Assuming the total duration of the nCIE is also known, varying the duration symmetry still causes variability in the calculated total carbon input. Increasing the relative onset duration from rapid to slow for a nCIE of a given size and total duration generally increases the total carbon input required (figure 4 —compare 4 (b) to 4 (c), figure S2— moving from the top to bottom row within each column , i.e. comparing subplots a, e, and i for a given nCIE size , figure S3). The effect is more pronounced for longer total durations. Whether a nCIE ends with an undershoot or an overshoot in surface DIC δ 13 C does not impact the total mass of carbon input required during the onset phase.

Figure 4.  Gross carbon input and maximum sustained carbon fluxes for simulated nCIEs. (a) The mass of carbon (left panel) and the maximum sustained flux (right panel) required to produce a prescribed, symmetric nCIE of a given size forced with carbon of predetermined isotope composition against the total duration of the nCIE. (b), (c) The mass of carbon (left panel) and the maximum sustained flux (right panel) required as a function of nCIE total duration and nCIE size for an excursion forced with carbon of δ 13 C −22‰ with a rapid (b) and slow (c) onset (also see supplementary information, figures S2 and S4).

Total carbon removal necessary to restore surface DIC δ 13 C for a nCIE of a given size and shape is similarly controlled to a first order by the imposed isotope composition of the removed carbon. In all our experiments, additional carbon removal occurs via the same isotopic composition as carbon input, allowing us to make a straightforward comparison between the relative masses of carbon input and removal, which we illustrate as the net carbon input to the exchangeable reservoir (figure S4). nCIEs with a δ 13 C overshoot (figure S4, left columns) are generally created by net removal of carbon over the total nCIE duration (indicated by blue colors) except for those with a long total duration of 300 kyr. nCIEs ending with a δ 13 C undershoot (figure S4, right columns), or nCIEs that are symmetrical in size ('no-shoot', figure S4, middle columns) always require a larger mass of carbon input compared to carbon removal (indicated by red colors). In other words, the average carbon isotopic composition of the surface DIC pool is exactly restored, but to achieve this, less carbon is removed than is added. Similarly, nCIEs that are symmetrical in size or with an undershoot leave the exchangeable reservoir significantly larger than at the experiment onset, particularly in the case of the largest nCIEs with the longest duration. In contrast, nCIEs with an overshoot always leave the exchangeable reservoir smaller than at the experiment onset, regardless of nCIE size or duration (figure S5).

Rate of carbon input to generate a nCIE of a given size also depends to a first order on the source of carbon input (figures 4 , S5). The maximum sustained rates of carbon input, calculated from 1000-year bins of the yearly average rate, exceed 20 Pg C yr −1 and are required to generate the 6‰ nCIE using volcanic carbon with δ 13 C of −6.0‰. Total event duration is significant for determining rate of carbon input for a nCIE of a given size and carbon source. Decreasing total duration from 300 to 50 kyr more than doubles the maximum rate of carbon input for all nCIE sizes (figure S6 —moving from right to left within each subplot ). In other words, compared with the total carbon input, the rate of carbon input is more sensitive to calculated event duration. Rate is also sensitive to assumptions about duration symmetry. For a nCIE of a given duration, varying the shape from a slow onset to a rapid onset can result in more than a doubling of the maximum sustained rate of carbon emissions. Hence, the relationship between nCIE duration or shape and maximum carbon flux is the opposite as between nCIE duration or shape and gross carbon input (figure 4 (a)). Maximum carbon flux is highest for shorter, rapid onset events whereas gross carbon input is highest for longer, slower onset events. Overall, our ensemble results in an enormous range of maximum sustained rates in carbon input during nCIE onset phases. The smallest nCIEs require rates of ∼0.01 Pg C yr −1 assuming depleted carbon sources of either biogenic methane or organic carbon. However, even the smaller nCIEs of 0.5 and 1.0‰ require relatively large sustained rates of carbon input (between 0.03 and 1.91 Pg C yr −1 ) if the assumed carbon source is volcanism with a δ 13 C of −6‰. None of our simulated nCIEs forced with biogenic methane ( δ 13 C −60‰) or organic carbon ( δ 13 C −22‰) require rates of carbon input reaching the current anthropogenic emission rate of 10 Pg C yr −1 . Even a 6‰ nCIE occurring over 50 kyr with a rapid onset over just 12.5 kyr requires a maximum sustained input of only about 1.4 Pg C yr −1 assuming an organic carbon ( δ 13 C −22‰) source. In fact, only the experiments with volcanic ( δ 13 C −6‰) carbon as the source ever require input rates in excess of the current anthropogenic value. All nCIEs forced with the mixture of volcanism and organic carbon ( δ 13 C −12‰) have maximum diagnosed emissions less than 6 Pg C yr −1 .

Carbon cycle and climate impacts

We focus on carbon cycle and climate changes that could feasibly be estimated using available proxies, including the change in atmospheric CO 2 (figures 5 , S7), surface ocean pH (figure S8), surface ocean saturation state (figure S8) and SST (figure S9). Given the dynamic ocean model in cGENIE, ocean circulation in our experiments is not fixed, yet we find minor changes of less than ∼3% in ocean overturning at the nCIE peak for most experiments (less than 1 Sv for all experiments except the 6‰ nCIEs forced with −6‰ volcanic carbon, which still show less than 3 Sv change at the nCIE peak). These subtle changes in ocean circulation also result in small changes in export production, which, in our model, is a function only of phosphate availability with modifiers for light limitation and sea ice extent (although no sea ice occurs in our experiments). These export production changes are small relative to changes in the size of the atmospheric and inorganic ocean carbon reservoirs (less than 1 Pg C yr −1 change at the nCIE peak in all but a few 6‰ nCIE experiments that show a maximum change of 3 Pg C yr −1 at the nCIE peak). The simulated changes to the carbon cycle are thus driven primarily by the total mass and rate of carbon input and associated feedbacks in the carbonate chemistry—the focus of our discussion henceforth—rather than changes in primary productivity or ocean circulation.

Figure 5.  Gross carbon input required to produce nCIEs of given size (a)–(d) and the maximum atmospheric CO 2 rise associated with each (e)–(h), for nCIEs forced with carbon of volcanic origin ( δ 13 C −6‰) (a), (e), a mixture of organic and volcanic carbon ( δ 13 C −12‰) (b), (f), organic carbon ( δ 13 C −22‰) (c), (g), and biogenic methane ( δ 13 C −60‰) (d), (h). The range of gross carbon input and atmospheric CO 2 rise for a given nCIE size results from different nCIE durations and shapes. The horizontal dashed lines (a)–(d) indicate the mass of carbon input calculated using a simple mass balance approach (equation (1)).

Our experiments result in an extremely large range of rates and total masses of carbon input (figure 4 ) that diverge from estimates based on the simple mass balance approach (figure 5 ). The most pronounced difference between the mass balance approach and our nCIE simulations occurs for the nCIE of 6‰ with a 225 kyr-long onset phase forced with δ 13 C carbon of −6‰. Simple isotope mass balance predicts that ∼147 200 Pg C input is required, while cGENIE requires nearly three times as much carbon input (∼413 800 Pg C). We use the results for environmental variables, particularly temperature, to test whether these results are realistic. For instance, the maximum atmospheric CO 2 reached in any of our experiments is over 120 000 ppm CO 2 , which is equivalent to slightly more than seven doublings from the initial concentration of 834 ppm. In cGENIE, the imposed radiative forcing due to CO 2 doubling is ∼4 W m −2 resulting in a typical surface temperature rise of 3.2 °C per CO 2 doubling (figure S12). The largest increases in atmospheric CO 2 occur in our long duration (300 kyr) experiments with a 6‰ nCIE driven by a −6‰ (volcanic) source, leading to an increase in average surface air temperature of almost 28 °C or an absolute maximum average surface air temperature of ∼50 °C. SST rises by ∼22 °C. In contrast, when the most isotopically depleted carbon source is assumed, this yields an increase in atmospheric CO 2 equivalent to approximately one doubling and SST warming of just 2.6 °C. The smallest nCIEs of 0.5‰ lead to a minor increase in atmospheric CO 2 of less than 150 ppm if the assumed carbon source is either organic carbon or biogenic methane. The associated increase in SST is just a few tenths of a degree Celsius. For a nCIE of a given size and carbon source, the maximum increase in CO 2 and maximum increase in SST both correspond to the maximum carbon addition rate rather than the total mass of carbon added, such that shorter durations and rapid onsets lead to greater increases in CO 2 and temperature. The sole exception occurs for 6‰ nCIEs forced by volcanic carbon (−6‰), where larger increases in CO 2 and SST occur for relatively longer duration events with slower onsets. For these nCIEs only, the maximum change in CO 2 and SST corresponds to the largest gross carbon input rather than the highest carbon input rate. The atmosphere in these scenarios becomes a proportionally larger carbon reservoir than the ocean, i.e. the ocean contains 17 121 Pg C at the nCIE peak, while the atmosphere contains nearly double that mass (27 429 Pg C) as a consequence of reduced CO 2 solubility with extreme warming. This means that ocean uptake is unable to remove excess CO 2 even when that CO 2 is emitted relatively slowly, so it continues to accumulate in the atmosphere. It is important to note that such large masses and rates of carbon input may not be representative of the events that occurred during any time in the Mesozoic or Cenozoic.

With greater atmospheric carbon input, greater quantities of CO 2 dissolve into the surface ocean, lowering surface ocean pH and the saturation state with respect to calcite and aragonite (Ω cal and Ω arg , respectively). The largest change in mean surface ocean pH (a decrease of 1.7) occurs in 6‰ nCIEs forced with volcanic carbon. Aside from the 6‰ nCIEs forced by enormous quantities of volcanic carbon described above, the relative decline in surface ocean pH for each experiment is equivalent to the relative increase in CO 2 —in other words, a shorter onset duration and hence more rapid rate of carbon input leads to a larger decline in surface ocean pH for a nCIE of a given size and carbon source. The largest change in saturation state with respect to calcite (a decrease of 5) occurs in 6‰ nCIEs forced with volcanic carbon that have the shortest onset durations of 12.5–25 kyr. In the initial model state prior to carbon emissions, the surface ocean is everywhere oversaturated with respect to calcite (Ω cal  > 1) and 99.2% of the grid cells are oversaturated with respect to aragonite (Ω arg  > 1). While aragonite undersaturation (Ω arg  < 1) can occur in parts of the surface ocean with very modest carbon forcing, calcite undersaturation requires input greater than 10 000 Pg C. Both calcite and aragonite undersaturation occurs predominately at the high latitudes where carbon uptake is maximized due to the higher solubility of CO 2 . Carbon forcing greater than 40 000 Pg C over 12.5 kyr or shorter is required to drive Ω cal  < 1 at low latitudes.

Onset duration (or the time to the nCIE peak) controls whether or not the response of the mean surface ocean pH and saturation state behave similarly in response to a given carbon input (figure S8). As nCIE duration increases, the magnitude of the surface pH decrease is slightly reduced (with the exception of 6‰ nCIEs forced by volcanic carbon (−6‰)), but the magnitude of the surface saturation state decrease is more notably reduced. The same relative effect is seen as a function of temporal symmetry—a rapid onset and slow onset of a nCIE with the same total duration show similar declines in surface ocean pH but the rapid onset nCIE shows a larger decline in saturation state. Hence, the mean surface ocean pH is more sensitive to total C input and surface saturation state is more sensitive to C flux. These results are consistent with the findings of Hönisch et al ( 2012 ) who demonstrated that ocean pH and saturation state change are progressively decoupled when carbon input occurs over long timescales. Notable decoupling begins for carbon input over 10 4 years or more.

We can also evaluate how each of the above variables evolves with time across each experiment. As an example, we show the response of atmospheric CO 2 , surface ocean pH and saturation state with respect to calcite, deep sea carbonate content (wt% CaCO 3 ), weathering flux (in terms of Ca 2+ ) and SST for a modeled nCIE similar to the Eocene Thermal Maximum 2 (ETM-2, 53 Ma) (figure 6 (a)). We take a nCIE of 1‰ with a total duration of 100 kyr and a symmetric shape (50 kyr onset duration) as the best approximation and evaluate the modeled response of the above variables across the experiment duration. Atmospheric CO 2 and SST peak at the same time as gross C input, coincident with minimum δ 13 C in surface ocean DIC. Simultaneously, surface ocean pH and saturation state reach their minima while weathering fluxes reach their maxima. Sedimentary wt% CaCO 3 , however, shows a minimum that precedes the peak in SST and weathering flux and has already begun to rebound before the δ 13 C minimum. The later rebound in CaCO 3 shows maximum accumulation approximately coeval with maximum surface ocean saturation state. In a similar manner, a comparison is made between the PETM, OAE-1a, and the nCIE simulations performed to establish the framework presented here (figure S11).

Figure 6.  Carbon cycle evolution and environmental impacts of a nCIE with a size of 1‰. (a) In the upper panel, bulk δ 13 C record of the ETM-2 from Site 1258 (Kirtland Turner et al 2014 ) (black line) and the simulated nCIE that best matches this record: symmetric in time with a total duration of 100 kyr (red line). Below, the evolution of the gross carbon input (solid), change in atmospheric CO 2 (dashed), change in surface ocean calcite saturation state (Ω cal , solid) and surface ocean pH (dashed), change in global mean sedimentary wt% CaCO 3 (solid), percentage of change in rock weathering rate relative to initial conditions (dashed), and the change in SST for 1‰ nCIEs, forced with −6‰, −12‰, −22‰, and −60‰ δ 13 C carbon. (b) The maximum change in carbon cycle and environmental parameters compared with initial model conditions as a function of onset duration for 1‰ nCIEs.

Diagnosed carbon input

Our experiments highlight the significance of considering timing in diagnosing the carbon input required to generate a nCIE. Of particular importance is the time to peak nCIE (onset duration), which is controlled by both nCIE duration and nCIE shape in our experimental framework. Overall, we find that greater carbon input is necessary to generate a nCIE with a longer onset duration, but the rise in atmospheric CO 2 decreases with onset duration. The experiments start from steady state with respect to the exchangeable carbon reservoir (carbon inputs from weathering fluxes and volcanism are balanced by sedimentary carbonate burial), on top of which carbon inputs diagnosed by the inversion scheme are added from an external, specified source. Carbon addition diagnosed by the inversion scheme during the nCIE onset directly increases the size of the exchangeable carbon reservoir. The exchangeable reservoir also grows or shrinks because of the indirect effects of global temperature and ocean chemistry on weathering rates and the preservation of sedimentary CaCO 3 . These feedbacks operate over characteristic timescales, such that nCIE duration exerts an important control on the total carbon mass in the exchangeable reservoir as well as the relative distribution of carbon among atmospheric CO 2 and the oceanic DIC and DOC pools.

At the start of each experiment, the exchangeable reservoir totals just over 31 800 Pg C (atmospheric CO 2 of ∼1800 Pg C, marine DIC of ∼30 000 Pg C, and marine DOC of ∼6.7 Pg C). For a 6‰, 300 kyr nCIE with a relatively rapid onset (75 kyr) driven by −22‰ carbon, the masses of these reservoirs total just over 48 000 Pg C (atmosphere ∼7000 Pg C, DIC ∼41 000 Pg C, and DOC ∼6.9 Pg C) at the nCIE peak, an increase of about 17 000 Pg C over initial conditions. However, the inversion scheme diagnoses a gross C input over this interval of 13 760 Pg C. Thus >3000 Pg C (more than 20% of the total exchangeable carbon reservoir increase) is attributable to excess weathering not balanced by increased CaCO 3 burial by the time of the nCIE peak. Further, there has been a relative redistribution of carbon such that the atmosphere is a proportionally larger carbon pool (although DIC still dominates the exchangeable reservoir mass) because as atmospheric CO 2 rises and surface ocean pH declines, the ocean's buffering capacity is reduced.

A mass balance framework utilizes only information about the initial mass of the exchangeable carbon reservoir, the size of the nCIE, and the inferred carbon source. Our more nuanced framework, by incorporating inorganic carbon cycle feedbacks, also utilizes constraints provided by age models on the total and relative duration of a nCIE and provides a refined first order estimate regarding the range of possible carbon fluxes and cumulative input masses. Figure 5 illustrates the difference between the simple isotope mass balance calculations for carbon input and our cGENIE model results for gross carbon addition. While the simple isotope mass balance approach (equation (1)) provides a single value for a particular size nCIE given an assumed carbon source (with specified δ 13 C), our experiments generate a range of estimates for carbon input, depending on the duration and shape of the nCIE. The discrepancy between our cGENIE diagnosed carbon inputs and a simple mass balance approach is most pronounced for larger nCIEs generated using carbon sources with higher δ 13 C. For instance, assuming a volcanic carbon source (figure 5 (a)), the isotope mass balance approach provides an estimate of input mass that falls nearly in the middle of the range calculated by cGENIE for a 0.5‰ and 1‰ nCIE, but isotope mass balance gives a value closer to the lower range of diagnosed carbon inputs for nCIEs of 3‰ and 6‰. This increasing discrepancy between isotope mass balance and our results for large input masses is due to the temperature-dependent weathering parameterization (i.e. weathering increases by more and thus gross carbon must increase by relatively more to compensate as total carbon input increases).

Both our approach and the simple isotope mass balance (equation (1)) require information about initial carbon cycle conditions. In the mass balance approach, this is simply the mass of the total exchangeable reservoir. Our approach requires not only this information, but also makes presumptions about the initial buffering capacity of the oceans, which will influence how carbon is exchanged between reservoirs and how much seafloor carbonate dissolves. These carbon cycle assumptions must be considered when comparing our results against particular geological events, especially those that occurred prior to the advent of widespread pelagic calcification during the Jurassic (∼170 Ma) (Arvidson et al 2014 ).

We do not explicitly test the impact of varying initial carbon cycle conditions on our results; however, we can infer the general impact of particular assumptions. While it is likely that the marine DIC pool (by far the largest of the exchangeable carbon pools) was similar in mass through much of the Cenozoic, it was likely larger during much of the Mesozoic (e.g. Ridgwell 2005 ). If the mass of the total exchangeable reservoir (atmospheric CO 2 and ocean DIC and DOC) was significantly larger, the required carbon input of a given isotopic signature for a given nCIE would have been larger. Varying initial carbon cycle conditions, including alkalinity or major ion composition, would have a more nuanced influence, altering the relative partitioning of carbon between reservoirs and controlling the strength of feedbacks that are sensitive to this distribution. For example, initial carbon cycle conditions characterized by higher relative partitioning into atmospheric CO 2 (lower surface ocean pH) requires relatively larger masses of CO 2 emitted to achieve the same nCIE in the surface ocean DIC pool because a greater proportion of emissions will remain in atmosphere, i.e. the global mean Revelle factor is higher in a high pCO 2 /low pH world. With a greater increase in atmospheric CO 2 , the resultant enhanced weathering that releases relatively isotopically heavy alkaline carbon species will dampen the signal of the 13 C-depleted emissions and hence require even greater 13 C-depleted CO 2 emissions to generate the same nCIE in the surface ocean. Thus, when interpreting an individual geologic event in the context of our hypothetical framework, it is necessary to consider whether initial mean surface ocean pH is likely to have been lower or higher than what is modeled here (∼7.7).

Diagnosed carbon removal

Restoration of surface DIC δ 13 C to pre-excursion values during the recovery phase requires the addition of relatively heavy carbon (via carbonate dissolution and weathering) and/or removal of isotopically light carbon. The model calculates fluxes of carbon (and its isotopes) both within the exchangeable reservoir and including sediment and weathering feedbacks, and then compensates for any remaining deviations of the surface ocean DIC δ 13 C pool from the target curve through removal of CO 2 with a specified δ 13 C from the atmosphere. In other words, carbon simply disappears from the model atmosphere if the simulated carbon cycle feedbacks have failed to restore surface ocean DIC δ 13 C sufficiently to match the prescribed curve. This process is conceptually simple, but it has consequences that are most likely not realistic. First, this diagnosed additional atmospheric carbon removal is not simulated as any particular physical mechanism. Second, the fact that the carbon removal flux has a specified isotopic composition (here we use the same value as the carbon input), means that we are not adjusting the isotopic composition of the removed carbon based on the composition of exchangeable reservoir or based on likely fractionations of real removal processes (e.g. organic matter formation). Third, our method does not account for removal of carbon at a different isotopic composition than the input, though in reality these values may be very different (e.g. input of volcanic CO 2 followed by removal via organic carbon burial). An alternative approach for calculating carbon removal, even without explicitly modeling organic carbon burial, would be to remove carbon with an isotopic composition matching that of the modeled particulate organic carbon pool (e.g. Gutjahr et al 2017 ), rather than using an assigned value.

Only nCIEs with an undershoot where the final δ 13 C is lower than the initial δ 13 C, and/or a long duration and slow recovery result in diagnosed carbon removal fluxes substantially less than input fluxes. In other words, they show a large positive net carbon input (figure S4). This indicates that modeled feedbacks are nearly sufficient to match the surface DIC δ 13 C signature in these cases and little additional diagnosed carbon removal is necessary. In modeled nCIEs where the diagnosed mass of carbon removal rivals or even exceeds the diagnosed carbon input, this implies that the carbonate compensation and weathering feedbacks alone were insufficient to drive the recovery of surface DIC δ 13 C and additional carbon removal (modeled as CO 2 artificially removed from the atmosphere) was necessary. A deficiency in our experiments is thus the lack of organic carbon burial, which might help explain the recovery of surface ocean DIC δ 13 C without requiring an additional removal flux via our inversion methodology for the larger and/or shorter duration nCIEs. Given that a number of nCIEs in the geologic record are followed by black shale deposition and associated positive δ 13 C excursions, e.g. the Toarcian and Aptian OAEs, there is clear evidence that organic carbon feedbacks not only played a role in recovery of the exchangeable reservoir from carbon input but often led to δ 13 C 'overshoot' behavior (Jenkyns 2010 ).

The change in atmospheric CO 2 and associated warming generated in each of our experiments allows us to reasonably rule out certain carbon input scenarios for certain nCIEs. In particular, the massive carbon inputs required to generate 6‰ nCIEs using volcanic carbon of −6‰ raise atmospheric CO 2 to levels that lead to an average ocean temperature greater than 40 °C, inconsistent with data for even the Mesozoic greenhouses. The highest reconstructed low latitude surface temperatures during the Cretaceous are reconstructed from the TEX 86 archaeal lipid SST proxy, and are a maximum of ∼36 °C (Schouten et al 2003 ). Further, evidence for SST in excess of 40 °C during the PETM from Tanzania in combination with the exclusion of planktic foraminifera has been provided as evidence of a temperature threshold for these organisms (Aze et al 2014 ). It seems likely that widespread temperatures this high would have resulted in significant extinction and widespread dead zones. Adding the effects of severe thermal stress on marine organisms (not modeled here) could increase CO 2 even further if the biological carbon pump were to collapse. This suggests that large nCIEs occurring over the timescales modeled here and similar to several Mesozoic nCIEs are unlikely to have been driven by isotopically heavy carbon input (e.g. mantle-derived volcanism) alone. nCIEs of 3‰ forced with −6.0‰ carbon and 6‰ nCIEs forced with −12‰ carbon have maximum CO 2 concentrations 7500–17 000 ppm and maximum global mean SSTs of 33 °C–36 °C, more consistent with proxy temperature records.

Our experiments highlight the importance of nCIE duration and shape for determining carbon input rate, which has significant impacts on atmospheric CO 2 , SST and saturation state (figure S10). While nCIEs with short onset durations require less total input of carbon than nCIEs with longer onset durations, maximum atmospheric CO 2 concentrations are highest in the shortest nCIEs. Again, this can be attributed to marine carbonate compensation and terrestrial rock weathering, which both act to stabilize ocean saturation state and modulate atmospheric CO 2 concentrations over 10 4 –10 5 -year timescales (Walker et al 1981 , Archer and Maier-Reimer 1994 , Archer et al 1997 , Archer 2005 , Archer et al 2009a , Goodwin and Ridgwell 2010 ). In particular, the temperature-dependent weathering feedback in cGENIE operates with an e -folding timescale of ∼240 kyr (Colbourn et al 2015 ). As carbon input extends over intervals of time commensurate with the e -folding weathering timescale, the required total carbon input increases while the effect of those emissions on atmospheric CO 2 (and hence temperature rise) is limited.

The differential sensitivity of surface ocean saturation state and pH to nCIE onset duration (figure S8) that occurs in our experiments has been noted previously (Hönisch et al 2012 ) and is a further example of how the timescale of carbon release interacts with the timescales of negative inorganic carbon cycle feedbacks (Hönisch et al 2012 ). A consequence of the weathering feedback is that when carbon input is sufficiently slow, the dominant sedimentary response is an increase in CaCO 3 accumulation rate. In our experiments, modeled sedimentary CaCO 3 concentrations drop initially in response to carbon addition, but after approximately 20–30 kyr (or less, for the shortest onset experiments) global sedimentary wt% CaCO 3 starts increasing. In fact, for most of our experiments this carbonate overshoot (e.g. Penman et al 2016 ) exceeds initial dissolution in terms of the change in global mean wt% CaCO 3 . It is important to note that we employ a fixed rain ratio (i.e. constant ratio of particulate organic carbon to particulate inorganic carbon throughout our experiments) and fixed remineralization profiles so that carbonate fluxes only change along with changes in calculated export productivity. The duration of carbonate dissolution is hence related to the weathering timescale and not to the duration of carbon input. As enhanced weathering delivers excess alkalinity to the oceans, carbonate burial will recover and rebound, regardless of whether carbon input to the atmosphere has ceased.

Comparison with past nCIEs

A primary goal of our ensemble is to provide a framework for the interpretation of past geological events. Below, we provide examples in comparing our model experiments to three events: ETM-2, the PETM and OAE-1a.

ETM-2—The Eocene Thermal Maximum 2 (ETM-2, ∼54 Ma) is a relatively short-lived warming event marked by a symmetric nCIE of 1.0 to 1.5‰ and widespread deep sea CaCO 3 dissolution (Lourens et al 2005 , Stap et al 2009 ) (figure 2 (c)). The nCIE scenario modeled in this study that is most similar to the ETM-2 is the symmetric 1‰ nCIE with a total duration of 100 kyr without under- or overshoot in surface DIC δ 13 C (figure 6 (a)). To produce a nCIE of this size with an isotopically heavy carbon input (−6‰), approximately 5200 Pg C is required, resulting in atmospheric CO 2 increase of 900 ppm and SST increase of 2.6 °C. An input of isotopically lighter carbon (−12 to −22‰) over 50 kyr produces a 1‰ nCIE with 2700 to 1500 Pg C respectively, and leads to a global mean SST increase of 1.5 °C–0.8 °C. Previous studies based on proxy data estimate (regional) SST increases during the ETM-2 of 3 °C–5 °C (Lourens et al 2005 , Sluijs et al 2009 ), which fits best to a carbon input of mantle-derived volcanic source. However, the orbital pacing of a sequence of early Eocene hyperthermals, including the ETM-2, seems inconsistent with a volcanic origin. Increases in SST of 1.5 °C–0.8 °C produced by −12 and −22‰ carbon input are low compared to available SST proxies, but the maximum ETM-2 magnitude of 1.5‰ recorded in bulk carbonate is 0.5‰ larger than the 1‰ nCIE we compare to here and the true nCIE magnitude may have been even larger (Sluijs et al 2009 ). An nCIE of 1‰ driven by isotopically light (−60‰) methane requires ∼600 Pg C, produces an increase in atmospheric CO 2 of only 80 ppm and a 0.3 °C SST increase. The latter would be nearly undetectable in most noisy proxy data. Furthermore, the widespread deep-sea carbonate dissolution associated with the ETM-2 does not result from experiments with isotopically lighter carbon sources. Less than 2.5 wt% global average CaCO 3 decline results from a 1‰ nCIE driven by either −60‰ or −22‰ carbon inputs. Hence, a larger carbon input (and therefore a carbon input with mean δ 13 C signature heavier than −22‰) is most consistent with the extent of environmental changes during the ETM-2. An alternative scenario that could explain the large temperature increase and globally widespread carbonate dissolution that is that the onset occurred on timescales much shorter than 50 kyr. nCIEs with an onset duration shorter than 50 kyr result in a significant drop in surface ocean calcite saturation state (Ω cal ) which promotes the dissolution of CaCO 3 (figures 6 (b) and S8, S10). Likewise, the SST rise associated with a more rapid nCIE onset is larger compared to a nCIE onset duration over 50 kyr (figures 6 (b) and S9).

PETM (∼56 Ma) is the greenhouse gas-driven global warming event most often suggested as an analog for the modern (e.g. Zeebe and Zachos 2013 ). Many more records of the PETM nCIE from a greater variety of settings are available in comparison to other Mesozoic and Cenozoic hyperthermals (McInerney and Wing 2011 ). The nCIE varies in size between different reservoirs, but the average bulk carbonate nCIE is closest in size to the 3‰ nCIEs modeled here (figures 2 (b)). The PETM is well known for its asymmetric shape, with a rapid onset of <10 kyr and a total duration of ∼200 kyr (McInerney and Wing 2011 , Kirtland Turner 2018 ). None of our experiments shows an onset as rapid as the PETM—the most rapid modeled onset for a 100 kyr nCIE is 25 kyr. We compare the PETM to the 100 kyr, rapid onset 3‰ nCIE without under- or overshoot in surface DIC δ 13 C (figure S11(b)). Estimated total carbon input is between 1600 to more than 40 000 Pg C depending on carbon source. Only the −12‰ carbon source leads to an increase in SST (5 °C) consistent with compiled temperature proxy records (Dunkley Jones et al 2013 ), resulting in an increase in atmospheric CO 2 levels by ∼2500 ppm and declines in surface ocean pH and calcite saturation state (Ω cal ) of 0.47 and 2.7, respectively. The total carbon input for this scenario (>10 000 Pg C) is also consistent with recent estimates (Gutjahr et al 2017 ). However, the onset duration of the PETM is estimated to be shorter than 25 kyr and we can use our framework to explore the environmental consequences of more rapid onset duration as well. When a 3‰ nCIE onset is produced over 12.5 kyr (from the experiment with a modeled total duration of 50 kyr) using a carbon source with δ 13 C of −22‰, approximately 10 000 Pg carbon input is required. This increases atmospheric CO 2 levels by 3200 ppm, the global mean SST rises by 5.6 °C, surface pH drops 0.57 units and Ω cal declines by 3.4.

OAE-1a—The Aptian Ocean Anoxic Event (OAE-1a) is one of the two major Cretaceous OAEs with a recorded nCIE preceding wide-spread organic carbon burial (Menegatti et al 1998 , Herrle et al 2004 , Jenkyns 2010 ) and might hold important information on carbon reservoir changes involved in the expansion of marine anoxia during this time. Aptian nCIEs are most commonly recorded with sizes ranging from −1 to −3‰. Using a nCIE at the upper limit of that interval from carbonate deposits at the Resolution Guyot (Jenkyns 1995 ) and age models based on cyclostratigraphy (Malinverno et al 2010 ), the nCIE at the onset of OAE 1a most closely resembles our 300 kyr-long simulations with rapid onset and δ 13 C values ending in an overshoot (figure S11(a)). nCIEs of this shape and duration can be produced by biogenic methane emissions ( δ 13 C−60‰) without drastically perturbing climate and ocean carbonate chemistry, but such a forcing mechanism cannot account for the reconstructed simultaneous rise in SST of 2 °C–5 °C (Mutterlose et al 2014 , Naafs and Pancost 2016 ), the atmospheric CO 2 increase of a few hundred to several thousand ppm (Naafs et al 2016 ), or the crisis of marine calcifying nannoplankton (Erba et al 2010 ). A purely volcanic source of carbon results in a p CO 2 rise of 10–20 times pre-nCIE values, a stark decrease in surface pH and ocean calcite saturation, and a rise in global mean SST up to 10 °C. Those environmental impacts are far more extreme than the proxy-based reconstructions suggest. Based on our framework and the age model provided by Malinverno ( 2010 ), the Aptian nCIE was most likely caused by a combination of organic and mantle carbon sources, resulting in the net emission of carbon of intermediate isotopic composition. However, recently published high-resolution records from shallow carbonate platforms suggest that the nCIE onset might have lasted significantly longer (Kuhnt et al 2011 , Lorenzen et al 2013 , Graziano and Raspini 2018 ), in which case a forcing from δ 13 C −6‰ volcanic carbon becomes more plausible for the OAE1a since longer nCIE onsets result in reduced impacts in climate and ocean chemistry, but a slight increase in the total mass of carbon that needs to be added to the ocean-atmosphere system (figure S10).

Summary/Conclusion

Our large ensemble of modeled nCIEs provides a template for interpreting past geologic events in terms of required carbon input and likely environmental consequences. We include the effects of various feedbacks such as changes in ocean solubility, carbon speciation, carbonate compensation and temperature-dependent weathering on the global carbon cycle. The earth system modeling approach allows us to track changes in the partitioning and fractionation of carbon between various carbon pools within the exchangeable reservoir. Our four dimensions of variability in defining modeled nCIEs (including size, carbon source, duration, and shape) adds two new dimensions compared to the conventional isotopic mass balance approach that neglects variability in duration and shape. Our results highlight the significant variability these two factors can generate in both the total carbon input required to generate a nCIE of a particular magnitude with a particular carbon source, but also the maximum rate of carbon input as a result of the interaction with modeled carbon cycle feedbacks. Thus, our experiments can be used to bracket the carbon emissions scenarios capable of driving any number of past nCIEs. Furthermore, these experiments demonstrate how environmental impacts scale with all four dimensions of variability. Hence, a comparison of available proxy data (e.g. changes in temperature, surface ocean pH, or changes in saturation state inferred from sedimentary carbonate dissolution) to our results can also be used to evaluate the likelihood of various carbon sources for a nCIE of a given magnitude.

Acknowledgments

While working on this manuscript PV and SKT were supported by a Heising-Simons Foundation award, MA was funded by NERC GW4+ PhD studentship S136361, and SEG was funded by NERC Independent Research Fellowship NE/L011050/1 and NERC large grant NE/P01903X/1. We thank James Rae and an anonymous reviewer for suggestions that greatly improved the manuscript.

Data availability

The specific version of the cGENIE.muffin model used in this paper is tagged as release v0.9.6 and has been assigned a DOI ( https://doi.org/10.5281/zenodo.3338584 ). The code is hosted on GitHub and can be obtained by cloning: https://github.com/derpycode/cgenie.muffin , changing directory to cgenie.muffin, and then checking out the specific release: $ git checkout v0.9.6. Configuration files for the specific experiments presented in this paper can be found in the directory: genie-userconfigs\MS\vervoortetal.2019. Details of the experiments, plus the command line needed to run each one, are given in the README.txt file in that directory. All other configuration files and boundary conditions are provided as part of the release. A manual detailing code installation, basic model configuration, plus an extensive series of tutorials covering various aspects of muffin capability, experimental design, and results output and processing, is provided on GitHub. The latex source of the manual, along with a pre-built PDF file can be obtained, by cloning: https://github.com/derpycode/muffindoc . Model output files of this study are available from the corresponding author upon reasonable request.

Supplementary data (4.11 MB, PDF)

The grandest of them all: the Lomagundi–Jatuli Event and Earth's oxygenation

* Correspondence: [email protected]

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A.R. Prave , K. Kirsimäe , A. Lepland , A.E. Fallick , T. Kreitsmann , Yu.E. Deines , A.E. Romashkin , D.V. Rychanchik , P.V. Medvedev , M. Moussavou , K. Bakakas , M.S.W. Hodgskiss; The grandest of them all: the Lomagundi–Jatuli Event and Earth's oxygenation. Journal of the Geological Society 2021;; 179 (1): jgs2021–036. doi: https://doi.org/10.1144/jgs2021-036

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The Paleoproterozoic Lomagundi–Jatuli Event (LJE) is generally considered the largest, in both amplitude and duration, positive carbonate C-isotope ( ⁠ δ 13 C carb ) excursion in Earth history. Conventional thinking is that it represents a global perturbation of the carbon cycle between 2.3–2.1 Ga linked directly with, and in part causing, the postulated rise in atmospheric oxygen during the Great Oxidation Event. In addition to new high-resolution δ 13 C carb measurements from LJE-bearing successions of NW Russia, we compiled 14 943 δ 13 C carb values obtained from marine carbonate rocks 3.0–1.0 Ga in age and from selected Phanerozoic time intervals as a comparator of the LJE. Those data integrated with sedimentology show that, contra to consensus, the δ 13 C carb trend of the LJE is facies (i.e. palaeoenvironment) dependent. Throughout the LJE interval, the C-isotope composition of open and deeper marine settings maintained a mean δ 13 C carb value of +1.5 ± 2.4‰, comparable to those settings for most of Earth history. In contrast, the 13 C-rich values that are the hallmark of the LJE are limited largely to nearshore-marine and coastal-evaporitic settings with mean δ 13 C carb values of +6.2 ± 2.0‰ and +8.1 ± 3.8‰, respectively. Our findings confirm that changes in δ 13 C carb are linked directly to facies changes and archive contemporaneous dissolved inorganic carbon pools having variable C-isotopic compositions in laterally adjacent depositional settings. The implications are that the LJE cannot be construed a priori as representative of the global carbon cycle or a planetary-scale disturbance to that cycle, nor as direct evidence for oxygenation of the ocean–atmosphere system. This requires rethinking models relying on those concepts and framing new ideas in the search for understanding the genesis of the grandest of all positive C-isotope excursions, its timing and its hypothesized linkage to oxygenation of the atmosphere.

Supplementary material : C–O isotope data, figure S1, tables S1–S5 and the dataset for δ 13 C carb values are available at https://doi.org/10.6084/m9.figshare.c.5471815

Evidence of the oxygenation of Earth's surface environments during the Paleoproterozoic is based on a now familiar list of temporally linked phenomena that includes geological features (decline of banded-iron formation, cessation of uraninite and pyrite as resedimented detrital particles, advent of non-marine red beds; e.g. Roscoe 1969 ), loss of sulphur mass-independent isotope fractionation ( Farquhar et al. 2000 ), Lomagundi–Jatuli and Shunga C-cycle perturbations ( Schidlowski et al. 1976 ; Karhu and Holland 1996 ; Melezhik et al. 1999 a ) and the hypothesised window of Cyanobacteria evolution (e.g. Fischer et al. 2016 ; Sánchez-Baracaldo and Cardona 2020 ). Of those, the Lomagundi–Jatuli Event (LJE) has become essentially synonymous with tracking the trend of atmospheric oxygenation (e.g. Karhu and Holland 1996 ; Bekker and Holland 2012 ; Lyons et al. 2014 ). The LJE is the largest positive carbonate–carbon isotope ( ⁠ δ 13 C carb ) excursion in Earth history, marked by δ 13 C carb values between +5 and 10‰ (and higher) in marine carbonate units tens to several hundreds of metres thick that were deposited between c . 2.3 and 2.1 Ga ( Melezhik et al. 2007 ; Martin et al. 2013 ; Gumsley et al. 2017 ). Two contrasting hypotheses have been championed for the genesis of the LJE. The first is the consensus view, which interprets the LJE as a synchronous and global-scale disturbance of the carbon cycle linked to changes in the oxygenation state of the ocean–atmosphere system such that, following the Great Oxidation Event ( Holland 2006 ; although see Ohmoto 2020 for an alternative perspective), a biogeochemical feedback was established with atmospheric O 2 rising and falling in concert with co-varying fluctuations between oxidative weathering of continental landmasses, nutrient fluxes and primary productivity ( Karhu and Holland 1996 ; Bekker and Holland 2012 ; Planavsky et al. 2012 ; Canfield et al. 2013 ; Scott et al. 2014 ; Bellefroid et al. 2018 ; Miyazaki et al. 2018 ; Ossa Ossa et al. 2018 ; Hodgskiss et al. 2019 ). The second view is advocated by a minority of workers such as Melezhik et al. (1999 b ) and Frauenstein et al. (2009) who interpret high C-isotope values of the LJE as due to processes bespoke to palaeoenvironmental settings within individual sedimentary basins (e.g. organic burial rate, sediment flux, evaporation, methanogenesis) that enhance a plausibly global signal. Central specifically to the consensus view is the conjecture that the highly positive δ 13 C carb values of the LJE are representative of the dissolved inorganic carbon (DIC) reservoir of the global ocean which, in turn, underpins the paradigm that the carbon cycle of the LJE and atmospheric oxygenation are directly interrelated ( Schidlowski 1988 ; Karhu and Holland 1996 ; Planavsky et al. 2012 ; Lyons et al. 2014 ; Daines et al. 2017 ; Bellefroid et al. 2018 ). Here we assess this paradigm by analysing the relationship between carbon isotope data and facies (i.e. palaeoenvironment) for LJE-bearing marine carbonate rocks worldwide ( Fig. 1 ). Because many LJE-bearing successions are lean in organic carbon, our focus is on carbonate–carbon isotope data.

The LJE and the carbon cycle

The connection between key fluxes of carbon as carbonate precipitated out of the marine DIC reservoir and the amount buried as organic matter, including the respective isotopic compositions of each flux, has been commonly evaluated within a framework of mass balance and used in evaluating the pattern and tempo of the global carbon cycle (e.g. Schidlowski 1988 ; Kump 1991 ; Hayes and Waldbauer 2006 ; Mason et al. 2017 ). With few exceptions, the δ 13 C value of marine DIC has remained largely within a window of 0 ± 4‰ for most of geological time (e.g. Schidlowski 1988 ; Prokoph et al. 2008 ). The LJE is one of the most remarkable of those exceptions, and hypotheses relying on mass balance have struggled to explain the vast amounts of organic matter that would need to be buried to generate such positive δ 13 C carb values (e.g. Karhu and Holland 1996 ; Aharon 2005 ; Holland 2006 ) or have opted to offer speculations invoking an unprecedented spike in primary productivity (e.g. Bekker and Holland 2012 ). The postulated net outcome of either is an extraordinary pulse in atmospheric oxygen. Other models invoke tectonics driving exhumation and erosion of older sedimentary rocks that, in turn, drive fluctuations in the isotopic composition of the carbon flux entering the marine realm to generate C-isotope excursions in lieu of changes to primary productivity (e.g. Kump 1991 ; Miyazaki et al. 2018 ), or attribute C-isotope excursions to changing intensities and proportions of chemical versus physical weathering, in part linked to tectonics, such as supercontinent cycles (e.g. Shields and Mills 2017 ). Our purpose is not to evaluate the veracity of these various models. Rather, our work assesses the key premise that underpins the LJE paradigm, namely, that the magnitude and duration of its δ 13 C carb values are an accurate archive of the C-isotopic composition of the global ocean between 2.3 and 2.1 Ga. All concepts and models that use the LJE as evidence of the redox evolution of Earth's surface environments and initial rise and proliferation of free di-oxygen rely on that premise to be true.

We compiled a database consisting of 14 943 published δ 13 C carb data: 11 557 data are for the time interval 3.0–1.0 Ga, which includes 2038 δ 13 C carb data from LJE-bearing rocks worldwide. Of the latter, 188 are new δ 13 C carb and δ 18 O carb isotope data obtained on carbonate rock samples from outcrops of the LJE-bearing Tulomozero Formation in the Onega Basin, NW Russia, at Raiguba (62°22.107′N, 033° 47.129′E) and Shunga (62°36.697′N, 034° 49.457′E) and the portion of the Onega Parametric Hole drill core containing the Tulomozero Formation and lower part of the overlying Zaonega Formation. The remaining 3386 data are from Phanerozoic carbonate rocks deposited in environments ranging from sabkha to open ocean and used as a comparator for the LJE. All data and their sources are reported in the Supplementary material . For the new data, measurements were made on a Thermo Scientific Delta V Advantage continuous flow isotope ratio mass-spectrometer in the Department of Geology, University of Tartu, Estonia, following standard protocols. C and O data are reported in per mil (‰) deviation relative to the Vienna PeeDee Belemnite (V-PDB) and standard reproducibility was better than ±0.2‰ at 1 σ ⁠ . In constructing the database of published δ 13 C carb values for the 3.0–1.0 Ga rocks, we included only those data that record primary depositional (or nearly so) conditions as per original authors’ reporting of petrographic features, C–O isotope cross-plots and key element ratios. We excluded data from rocks that experienced significant post-depositional isotopic resetting and from features of clearly later diagenetic origin (e.g. concretions, cements), as well as carbonate rocks associated with banded-iron formation. Data are evaluated in 100 Myr bins (geons of Hofmann 1990 ), using the inferred depositional ages reported in the literature.

Sample means were determined by the bootstrap method using an approach described in Keller and Schoene (2012) and Cox et al. (2018) which enables estimation of the sampling bias on statistics (mean, median, etc.) whereby a synthetic dataset (bootstrap sample) is created by random independent sampling with replacement from an existing sample (population). The statistics of interest are estimated for each bootstrap sample and each step is repeated numerous times obtaining estimates that can be treated for additional statistical inferences (mean, standard deviation, confidence interval, etc.). The bootstrapped means and confidence intervals reported in Table 1 and Supplementary material were calculated from 10 000 repetitions. The sample bias of the binned data was assessed further by jackknife estimates ( Tukey 1958 ) that were in all cases in agreement with bootstrapped means (jackknife bias = 0). Jackknife procedure is similar to the bootstrap method but sampling is done without replacement and was developed for estimating the variance and bias of large datasets. During the jackknife procedure, a statistic estimate is calculated leaving out one observation at a time from the sample set. Similar to the bootstrap method, the statistic of an estimate for the bias can be calculated from the population of the repeated calculations.

Facies of LJE-bearing successions and C-isotope values

We focus here on two archetypal LJE-bearing successions: the Franceville Basin, Gabon, and the Karelia (Onega Basin)–Kola (Pechenga–Imandra Varzuga Belts) regions, Russia. These have been studied extensively by many workers including ourselves, the former by Préat et al. (2011) , Canfield et al. (2013) , Ossa Ossa et al. (2018) and Bakakas Mayika et al. (2020) and the latter by Galimov et al. (1968) , Yudovich et al. (1990) . Akhmedov et al. (1993) , Karhu (1993) and Tikhomirova and Makarikhin (1993) and via the International Continental Scientific Drilling Program's Fennoscandia–Arctic Russia Deep Early Earth Project (FAR-DEEP; Melezhik et al. 2013 a ). Because exposure is poor in both regions, building sedimentological and stratigraphic frameworks relies on drill core to supplement outcrop-based observations. As examples, we highlight the Onega Parametric Hole and FAR-DEEP cores in the Onega Basin and LST12 core from the Lastoursville area of the Franceville Basin. These cores are representative of the sedimentology and stratigraphy common to LJE-bearing successions in those regions and, incidentally, to many other LJE-bearing localities elsewhere.

In both the Franceville and Onega Basins the LJE-bearing successions begin with interbedded pale grey to pink dolostone and red–brown–grey mudstone and dolomarl containing variable proportions of shallow-water sedimentary structures including stromatolites, evaporite fabrics and (palaeo)karst, tidal couplets and cross-bedded grainstones, and ripple and herring-bone cross-lamination replete with reactivation surfaces and mud drapes ( Fig. 2 ). These facies occur in units many tens to several hundreds of metres thick and pass upward into very fine dolostone, dolomarl, mudstone and shale in units many tens of metres thick marked by sets of planar- to wavy-parallel laminae with small ripples, in places hummocky cross-stratification, and millimetre- to centimetre-thick graded beds and rhythmite ( Fig. 3 ); colours vary from grey to black excepting one 10–30 m thick unit in the Onega Basin that is cream–pink–green in colour (more on this unit below). The vertical facies successions in both basins offer clear sedimentological evidence for a transition from nearshore-marine–intertidal and in places coastal sabkha settings for the pink–grey dolostone interval into open and deeper marine settings (i.e. depths near or below storm-wave base) for the overlying fine dolostone–dolomarl–mudstone interval. This interpretation is in general agreement with all previous workers (e.g. Brasier et al. 2011 ; Préat et al. 2011 ; Melezhik et al. 2013 b ; Ossa Ossa et al. 2018 ; Bakakas Mayika et al. 2020 ) and permits us to recognize three main palaeoenvironmental clusters: intertidal and in places sabkha settings, nearshore-marine–inner shelf settings, and open and deeper marine settings.

The LJE-bearing successions in the Franceville Basin and Karelia–Kola regions share another trait; they display an overall declining stratigraphic trend in δ 13 C carb values from c. +6–10‰ in the coastal–nearshore-marine intervals to 0–5‰ in the overlying open- and deeper-marine intervals. In the consensus model, this trend is interpreted as recording the termination of the LJE (e.g. Melezhik et al. 2007 ; Canfield et al. 2013 ; Ossa Ossa et al. 2018 ). A salient observation, though, is that this trend coincides with facies changes such that C-isotope values correlate directly with palaeoenvironment ( Table 1 ; Fig. 4a ): the mean value for coastal intertidal–sabkha facies is +9.3 ± 1.7‰, for nearshore marine–inner shelf facies it is +6.8 ± 1.5‰ and for open- and deeper-marine facies it is +2.0 ± 2.1‰. Thus, the high δ 13 C carb values that define the LJE in the Karelia–Kola and Francevillian successions are an expression of facies; they are present in nearshore-marine–coastal–sabkha settings but minor in open- and deeper-marine settings. The question that arises is: is it merely a coincidence that facies changes and the trend of δ 13 C carb values are synchronized in those regions?

Assessing the LJE globally

Golovkinsky–Walther's Law is a fundamental guiding principle in stratigraphy. First articulated in the mid-1800s by Nikolai Golovkinsky working in the Perm district of Russia ( Nurgalieva et al. 2007 ) and later independently by Johannes Walther working in the Austrian Alps ( Walther 1894) , it states that in a vertical succession of strata unbroken by significant hiatal surfaces, rocks layered one on top of the other were deposited in coeval, laterally adjacent environments. Given that C-isotope values and facies changes co-vary in the Francevillian and Karelia–Kola LJE-bearing successions, it is important to assess if the trend in δ 13 C carb in those successions can be attributed to original environmental isotopic gradients now superposed stratigraphically, as per Golovkinsky–Walther's Law, rather than recording global ocean DIC as per the consensus view.

To determine this, we expanded our analysis to encompass published data for LJE-bearing rocks worldwide and focused on studies in which authors provided sufficient sedimentological details to enable assigning their facies interpretations and δ 13 C carb data into our palaeoenvironmental categories of intertidal–coastal–sabkha, nearshore marine–inner shelf, and open- and deeper-marine. Strikingly, even though δ 13 C carb values in the worldwide dataset range between c. −10‰ and c. +26‰, for the entire 200–300 million year duration of the LJE there is a strong co-dependence between facies changes and δ 13 C carb values ( Table 1 , Fig. 4b ): the mean value for the open-marine realm was +1.5 ± 2.4‰, for the nearshore-marine–inner shelf +6.2 ± 2.0‰ and for intertidal–sabkha settings +8.1 ± 3.8‰. To place the LJE in context, we extended our analyses further to include marine carbonate rocks from 3.0 to 1.0 Ga, and also from times of major Phanerozoic evaporite deposits (Permo-Triassic, Messinian, modern sabkhas), given that LJE-bearing successions can contain variable amounts of evaporite pseudomorphs. This analysis shows that δ 13 C carb values of open- and deeper-marine carbonate rocks for all assessed time periods, including LJE-bearing successions, were consistently within 0 ± 4‰ and comparable to that for the modern open ocean DIC reservoir ( Fig. 4c ). The data confirm that the uniquely highly positive δ 13 C carb values of the LJE are themselves facies dependent, found dominantly in nearshore-marine and coastal settings and mostly absent in open- and deeper-marine settings. Hence, these highly positive δ 13 C carb values are not representative of either the global DIC pool or the operation of the global carbon cycle.

The significance of high C-isotope values occurring in deeper-water facies

In a few LJE-bearing successions (e.g. Tulomozero–Zaonega Formation; Silverton Formation, South Africa; Frauenstein et al. 2009 ) high δ 13 C carb values are known for rocks interpreted as recording more open- and deeper-marine settings. We have first-hand knowledge of one of those and offer it as both an exemplar and explanation for such occurrences (see Fig. 5 ). In the Onega Basin, the upper part of the LJE-bearing Tulomozero Formation consists of sabkha and shallow-marine evaporite–fabric-bearing dolostone and mudstone ( Brasier et al. 2011 ; Melezhik et al. 2013 b ) with δ 13 C carb between +6 and 12‰. Above these rocks is a several tens-of-metres thick unit consisting of centimetre- to decimetre-thick beds of grey to dark grey dolostone–dolomarl–mudstone with δ 13 C carb from +3 to 5‰, overlain by cream–pink–green fine dolostone–dolomarl marked by δ 13 C carb between +6 and 9‰ (these dolostones are termed krivozerite by Russian workers) and then a return to grey–dark grey dolostone–dolomarl–mudstone in which δ 13 C carb declines to 0‰. This interval passes upward into organic-rich and pyritiferous deep-marine mudstones of the Zaonega Formation (e.g. Črne et al. 2013 , 2014 ; Kreistmann et al. 2019 ; Paiste et al. 2020 ).

Assessed within the construct of conventional thinking about the LJE, such a fluctuating C-isotope pattern is taken as evidence of oscillating productivity–oxygenation episodes (e.g. Bekker and Holland 2012 ). However, there is a more likely, albeit less grand, explanation. Detailed petrography, mineralogy and sedimentology by Črne et al. (2014) showed that many carbonate beds in the lower part of the Zaonega Formation were resedimented (e.g. Fig. 3e ), emplaced by turbidity currents inferred to have originated from laterally adjacent shallower settings of the Tulomozero Formation. Such an interpretation is consistent with evidence for erosion and transport of carbonate detritus as per the abundance of cross-bedded doloarenite and dolorudite in the Tulomozero rocks (e.g. Fig. 2i ). Applying Occam's razor, the episodic return of high δ 13 C carb values in the deeper-water lower Zaonega Formation represents sediment derived from the 13 C-rich shallow-water Tulomozero Formation intermixed with carbonate of the open- and deeper-marine DIC pool with its ‘normal’ C-isotopic composition. We propose that other postulated open- and deeper-marine units with very positive δ 13 C carb values (e.g. Silverton Formation) may also reflect redeposition of 13 C-rich carbonate transported from adjacent shallower environments.

The LJE: a new understanding

Our analyses reveal that the highest-amplitude, longest-lived deviation from what is considered to be ‘normal’ C-cycle functioning over the past four billion years is tied directly to facies changes. Everywhere during the 200–300 million year duration of the LJE, the C-isotopic composition of facies recording open- and deeper-marine conditions remained ‘normal’ whereas those deposited in nearshore–coastal realms sustained 13 C-enriched isotopic compositions. Thus, the canonical image of the LJE as a high-amplitude C-isotope bulge punctuating an otherwise undisturbed c. two billion year continuum of relatively normal marine C-isotope values is misleading ( Fig. 6 ). Instead, our findings show that the C-isotope pattern of the LJE is a record of contemporaneous lateral gradients in the isotopic composition of DIC pools, ranging from normal open-marine values of c. 0‰ δ 13 C carb to extremely high values of +16‰ and even higher, in nearshore-marine–coastal settings. Stated simply, trends of C-isotope profiles in LJE-bearing successions are a consequence of Golovkinsky–Walther's Law, i.e. strata superposed during sedimentation occurring concurrently during lateral migration of coeval depositional environments characterized by distinct local DIC pools. We thus conclude that the δ 13 C carb trends do not record a global-scale perturbation of the carbon cycle, nor can they be used to infer a worldwide C-isotopic composition of marine DIC. In these aspects, the LJE is not a singularity in that the link between facies changes and positive δ 13 C carb excursions marked by sustained values of +5–10‰ and locally higher for stratigraphically significant intervals is known from other times in Earth history. Studies combining careful sedimentology and petrography with isotope geochemistry show that co-variation between facies and δ 13 C carb values is common and can modify global signals; examples include the Cryogenian Tayshir Member of the Tsagaan Oloom Formation in Mongolia ( Macdonald et al. 2009 ; Bold et al. 2016 ) and Etina Formation in Australia ( Rose et al. 2012 ), Ediacaran Hüttenberg Formation in Namibia ( Cui et al. 2018 ), end-Ordovician Hirnantian strata ( Jones et al. 2020 ) and Silurian Ireviken and Lau Events in the Baltic Basin ( Wigforss-Lange 1999 ; Rose et al. 2019 ). Studies of C-isotope process-response in recent and modern depositional environments provide additional credence to our scenario that the LJE is a record of lateral isotopic gradients of contemporaneous DIC pools. Those studies show shallow-marine settings may have 2–5‰ or more variability in δ 13 C carb relative to that of the open ocean (e.g. Swart 2008 ; Geyman and Maloof 2019 ). These findings are apropos to the LJE, consistent with and substantiating interconnectedness between facies changes and δ 13 C carb values. It is worth noting that, although exceptionally high δ 13 C carb values (>15‰) are known for some LJE-bearing strata, the number of such values total 24 out of the 2038 values we amassed (i.e., c. 1% of the data) making them more a curiosity than a norm, much like modern environments where carbonates form with δ 13 C carb in excess of +15‰ (e.g. Birgel et al. 2015 ).

Neither the modern nor ancient examples, though, explain why nearshore-marine and coastal settings during the LJE reached such high enrichments in 13 C. For this, we do not yet have an answer and at this time prefer not to offer speculative scenarios. We highlight, however, that many LJE-bearing successions are shallow-marine carbonate rocks associated with evaporitic and sabkha-like features. Evaporation pond brines are known to have δ 13 C values of +8–16‰ and brine-evaporation experiments have generated values of +16–35‰ ( Stiller et al. 1985 ), that overlap those of the LJE. Thus, modern and ancient examples hint of the possibility of a yet undetermined process-response link between C-isotope composition, evaporation and microbial ecosystems to create conditions for widespread 13 C-enrichment in shallow-marine environments during mid-Paleoproterozoic time.

The LJE and Earth's oxygenation: summary and conclusions

Our analysis integrating 14 943 δ 13 C carb measurements with sedimentology for marine carbonate rocks 3.0–1.0 Ga in age and, including appropriate Phanerozoic deposits, reveals that 13 C enrichment during the 200–300 Myr span of the LJE was restricted to specific environments: δ 13 C carb values from nearshore-marine and coastal–sabkha settings yield means of 6.2 ± 2.0‰ and 8.1 ± 3.8‰, respectively. In contrast, carbonate sediments deposited in open- and deeper-marine settings are marked by δ 13 C carb values averaging 1.5 ± 2.4‰, consistent with the mean C-isotope composition of oceans throughout most of geological time. These results indicate that high δ 13 C carb values, the hallmark feature of the LJE, archive locally heterogeneous C-isotopic composition of contemporaneous DIC pools of coeval depositional settings. Our findings necessitate rethinking of models that rely on the LJE as a proxy for the global carbon cycle and atmospheric oxygen levels and highlight an unresolved question: why, during the middle part of the Paleoproterozoic Era, did coastal–nearshore-marine and evaporite settings acquire such high 13 C-enriched values?

Acknowledgments

We thank the Institute of Geology, Karelian Research Centre of the Russian Academy of Sciences, Petrozavodsk, Russia, and the Department of Geology, Université des Sciences et Techniques de Masuku, Franceville, Gabon, for their hospitality and help in accessing drill cores and outcrops. We thank E. Stüeken and J. Raven for insightful comments that improved earlier versions of this manuscript, and D. Fike and A. Brasier for reviews. We also thank G. Shields for providing raw data compiled originally for Shields and Vezier (2002) .

Author contributions

ARP : conceptualization (equal), investigation (equal), writing – original draft (equal), writing – review & editing (equal); KK : conceptualization (equal), investigation (equal), writing – original draft (equal), writing – review & editing (equal); AL : conceptualization (equal), investigation (equal), writing – original draft (equal), writing – review & editing (equal); AEF : conceptualization (equal), writing – original draft (equal), writing – review & editing (equal); TK : conceptualization (equal), investigation (equal), writing – original draft (equal), writing – review & editing (equal); YED : conceptualization (equal), investigation (equal); AER : conceptualization (equal), investigation (equal); DVR : conceptualization (equal), investigation (equal); PVM : conceptualization (equal), investigation (equal), writing – original draft (equal); MM : conceptualization (equal), investigation (equal); KB : conceptualization (equal), investigation (equal); MSWH : writing – original draft (equal), writing – review & editing (equal)

K.K., A.L. and T.K. received funding from Estonian Science Agency Project PRG447 and Yu.D., A.R., D.R. and P.M. were supported by the state assignment of the Institute of Geology, Karelian Research Centre of the Russian Academy of Sciences.

Data availability

The datasets generated during and/or analysed during the current study are available in the Supplementary material included with this manuscript.

Scientific editing by Heda Agic

Data & Figures

Generalized map of Paleoproterozoic outcrop belts. Circled numbers indicate those successions utilized in this study. See Supplementary material for data and data sources.

Coastal–evaporitic–nearshore-marine facies in Lomagundi–Jatuli Event (LJE)-bearing strata of the Onega (a–c, e, f, h, k–m) and Franceville (d, g, i, j) Basins. ( a ) Stromatolites. ( b ) Tepee in red–grey mudstone with evaporite pseudomorphs. ( c ) Evaporite pseudomorph in red–grey mudstone. ( d ). Tepee developed on palaeokarst breccia and eroded by overlying dolostone grainstone. ( e ). Poorly sorted coarse doloarenite and mudstone overlain by disrupted red–brown mudstone with abundant chicken wire fabric. ( f )–( h ) Micritic dolostone broken and disrupted by variably developed palaeokarst and evaporite pseudomorph fabrics. ( i ), ( j ) Cross-bedded doloarenite. ( k ) Herringbone cross-lamination with mud drapes. ( l ) Tidal couplets of graded fine doloarenite and red–grey mudstone–dolomarl. ( m ) Tidal bundle of fine doloarenite and grey dolomarl and mudstone with abundant millimetre-scale gypsum pseudomorph needles overlain by dolorudite. Scale bars c. 2 cm.

Open- and deeper-marine facies of LJE-bearing strata in Franceville (a–d) and Onega (e–g) basins. ( a ) Low-angle laminated graded fine doloarenite beds overlain by flake–breccia debrite (coin c. 2 cm). ( b ) Dark grey to black shale (outcrop c. 5 m in height; contact with dolostone of 3a at base of ledge); pale colours represent deeply weathered intervals. ( c ), ( d ) Thin graded beds of fine dolostone with sets of low-angle plane- to wavy-parallel laminae. ( e )–( g ) Grey and cream–pink–green fine dolostone (‘krivozerite’) in millimetre- to centimetre-thick graded beds marked by millimetre-scale ripples and plane- to wavy-parallel laminae; arrows in 3e denote individual graded beds. Scale bars c. 2 cm.

Box-and-whisker plots for δ 13 C carb data classified by palaeoenvironmental setting. ( a ) Data for the Francevillian and Karelia–Kola regions. ( b ) LJE data worldwide. ( c ) Timeline trend of palaeoenvironmental settings from Neoarchaean through to specific Phanerozoic time periods (Rec, Recent; Mess, Messinian; Perm, Permian; Trias, Triassic). See Supplementary material for C-isotope data.

C-isotope profile of Tulomozero and lower part of Zaonega Formations, Onega Basin. OPH, Onega Parametric Hole; R-S, Raiguba and Shunga localities. See Supplementary material for C-isotope data.

δ 13 C carb data for marine carbonate rocks between 3.0 and 1.0 Ga in age in 100 Myr age bins (see Supplementary material for sources of data). ( a ) LJE-bearing successions are in red and those recording the purported decline of the LJE in light red; running bootstrap average shown as a blue line. ( b ) 2D density plot that shows the abundance and consistency of δ 13 C carb values between 0 and 4‰ across the entire 2 Gyr time span. ( c ). The lower panel shows the consensus view of a direct one-to-one match between the LJE and postulated rise in atmospheric p O 2 (PAL: present atmospheric level; adapted after Lyons et al. 2014 ). The upper panel shows the new understanding of the LJE excursion as a consequence of palaeoenvironmental setting (consensus view is shown by dashed outline). The light-grey bar highlights the LJE. Deeply negative δ 13 C carb values that post-date the LJE have been shown in two studies of the Onega Basin rocks to reflect post-depositional overprinting or methane recycling ( Črne et al. 2014 ; Kreistmann et al. 2019 , 2020 ).

Summary δ 13 C carb data for Lomagundi–Jatuli Event successions (N = number of measurements; C.I. = confidence interval). See Supplementary material for data and data sources

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Shuram Excursion

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The Shuram excursion represents the greatest negative carbon isotopic excursion in earth history, and provides an important chemostratigraphic marker horizon of global extent. The excursion is linked to the second great oxygenation event in earth history, an oxygen crisis that resulted in a transition from sulfidic oceans to a marine realm rich in sulfate. The Shuram excursion (560–550 Ma) is represented in Sonora, México by the Clemente oolite of the Clemente Formation. Ediacaran fossils (such as the Clemente biota of Unit 4 of the Clemente Formation) occur in rocks deposited below the excursion. The age of the Clemente Ediacaran biota thus falls between 550 and 560 Ma. In spite of the fact that the Sturtian glaciation apparently triggered the earliest known mass extinction on earth (the Tindir Mass Extinction ), several lines of evidence suggest that the biosphere controlled the timing of and the onset of the Late Proterozoic glaciations, and that it also controlled the timing of the melting of the ice. Furthermore, it appears that the biosphere itself influenced the timing of the appearance of the Ediacaran biota. Whereas snowball earth events lurched suddenly from very cold (tillites) to very hot (cap carbonates) climate, the sequence going from the Gaskiers glacial event ( c. 580 million years ago) to the Shuram was part of a wild climatic gyration where the earth went from hot (intense granite weathering at high latitudes) to cold (Gaskiers glaciation) to hot (Shuram event). The Shuram is the greatest negative carbon isotopic excursion in earth history, possibly because this is the moment in earth history when the burrowing animals assert themselves in a geochemical sense, and by remobilizing sea floor carbon, forestall a major glaciation.

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McMenamin, M.A.S. (2018). Shuram Excursion. In: Deep Time Analysis. Springer Geology. Springer, Cham. https://doi.org/10.1007/978-3-319-74256-4_2

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The Ediacaran Shuram Excursion - new research published in Nature.

24 January 2022

This research investigates organic-rich shales deposited in South China during the late Ediacaran Period (ca. 560-551 Ma) and provides an exceptional opportunity to understand the evolution of the paleoenvironmental conditions during this period.

Picture footnote: Modern global primary productivity levels. The production of photosynthetic organic matter increases and decreases coinciding with major Earth system processes. Copyright ©: Ocean Colour CCI, Plymouth Marine Laboratory/ESA. 

Interestingly, the most negative carbon isotope excursion in Earth history, known as the Shuram excursion, is recorded in these deposits. Results obtained from carbon and nitrogen isotopes, together with Raman structural heterogeneities observed in the organic matter, described a dynamic environmental scenario where a new equilibrium in the C and N cycles was established. In this new scenario, high levels of primary production of organic matter produced a change from heterotrophic to autotrophic metabolic dominance, which became the main source of organic matter in sediments and modulated the recovery of the Shuram excursion to pre-excursion values.

Dr Fuencisla Cañadas  writes about her esearch:

“ My research includes early Earth paleoenvironmental reconstructions to understand the interplay between major environmental changes and biological evolution. I seek to constrain the environmental conditions required for life to emerge and evolve, and its applicability and astrobiological implications on other terrestrial planets, like Mars.

Currently, I’m a Marie Curie postdoctoral fellow at the Centre for Astrobiology (Spain) working on the MaPLE (Mars Phosphorus and Life) project which investigates the P and Fe cycles evolution and nutrient availability during the Mesoarchean (~ 3 Ga) in a carbonate and iron-rich environment. This environment is used as analogue for the Jezero crater, in Mars, where the rover Perseverance, from the NASA Mars 2020 mission, searches for signs of ancient life.

Could carbonates on early Mars have accumulated enough dissolved P to become favourable environments for the emergence and evolution of life? I hope to answer this question soon!

• Extensive primary production promoted the recovery of the Ediacaran Shuram excursion. Cañadas, F., Papineau, D., Leng, M.J. et al. Nature Commun 13, 148 (2022). DOI
• Dr Fuencisla Cañadas PhD profile , lead author of the study completed her study at UCL under the supervision of Dr D. Papineau. 
• Dr Dominic Papineau's academic profile

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James Eguchi, Charles W Diamond, Timothy W Lyons, Proterozoic supercontinent break-up as a driver for oxygenation events and subsequent carbon isotope excursions, PNAS Nexus , Volume 1, Issue 2, May 2022, pgac036, https://doi.org/10.1093/pnasnexus/pgac036

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Oxygen and carbon are 2 elements critical for life on Earth. Earth's most dramatic oxygenation events and carbon isotope excursions (CIE) occurred during the Proterozoic, including the Paleoproterozoic Great Oxidation Event and the associated Lomagundi CIE, the Neoproterozoic Oxygenation event, and the Shuram negative CIE during the late Neoproterozoic. A specific pattern of a long-lived positive CIE followed by a negative CIE is observed in association with oxygenation events during the Paleo- and Neo-proterozoic. We present results from a carbon cycle model designed to couple the surface and interior cycling of carbon that reproduce this pattern. The model assumes organic carbon resides in the mantle longer than carbonate, leading to systematic temporal variations in the δ 13 C of volcanic CO 2 emissions. When the model is perturbed by periods of enhanced continental weathering, increased amounts of carbonate and organic carbon are buried. Increased deposition of organic carbon allows O 2 accumulation, while positive CIEs are driven by rapid release of subducted carbonate-derived CO 2 at arcs. The subsequent negative CIEs are driven by the delayed release of organic C-derived CO 2 at ocean islands. Our model reproduces the sequences observed in the Paleo- and Neo-proterozoic, that is oxygenation accompanied by a positive CIE followed by a negative CIE. Periods of enhanced weathering correspond temporally to supercontinent break-up, suggesting an important connection between global tectonics and the evolution of oxygen and carbon on Earth.

The Proterozoic hosts Earth's most dramatic oxygenation events and CIEs. Using a geochemical model that considers the links between the Earth's surface and interior carbon cycles, we demonstrate that systematic changes in δ 13 C of volcanic outgassing can reproduce the major CIEs of marine carbonates for nearly the entirety of Earth history, while also capturing the broad trends of atmospheric oxygen evolution. Systematic changes in δ 13 C of volcanic outgassing are the result of longer mantle residence times of graphitized organic carbon compared to carbonate. Timings of model perturbations correspond to supercontinent break-ups, which suggests that supercontinent break-ups are major drivers of atmospheric oxygenation and subsequent positive and negative CIEs.

Carbon and oxygen play critical roles in the story life on Earth. The cycling of these 2 elements is intimately linked through oxygenic photosynthesis and aerobic respiration. These links are evident in the geologic record, particularly during the Proterozoic. The Paleoproterozoic hosts the Great Oxidation Event ( 1–3 ) and the associated Lomagundi carbon isotope excursion (CIE) ( 4 ) (Figure  1a ), while the Neoproterozoic hosts the Neoproterozoic Oxygenation Event ( 5–7 ) with an associated broad positive CIE ( 8 ) (Figure  1a and  b ). The association between changing atmospheric oxygen and the carbon isotope record is a result of oxygenic photosynthesis and the burial of organic matter ( 9 , 10 ). Free oxygen accumulates in the atmosphere when organic carbon is produced during oxygenic photosynthesis and subsequently buried, which precludes oxygen consumption through aerobic respiration. Organic C produced during oxygenic photosynthesis is depleted in 13 C, leaving the global reservoir from which marine carbonates precipitate enriched in 13 C. Therefore, when the ratio of carbon buried as organic C relative to inorganic carbonate ( f org ) increases, atmospheric oxygen levels increase, and δ 13 C values of marine carbonates (δ 13 C carb ) increase concomitantly. This biological link between oxygen and carbon, 2 elements essential to Earth's habitability, has led to speculation on the mechanisms controlling their evolutionary history ( 9–11 ).

Carbon isotope record for marine carbonates with major CIEs described in the text. (a) Compilation of δ 13 C carb for Archean to present (from 8 ). (b) Compilation of δ 13 C carb for Neoproterozoic (from 74 ) showing the broad positive CIE punctuated by negative CIEs.

In addition to extreme positive CIEs, the Proterozoic also hosts some of the largest negative CIEs in the geologic record ( 12 ). According to the conventional view of the carbon cycle, decreased f org can cause negative CIEs. However, the extreme magnitude of some Proterozoic negative CIEs, such as the Ediacaran Shuram anomaly, reach δ 13 C carb of ∼ −15‰ ( 13 ) (Figure  1b ), making them difficult to explain using the conventional mechanisms of changing f org . To explain these extremes for Proterozoic negative CIEs, authors have invoked perturbations to the global carbon cycle that are not seen on the modern Earth, such as the large-scale oxidation of reduced forms of carbon—dissolved organic matter and methane in particular ( 14–16 ). Another suggestion is that Proterozoic negative CIEs could be the result of authigenic carbonate production, acting either at the local or global scale ( 17 , 18 ). Other researchers have questioned the primary nature of large negative CIEs and propose that they are the result of local alteration during burial ( 19 ), or that they record local shallow water processes rather than large changes to the global carbon cycle ( 20 ).

Due to their temporal association with critical points of biological evolution ( 13 ), it is important to understand if extreme negative CIEs, such as the Shuram, are primary signals in the δ 13 C record. An argument against a primary origin for these large negative CIEs is that they are inconsistent with the way the modern C cycle behaves and, therefore, require extreme perturbations to the ocean–atmosphere C cycle ( 14–16 ). If the main input of CO 2 into the ocean–atmosphere system, volcanic CO 2 outgassing, is constant at ∼ −5 ‰, it becomes difficult for modern global carbon cycle processes to shift δ 13 C carb to values as low as ∼ −15 ‰ ( 21 , 22 ). However, the assumption that the δ 13 C of global volcanic CO 2 (δ 13 C volc ) emissions has remained constant at ∼ −5 ‰ throughout Earth history may be incorrect ( 11 , 23 , 24 ). Large quantities of surficial C are subducted into the Earth's interior, and much of that subducted C is recycled back to the surface through volcanism ( 25–27 ). We know that δ 13 C of surficial C reservoirs have changed through time (Figure  1 ), therefore, it may be reasonable to assume that δ 13 C volc , which is likely to be heavily influenced by subducted surficial C ( 26 , 28 ), has also changed through time. We also note that differential weathering of continentally derived carbonates and organic C has the potential to change the δ 13 C of C entering the ocean. However, oxygen levels may act to regulate the relative weathering fluxes of the 2 continental C reservoirs, thus acting as a feedback that effectively prevents weathering of continentally derived C from driving long-lived CIEs in marine carbonates ( 29 ). If correct, we are left with volcanic outgassing as the primary flux capable of altering the isotopic composition of C entering the ocean–atmosphere system. Here, we employ a novel carbon cycle model that accounts for variations in δ 13 C volc to test whether they can explain the positive and negative CIEs of the Proterozoic, thereby providing a new mechanism for the extreme CIEs of the Proterozoic as primary signals of perturbations to the global C cycle.

Following enhanced burial of C on the seafloor, some fraction of carbonate and organic matter will be subducted into the mantle, while the remainder will be deposited on continental shelves and become part of the continental inventory through continental collision and uplift. How we treat carbonate and organic C in the mantle, and specifically their assumed distinct behaviors, is a novel aspect of our model. Central to our results, the model assumes that organic C has a longer residence time in the mantle than carbonate. Under subarc conditions, inorganic carbonate is more easily transported out of the slab, as compared to graphitized organic C, due to its higher solubility in fluids and melts ( 24 , 26 , 32 , 33 ). This behavior has been observed in subducted lithologies, which show evidence for significant carbonate loss, while retaining significant amounts of graphitized organic C ( 34 ). Therefore, the CO 2 emitted at arc volcanoes is likely to be preferentially sourced from subducted carbonates compared to organic C. The possibility of preferential carbonate release at arc volcanoes may be supported by the observation that on a global scale, the flux-weighted mean of δ 13 C volc at arc volcanoes is ≈ −3 ‰ ( 23 ), which is heavier than δ 13 C volc at mid-ocean ridges, which are thought to be dominated by primordial mantle C.

Subducted carbonates may be recycled back to the surface via arc volcanism on timescales of tens of millions of years ( 35 ). Therefore, some tens of millions of years after the increased burial of carbonate and organic matter at the surface, there will be increased outgassing of carbonate-derived CO 2 at arc volcanoes, thus tipping the balance of surface inputs toward returning carbonate C to the surface and away from returning organic C. In our model, this step initiates the rising limb of a positive CIE. Release of subducted carbonate C, although a fundamentally different process, is analogous to carbonate platform weathering, which similarly returns carbonate C to the system and has been invoked as a mechanism for driving the Late Ordovician positive CIE ( 36 ).

After carbonate C is released at subarc depths, the subducting slab will be enriched in organic C relative to inorganic (carbonate) C as it descends deeper into the mantle. Low δ 13 C values recorded in eclogitic diamonds may provide evidence for the deep subduction and retention of low δ 13 C values in subducted organic C ( 37 ). The slab may then become entrained in upwelling mantle plumes and melt as it nears the surface, releasing organic C-derived CO 2 at plume-fed volcanoes, such as ocean island centers. Although the isotopic composition of CO 2 emitted at ocean islands remains poorly constrained, there are suggestions that CO 2 in samples from the Pitcairn hotspot may be isotopically light compared to mid-ocean ridges ( 38 ). Additionally, a recent study on kimberlites, which may be derived from mantle plumes similar to ocean island basalts, showed that δ 13 C in many Phanerozoic examples exhibit low values, which the authors attribute to subducted organic C ( 39 ). The model assumes that organic C is released on the order of hundreds of millions of years after subduction, corresponding to the timescale of convective overturn in the mantle ( 24 , 40 ). Radiogenic isotopes have also been used to suggest that crustal recycling at Mauna Loa occurs on the order of 200–650 million years ( 41 ). It follows that the enhanced flux of subducted organic C will be released at ocean island volcanoes on the order of hundreds of millions of years after the initial C burial event at the surface, and the release of organic C-derived CO 2 will decrease δ 13 C volc , abruptly terminating the long-lived positive CIE and driving the negative CIE.

In sum, in response to a strengthened silicate weathering feedback, the model predicts atmospheric oxygenation driven by enhanced burial of organic matter contemporaneously with increased carbonate burial. This trigger and the corresponding impacts on the carbon cycle are associated with the onset of a long-lived positive CIE due to the preferential release of carbonate C at arcs. Isotopically heavy carbonates will continue to be deposited and subducted until the initial pulse of subducted organic matter is returned to the surficial system at ocean islands, terminating the positive CIE and driving a negative CIE. In the following section, we investigate whether the model can reproduce the series of oxygenation events and CIEs of the Proterozoic.

The Proterozoic begins with the Great Oxidation event and associated Lomagundi positive CIE (Figure  1a and  b ) ( 3 ), which are directly followed by the Shunga negative CIE ( 42–44 ) (Figure  1b ). This sequence of events is identical to the generic model scenario described above. To generate the model run shown in Figure  2 , the only parameters that change are k , which accounts for the strength of the silicate weathering feedback, and χ, which controls the fraction of buried carbon that is subducted into the mantle. We note that f org remains at 0.20 for each model run, so all CIEs in the simulations result solely from changes in δ 13 C volc . At 2.4 Ga, we prescribe an instantaneous increase in k , followed by a linear decay over a time span dictated by tectonic cycles (described below; Figure  2e ). The increase in k is coupled with an immediate transition to a higher value of χ that persists for the duration of increased k (Figure  2e ). This combination simulates increased continental weathering accompanied by a rapid shift in the location of C deposition from dominantly on continental shelves to dominantly on oceanic crust. The rationale behind our decisions to increase k and χ will be discussed below. This perturbation causes an initial spike in the weathering flux, increasing the size of the crustal and mantle reservoirs of organic C, which increases atmospheric O 2 (Figure  2b – d ). Oxygen increases initially, but decays when organic C is released as CO 2 at ocean islands (Figure  2b and  c ). Release of organic C-derived CO 2 at ocean islands decreases atmospheric O 2 in the model because we assume that every mole of organic C that is oxidized and degassed as CO 2 leads to the consumption of 1 mole of O 2. The reduction of chemical species (likely Fe) results from the oxidation of organic C to CO 2 . This reduced chemical species will be erupted in association with ocean island basalts, along with the CO 2 , and will consume atmospheric O 2 when oxidized. This process is analogous to aerobic respiration in terms of the net consequences and has been previously recognized in C cycle redox models ( 45 ). The modeled perturbation of increased k and χ predicts increased organic C and carbonated deposition across the Archean–Proterozoic boundary (Figure  2d ). Consistent with this suggestion, a transition from very little marine carbonate precipitation in the Archean to appreciable amounts in the Proterozoic (Figure  2d ) has been identified in a recent compilation of carbonate formations through time ( 46 ). Increased depositional fluxes of organic C across the Archean–Proterozoic boundary has also been recognized in the continental sedimentary record ( 47 ).

Model results for atmospheric oxygen and δ 13 C of marine carbonates compared with natural data. (a) δ 13 C of marine carbonates and volcanic centers versus time. Blue data points are natural data from Krissansen-Totton et al. ( 8 ). Orange curve is model result for carbonates, red and green curves are modeled δ 13 C for arcs and ocean islands, respectively. (b) Atmospheric oxygen level (PAL) through time. Pink curve and blue-shaded region is proposed evolution of atmospheric oxygen based on various proxies ( 7 ). See ( 7 ) for detailed explanation of proxy curve. Orange curve is model result with oxidative weathering of crustal organic C and green-dashed curve is model result without oxidative weathering of crustal organic C. Orange downward pointing arrows with question marks were included to illustrate possible lower levels of O 2 if a complete consideration of oxygen sinks was included. (c) Modeled C fluxes from different volcanic settings and the C drawdown flux from atmosphere driven by silicate weathering. (d) Modeled C reservoirs through time. (e) Prescribed values of k (strength of silicate weathering feedback through time) and χ (fraction of buried C that is subducted) through time. k and χ are the drivers of all perturbations in the model. (f) Blue curve is covariance times the slope of δ 18 O-εHf in zircons from Keller et al. ( 53 ). Peaks in this curve are suggested to signal periods of enhanced subduction of continental weathering products. Orange curve is estimated continental sediment flux through time from Husson and Peters ( 56 ). (g) Frequency of zircons through time from Tang et al. ( 60 ) and times of supercontinent break-up and assembly from Condie and Aster ( 49 ).

A few tens of millions of years after the initial increase in k and χ, the arc CO 2 flux and δ 13 C arc increase, causing δ 13 C volc and in turn δ 13 C carb to rise (Figure  2a and  c ). Over the next few hundred million years, the arc CO 2 flux decays, so that by the time the increased flux of organic C is released at ocean islands, the ocean island CO 2 flux with low δ 13 C (Figure  2a ) dominates global volcanic CO 2 inputs (Figure  2c ). This progression leads to a rapid decrease in δ 13 C volc and a relatively abrupt transition from a positive CIE to a negative CIE (Figure  2a ).

Following the CIEs in the Paleoproterozoic, δ 13 C carb is relatively stable until around 1.4 Ga ( 8 ) (Figure  2a ), marked by the initiation of a broad positive CIE that persists until the Ediacaran (Figure  2a ). In the model, the duration of positive CIEs is controlled by the residence time of organic C in the mantle ( 24 ). The broad positive CIE at the end of the Proterozoic is significantly longer than the Lomagundi CIE, lasting close to ∼ 1 Gyrs (Figure  2a ). Therefore, unless mantle convection slowed significantly, it may be difficult to explain the events at the end of the Proterozoic via the same mechanism invoked for the Paleoproterozoic. However, this broad positive CIE in the late Proterozoic is not consistently positive but instead is punctuated by excursions to near-zero and sometimes negative δ 13 C values (Figure  2a ). Here, we test whether prescribing 2 discrete events during the second half of the Proterozoic can reproduce the observed late Proterozoic pattern. Below, we discuss how supercontinent cycles may trigger the enhanced continental weathering events required in the model to reproduce the observed series of oxygenation events and CIEs, and why the event in the Neoproterozoic may be a composite of 2 distinct events rather than 1.

To test the idea that the broad positive CIE at the end of the Proterozoic is a composite event, we prescribe the first of 2 increases in k and χ at 1.4 Ga (Figure  2e ). The prescribed increase in k is relatively small, so the model predicts correspondingly small CIEs and a small increase in atmospheric oxygen (Figure    2b ), which may be consistent with a proposed transient oxygenation event in the Mesoproterozoic ( 48 ). We prescribe a second and larger increase in k and χ at ∼800 Ma (Figure  2e ). The increased k and χ cause a spike in the burial flux of both carbonate and organic C (via weathering; Figure  2c ), leading to a second major step in atmospheric O 2 levels (Figure  2b ). The possibility of significantly increased atmospheric O 2 at 800 Ma is reviewed in Lyons et al. ( 7 ). This rise in O 2 is accompanied by a continuation of the broad positive CIE that lasts until around 550 Ma, when it is terminated by an extremely negative CIE (Figure  2a ) corresponding in the model to a spike in the ocean island CO 2 flux (Figure  2c ). The negative CIE, represented in the geologic record by the Ediacaran Shuram anomaly, is relatively short-lived and recovers rapidly and stabilizes at near-zero values (Figure  2a ). Thus, we see a repeat of the sequence of an oxygenation event closely accompanied by a positive CIE terminated by a negative CIE. The prescribed increases in k and χ at 800 Ma brings modeled oxygen levels to a peak of ∼ 0.5 present atmospheric level (PAL) by ∼550 Ma (Figure  2b ). We emphasize that the purpose of the model is not to closely reproduce atmospheric O 2 levels (especially in the Phanerozoic), but rather to broadly reproduce the increases in atmospheric O 2 that coincide with positive CIEs followed by negative CIEs. However, to illustrate that our model is not drastically inconsistent with present day O 2 levels of 1 PAL, we increase k into the Phanerozoic, so that modeled O 2 levels reach ∼1 PAL (Figure  2b and  e ). Due to low χ after 550 Ma (Figure  2e ), the modeled increase in Phanerozoic C burial occurs mostly on the continents and, therefore, exerts little effect on modeled δ 13 C (Figure  2a ).

We acknowledge that the prescribed changes in k are large (Figure  2e ); however, they may coincide with extreme events that may have drastically affected silicate weathering. Caves et al. ( 30 ) found that k may have varied by as much as a factor of 3 during the Cenozoic, which was likely tectonically quiescent compared to the supercontinent break-ups ( 49 ) and proposed rapid emergence of continents from the oceans ( 50–52 ) that helped define the Paleoproterozoic and Neoproterozoic. Additionally, proposed proxies for recycling of continental weathering products show extreme signals during the Paleoproterozoic and Neoproterozoic when compared to the Cenozoic ( 53 ) (Figure  2f ). Therefore, we argue that the changes in k and χ prescribed here may not be unreasonable and are supported by the geologic record (Figure  2f ). We emphasize that the sole driver of all oxygenation events and CIEs in the present model were changes to k and χ, and the resulting systematic variations in δ 13 C volc ; f org was held constant at 0.20 throughout the model run. This approach is an obvious oversimplification, but it highlights the fact that the long-term, first-order trends of the δ 13 C carb record can be reproduced by systematic changes in δ 13 C volc without any changes to the fraction of carbon buried as organic matter.

It is striking that with only simple assumptions about differential residence times of carbonate and organic C in the mantle ( 24 ) and prescription of 3 discrete weathering events (Figure  2e ), the model reproduces the broad trends of δ 13 C carb and major CIEs (Figure  2a ) for nearly the entirety of Earth history. Additionally, the model does a reasonable job of capturing the major trends in oxygenation and associated O 2 events suggested by proxy data ( 7 ) (Figure  2b ). However, we note that this is not intended to be an accurate model for atmospheric O 2 and may overestimate O 2 levels during the Proterozoic because it does not account for pyrite oxidation, nor does it account for the oxidation of reduced metamorphic and volcanic gases, all of which have been demonstrated to be important in regulating atmospheric oxygen levels ( 54 , 55 ). To illustrate the potential effects oxygen sinks may have on the model, we plot model runs with and without a simple formulation for the oxidative weathering of organic C ( 55 ) (Figure  2b ). Figure  2(b) shows that the inclusion of organic C weathering predicts lower O 2 levels. Therefore, a more complete consideration of oxygen sinks should be considered but is beyond the scope of the current work.

Despite some differences in magnitudes, the general agreement of our modeled δ 13 C carb and O 2 with the geologic record motivates us to ask whether there is justification for these 3 prescribed changes to k and χ in the model, and indeed there is. Figure  2(e) and (f) shows that the 3 discrete weathering events prescribed in the model coincide with increases in the covariance of zircon δ 18 O-εHf, which have been attributed to enhanced subduction of continental weathering products ( 53 ). The peaks in the zircon δ 18 O-εHf are followed by peaks in the continental sediment flux, with the delay between the 2 records being more evident for the Neoproterozoic when a better continental record is preserved ( 53 , 56 ) (Figure  2f ). The delay between zircon δ 18 O-εHf and the continental sediment flux record may reflect a shift in the dominant location of marine sedimentation from oceanic crust, where it can be subducted to produce a peak in the δ 18 O-εHf data, to continental shelves where it can be preserved ( 53 , 56 ). This shift is reflected in our model by increasing χ along with k at the initiation of an enhanced weathering event and keeping it elevated until the enhanced weathering ends (Figure  2e ). This sequence of events is potentially consistent with what would be expected during the breakup of a supercontinent as discussed below.

Supercontinent cycling has previously been proposed as a potential control on continental weathering and atmospheric oxygen ( 10 , 57–59 ). For example, Campbell and Allen ( 57 ) proposed supercontinent formation and accompanying mountain uplift as the main driver of major CO 2 drawdown and oxygenation events. Here, we invoke supercontinent break-up as the major driver because all 3 of our proposed weathering events appear to initiate in phase with troughs in the zircon frequency record ( 60 ), which have been ascribed to supercontinent break-up (Figure  2g ) ( 49 ).

There are several reasons that supercontinent break-up can lead to enhanced carbonate and organic C deposition and subduction. First, the initial stages of supercontinent break-up are often associated with the eruption of large volumes of basaltic lavas ( 61–64 ), which are highly weatherable ( 65 ) and can increase global fluxes of cations and nutrients to the ocean, stimulating carbonate precipitation and organic C burial. Eruptions of basalts will also be accompanied by the outgassing of large amounts CO 2 , which can also increase continental weathering fluxes, stimulating carbon burial and subsequent CO 2 drawdown ( 66 ) (Figure  3 ). Sea level is likely to be low during initial stages of supercontinent break-up due to dynamic uplift of supercontinents driven by arrival of mantle plumes ( 67 , 68 ), which will allow sediments to bypass continental shelves and be deposited on oceanic crust where they can be subducted (Figure  3 ). The intense CO 2 drawdown caused by initial stages of supercontinent rifting have also been proposed to be possible drivers of global glaciation ( 69 ), which can further lower sea level, exposing continental shelves and allowing for the large amounts of sediments derived from continental denudation to be deposited on oceanic crust where they can be subducted ( 53 ). In fact, the zircon δ 18 O-εHf data have been suggested to reflect extreme sediment subduction fluxes as a result of global glaciation ( 53 ). Therefore, we envision the initial stages of supercontinent break-up to increase C burial fluxes and for most of that burial to occur on oceanic crust where sediment will be subducted ( 53 ) (Figure  3 ), as simulated by our model perturbations of increased k accompanied by increased in χ (Figure  2e ).

Schematic diagram showing how supercontinent break-up can increase continental weathering and C deposition. Early stage of supercontinent break-up is associated with dynamic uplift and lowered sea level due to the presence of a mantle plume. Eruption of basalts increase continental weathering due to CO 2 emissions and weatherability of basalts. Lowered sea level allows the location of C burial to be dominated by oceanic crust, which will be subducted. Late stage of supercontinent break-up will generate rifted margins, which are primary environments for C burial. Late stage of supercontinent break-up will also have higher sea level due to cessation of the mantle plume. This will flood continental shelves, allowing the location of C burial to be dominated by continental shelves.

As supercontinent break-up reaches later stages, greater continental fragmentation increases the length of continental margins, thus increasing the global area of nearshore environments ( 70 ), which are the primary loci for both carbonate and organic C deposition ( 71 ) (Figure  3 ). Later stages of supercontinent break-up will generate new rifted basins, which are efficient traps for sediment and can favor large-scale C burial along continental margins. Additionally, smaller and more dispersed continents, in contrast to a supercontinent, have continental interiors that are closer to oceanic sources for precipitation, increasing continental area exposed to rainfall, thus increasing global continental weathering fluxes, leading to enhanced carbon burial ( 72 ). As the mantle plumes that drive the initial stages of supercontinent break-up subside and glaciers melt, sea level will rise ( 67 ), flooding continental margins, allowing sedimentation to shift from oceanic crust to continental shelves (Figure  3 ). Therefore, in the later stages of supercontinent break-up following the cessation of global glaciation, enhanced C burial is more likely to be accommodated in environments that become part of the continental reservoir ( 56 , 73 ). Figure  2(f) shows that the continental sediment accumulation rate transitions from decreasing with time to increasing with time during supercontinent break-ups ( 56 ). However, as noted above, the peak in the subduction flux (zircon δ 18 O-εHf data) ( 53 ) occurs prior to the peak in the continental sediment flux ( 47 ) (Figure  2a ), suggesting that initial stages of supercontinent break-up, and perhaps accompanying global glaciation, favor sedimentation on oceanic crust, while later stages of supercontinent break-up favor C burial on continental shelves ( 53 , 56 , 73 ) (Figure  3 ). In the model, this sequence is simulated by a transition to lower χ at the later stage of increased k (Figure  2e ). Therefore, we propose that supercontinent break-up drives enhanced weathering and C burial, with early stages of break-up favoring C subduction, while later stages favor C accumulation on continents. The initial stages of enhanced subduction of C drive CIEs through changes in δ 13 C volc driven by the differential mantle cycling of carbonates and organic C, while later stages of C accumulation on continents serve to stabilize O 2 levels ( 56 ).

The Proterozoic witnessed dramatic transitions in surface chemistry, biology, and tectonics. Our results suggest that major supercontinent break-up may have played a key role multiple times in the biogeochemical evolution of Earth with predictable and repeatable consequences that can be recorded in the geologic record as enhanced continental weathering resulting from supercontinent break-up, increased atmospheric oxygen through organic C burial, and a subsequent positive CIE followed by a negative CIE driven by variable residence times of carbonate and organic C in the mantle. We acknowledge that the primary nature of extreme negative CIEs, such as the Shunga in the Paleoproterozoic and the Shuram in the Neoproterozoic, is still highly debated, and that our study cannot speak to the voracity of the δ 13 C data. However, this study may aid in the debate by providing a previously unrecognized, predictable mechanism by which extreme negative CIEs can be explained as a systematic global shift in δ 13 C volc rather than secondary alteration. We also emphasize that the present model, despite including only an extremely simplified surface C cycle (see Materials and Methods), still captures the first-order long-term trends in atmospheric oxygen and δ 13 C carb . It does this by including the deep C cycle and specific differences in the cycling of carbonate and organic C following subduction. Thus, important messages in this contribution are that deep Earth processes play a vital role in mediating the surficial carbon cycle, and it is critical to consider the coupling between the surface and deep C cycles when investigating the long-term evolution of carbon and oxygen on Earth.

Modeling atmospheric oxygen levels and δ 13 C of carbonates

We used the carbon cycle model from Eguchi et al. ( 24 ), which tracks how a set of carbon reservoirs (C i ) respond to changes in carbon fluxes ( F i ) among these reservoirs. The surface reservoirs are the atmosphere–ocean (C atm ), inorganic carbonates (C carb ), and organic carbon (C org ; the model treats the ocean and atmosphere as a single reservoir). The transfer of carbon from the atmosphere–ocean reservoir into the carbonate and organic carbon reservoirs is controlled by a silicate weathering flux ( F w , which comprises F carb and F org ). This flux is proportional to a constant for the strength of the silicate weathering feedback ( k ) and the amount of CO 2 in the atmosphere–ocean (C atm ). Carbon that is fluxed out of the atmosphere–ocean is deposited as either inorganic carbonate or organic carbon. To demonstrate that a CIE is possible without changing f org , we hold f org constant at 0.20 throughout the model. To investigate whether the model can reproduce the proposed lower levels of atmospheric O 2 during the Proterozoic, we add an oxidative weathering term ( F ow ) from Bergman et al. ( 55 ), which depends on a weathering constant ( k ow ) and a term for uplift (U).

The model has 3 different mantle reservoirs for C—primordial carbon (C prm ), subducted carbonate (C mcarb ), and subducted organic carbon (C morg ). Primordial carbon, which existed in the mantle since Earth's accretion, receives no addition from subduction and is emitted at mid-ocean ridges ( F MORB ). Subducted carbonates and organic C have influxes from the surface through subduction ( F subc and F subo ). Subducted carbon is released from mantle reservoirs via arc volcanoes ( F arc ) and ocean island volcanoes ( F OIB ). Carbon fluxes at arcs and ocean island volcanoes are a sum of C fluxes from the primitive mantle ( F arcp and F OIBp ), subducted carbonates ( F arcc and F OIBc ), and subducted organic C ( F arco and F OIBo ). We prescribe variables to control the fraction of subducted carbonates (α carb ) and organic carbon (α org ) released at arc volcanoes, as well as variables to control the fraction of subducted carbonates (ε carb ) and organic carbon (ε org ) released at ocean islands. Eguchi et al. ( 24 ) found that C in carbonates is more efficiently released during subarc melting, while graphitized organic C is relatively refractory. Therefore, we treated carbonates as being completely released at arcs (α carb = 1 and ε carb = 0) and organic carbon as being completed released at ocean island volcanoes (α org = 0 and ε org = 1) when generating Figure 2 [see Figures S1–S7 (Supplementary Material) for model sensitivity to changes in these parameters].

A key feature of the model is the treatment of mantle residence times for the 2 forms of carbon. Subducted carbon released at arc volcanoes (predominantly inorganic carbonate) would have traveled on the order of hundreds of kilometers, while subducted carbon (predominantly graphitized organic C) released at ocean islands may have traveled to the deep mantle or core/mantle boundary on pathways of around 10,000 km before being re-emitted to the surface ( 24 ). If mantle convection occurs on the order of 1–10 cm/yr, subducted carbon will be released at arc volcanoes roughly 1–10 Myr after being subducted, while subducted carbon released at ocean island volcanoes will be released approximately 100–1,000 Myr after initial subduction. To account for these differences, we prescribe a timescale variable that controls how long subducted specific carbon pools remain in their respective mantle reservoir before being released at either arc volcanoes (τ arc ) or ocean island volcanoes (τ OIB ). By implementing these variables, the carbon emitted at arcs is proportional to the flux of carbon subducted τ arc years ago, while carbon emitted at ocean island volcanoes is proportional to the flux of carbon subducted τ OIB years ago. Additionally, the carbon emitted at arc volcanoes will have δ 13 C values influenced by inorganic (carbonate) C subducted τ arc years ago, while the carbon emitted at ocean island volcanoes will have δ 13 C influenced organic C subducted τ OIB years ago. This approach differs from traditional box models, in that it does not result in efficient mixing between carbon subducted at different times. Instead, it treats carbon cycling as something closer to a conveyor belt, where parcels of subducted lithologies retain the carbon inventory and δ 13 C signature they had at the time of their initial subduction rather than mixing with the entire mantle reservoir ( Figure S9 , Supplementary Material). This approach may be a better representation of what is occurring in nature because portions of the subducted slab that were recently subducted are spatially restricted from portions of the slab subducted much longer ago, and due to these spatial restrictions efficient mixing and equilibration seems unlikely ( Figure S9 , Supplementary Material). Finally, the total volcanic CO 2 outgassing flux |${\rm{(}}{{\rm{F}}_{{\rm{out}}}})$| is a sum of the fluxes at arc volcanoes, ocean island volcanoes, and mid-ocean ridge volcanoes, and atmospheric oxygen levels are directly proportional to the mass of organic carbon accumulated in all surface and mantle reservoirs.

The model run used to generate Figure  1 was designed to simulate increased strength of the silicate weathering feedback coupled with a shift to high fractions of C subduction (high χ). Figure S8 (Supplementary Material) illustrates how driving perturbations via changes in k differ from perturbations driving by changes in CO 2 emissions. To simulate this scenario, the model was run with the initial conditions and parameters given in Table S1 (Supplementary Material). After evolving with no perturbations for 2.5 billion years, we prescribed that k instantaneously increased from 1 × 10 −9 to 2 × 10 −3 at 2.4 Ga (Figure  2e ). We then prescribe that k linearly decays to 1 × 10 −5 over a duration of 350 Ma. Coincident with the period on increased k , we increase χ from 0.1 to 0.99 to simulate a shift from continent-dominated sedimentation to ocean-dominated sedimentation and subduction. All subsequent increases in k are accompanied by the same increase in χ. To reproduce the relatively minor oxygenation and CIEs occurring in the Mesoproterozoic, we prescribe that k instantaneously increased from 1 × 10 −5 to 2 × 10 −4 at 1.4 Ga. We then prescribe that k linearly decays to 2 × 10 −5 over a duration of 300 Ma. Finally, to reproduce the major oxygenation and CIEs of the Neoproterozoic, we prescribe that k instantaneously increased from 2 × 10 −5 to 9 × 10 −4 at 0.8 Ga. We then prescribe that k linearly decays to 7 × 10 −5 over a duration of 200 Ma. At this point O 2 levels are at ∼0.6 PAL. Therefore, we increase k to 1.2 × 10 −3 linearly over a timescale of 100 Ma. The timescales of k decay are of same order of magnitude as Wilson cycle timescales, which we have assumed are controlling changes in the strength silicate weathering feedback. Sensitivity analysis shows that model results are relatively insensitive to changes in this parameter (see Figure S6 , Supplementary Material). To better match the estimated duration of the different positive CIEs based on independent age models for the rock record, we also make minor changes to τ OIB along with perturbations to k . Specifically, at 1.4 Ga, we change τ OIB to 310 My, and at 0.8 Ga, we change τ OIB to 230 My. We feel these minor changes to τ OIB are justified because they lie well within the estimated range of mantle overturn times based on plate speeds of 1–10 cm/yr, as well as estimates of recycling times based on radiogenic isotopes ( 41 ). These minor variations in τ OIB may reflect minor variations in rates of mantle convection and travel paths of subducted lithologies. These are the only prescribed model perturbations to generate Figure  1 of the main text.

Code for model will be uploaded to corresponding author's github.

The authors thank James Kasting and Shanan Peters for their constructive comments, which greatly improved the manuscript.

J.E. acknowledges support by an appointment to the NASA Postdoctoral Program through the Astrobiology Institute administered by the Universities Space Research Association and Oak Ridge Associated Universities under contract with NASA. This research was also supported by the NASA Alternative Earths Astrobiology Institute under Cooperative Agreement No. NNA15BB03A issued through the Science Mission Directorate and the NASA Interdisciplinary Consortia for Astrobiology Research (ICAR) Program.

J.E. conceived the project and ran the model simulations. All authors refined the model in the context of geological observations. All authors contributed to the writing of the manuscript.

Model code used to generate Figure  2 are available on Github ( https://github.com/jameseguchi/Eguchi_et_al_2022 ).

Competing Interest: The authors declare no competing interest.

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