It is unclear why atmospheric oxygen remained trapped at low levels for more than 1.5 billion years following the Paleoproterozoic Great Oxidation Event. Here, we use models for erosion, weathering and biogeochemical cycling to show that this can be explained by the tectonic recycling of previously accumulated sedimentary organic carbon, combined with the oxygen sensitivity of oxidative weathering. Our results indicate a strong negative feedback regime when atmospheric oxygen concentration is of order pO2∼0.1 PAL (present atmospheric level), but that stability is lost at pO2<0.01 PAL. Within these limits, the carbonate carbon isotope (δ13C) record becomes insensitive to changes in organic carbon burial rate, due to counterbalancing changes in the weathering of isotopically light organic carbon. This can explain the lack of secular trend in the Precambrian δ13C record, and reopens the possibility that increased biological productivity and resultant organic carbon burial drove the Great Oxidation Event.
Atmospheric oxygen (pO2) rose from <10−5 present atmospheric level (PAL) at the Great Oxidation Event, as constrained by the disappearance of mass-independent fractionation of sulfur isotopes1 (MIF-S) ∼2.45–2.32 Ga. Oxygen levels were sufficient to oxygenate some deep ocean basins2,3 and deposit gypsum4,5 during the ‘Lomagundi’ carbon isotope excursion2,3,4,5,6,7 ∼2.22–2.06 Ga. Subsequently, paleosol oxidation state8 at ∼1.85 Ga and ∼1.1 Ga indicates pO2>0.01 PAL, the absence of detrital pyrite and uraninite after ∼2.1 Ga suggests9 pO2>0.05 PAL, and redox proxies of widespread deep ocean anoxia suggest pO2<0.5 PAL (assuming present ocean nutrient levels) until at least the latest Neoproterozoic10 and probably the mid-Palaeozoic Era11,12,13. Transient Proterozoic pO2 excursions cannot be ruled out by sparse data, and it has recently been suggested from a lack of chromium isotope fractionation in iron-rich sedimentary rocks14 that pO2<0.001 PAL during 1.8–0.8 Ga. This challenges previous inferences10,15,16,17 that Proterozoic pO2 was ∼0.01–0.1 PAL, themselves based on models of paleosol oxidation8 and of benthic sulfide oxidation18 that can be questioned. It is in turn challenged by subsequent work inferring pO2>0.04 PAL at ∼1.4 Ga from a lack of vanadium retention in marine sediments19,20,21, and work showing chromium isotope fractionation in carbonates ∼1.1 Ga onwards22. Atmospheric oxygen eventually approached modern levels6,11 during ∼0.6–0.4 Ga, with the first compelling evidence for pO2≥0.6 PAL from the appearance of Palaeozoic fossil charcoal23 at ∼0.4 Ga. Thus, despite uncertainty about the precise levels, it is clear that atmospheric oxygen was somehow trapped at much lower levels than today for >1.5 Gyr following the Great Oxidation Event.
Identifying the mechanisms responsible for stabilizing oxygen well below present levels poses an outstanding puzzle24,25,26,27. In particular, the residence time of atmospheric oxygen (∼8 Myr at pO2∼1 PAL), is short relative to geological timescales. Hence, to explain the long-term stability of pO2 requires negative feedback operating on the oxygen source(s) and/or sink(s). In the Phanerozoic, the major oxygen source is organic carbon burial (derived from oxygenic photosynthesis) and the largest sink is oxidative weathering of uplifted sedimentary organic carbon (kerogen). Models for Phanerozoic oxygen regulation11,28 tend to focus on strong negative feedbacks on organic carbon burial29 (that is, that the production rate of oxygen decreases as oxygen rises), and any negative feedback on oxidative weathering is estimated to be relatively weak30,31 (or non-existent28,32). This is because near modern pO2 (∼1 PAL), uplifted organic carbon is completely oxidized in slowly eroding soil environments32, meaning oxidative weathering is transport-controlled by the supply of reduced material, rather than kinetically controlled by the pO2 level. However, at high erosion rates, oxidative weathering is incomplete and detrital kerogen is preserved in marine sediments33,34,35, meaning that the global oxidative weathering flux is somewhat sensitive to pO2 variations even at the present day30,31. Here, we argue that the balance of mechanisms that regulated atmospheric oxygen at much lower Proterozoic levels was quite different, and that incomplete oxidative weathering played a key role. Furthermore, we show that this mechanism makes the carbonate carbon isotope (δ13C) record insensitive to changes in organic carbon burial rate, thus explaining the lack of secular trend in the Precambrian δ13C record.
Sedimentary reduced matter cycling
Our model for the regulation of atmospheric oxygen at low Proterozoic levels hinges on an explicit consideration of the accumulation and tectonic recycling of sedimentary reduced matter over Earth history (Fig. 1). Importantly, the recycling of sedimentary rocks through erosion, sedimentation and uplift, is quantitatively greater than their conversion by metamorphism, with a ratio of bulk rock fluxes for the modern Earth36 of ∼3.5:1 (Fig. 1a). Estimates of the potential sink of oxygen from oxidative weathering (based on the organic carbon, total sulfur and total iron content of sediments) are much larger than the sink from oxidizing volcanic/metamorphic reduced gases (Table 1).
In the modern oxygenated environment (Fig. 1d), much of the sedimentary organic carbon that is uplifted is oxidized32, with the remainder returning to the sediments as ‘detrital’ organic carbon37 (indicated by the thin looped black arrow going from and to the sediments in Fig. 1d). Thus today, organic carbon burial (and corresponding oxygen production) is balanced mostly by oxidative weathering of sedimentary organic carbon (∼3.75 × 1012 mol yr−1) with a smaller contribution (∼1.25 × 1012 mol yr−1) from oxidation of reduced metamorphic and volcanic gases11,38 (and an uncertain but potentially comparable contribution from oxidation of thermogenic methane; Table 1, addressed below). Oxidation of sulfides and ferrous iron in sediments and the upper crust are smaller sinks at present, because less than half of the sedimentary iron and sulfur are in reduced form.
Prior to the Great Oxidation Event under pO2<10−5 PAL (Fig. 1b), the oxidation of reduced sedimentary organic carbon would have been negligible, with oxygen stabilized instead by the oxygen sensitivity of reactions with reduced gases. Hence, reduced sediments would have been recycled repeatedly until they were deeply buried and metamorphosed. The size of the sedimentary organic carbon reservoir would then have been determined by the balance between input from the burial of newly generated organic carbon, and output via metamorphism. Given the relatively low rate of metamorphic conversion, even a modest rate of ‘new’ organic carbon burial would have allowed a large sedimentary organic carbon reservoir to accumulate during the Archaean6,39.
After the Great Oxidation Event (Fig. 1c), the rise of atmospheric oxygen would have enabled the oxidative weathering of uplifted sediments. We assume by this time the majority of organic carbon was produced by oxygenic photosynthesis. The Great Oxidation Event itself was triggered by a secular evolution from net reduced to net oxidized atmospheric inputs27,40,41,42. Therefore, the oxygen source required to trigger it need only have been slightly greater than the supply of reduced gases to the atmosphere and only a fraction of the tectonic supply of reductant in uplifted sediment. In this regime, redox balance requires that oxidative weathering of uplifted sediment is incomplete (limited by global oxygen supply), and the atmospheric oxygen level is determined by the land-surface integrated oxygen-sensitive kinetics of oxidative weathering.
Atmospheric oxygen in the aftermath of the Great Oxidation Event should therefore have been stabilized by the oxygen sensitivity of oxidative weathering. The resulting oxygen level and negative feedback strength would have depended on the kinetics of oxidative weathering at low pO2, which are determined by oxygen transport and reaction in soils and regolith, integrated over the continental surface. To quantify this, we used an existing reaction-transport model32,43 for oxidative weathering of organic carbon and pyrite and ran it repeatedly to span the wide range of erosion rates observed across the continental surface today44 (see ‘Methods’ section). Then we obtained a global oxidative weathering flux by weighting these results by the observed fractional areal contributions of different erosion rates across the continental surface44.
The results (Fig. 2) show that organic carbon (kerogen) is completely oxidized at pO2=1 PAL for low and intermediate erosion rates, but is incompletely oxidized at the highest erosion rates today; 50 cm kyr−1 (dominated by large islands of the Western Pacific) and 25 cm kyr−1 (dominated by the Himalayas) (Fig. 2a, see ‘Methods’ section). This is consistent with observations of detrital organic carbon from these regions reaching marine sediments34,35. It confirms that there is a negative feedback dependence of oxygen removal on pO2 near ∼1 PAL, but it is fairly weak.
As pO2 declines, the oxidative weathering flux declines and becomes more sensitive to pO2 variations, because oxidative weathering becomes kinetically-limited in a wider range of regions with progressively lower erosion rates (Fig. 2a,b). Initially, this amounts to a strengthening of the negative feedback on pO2. At pO2∼0.1 PAL, there is still a significant oxidative weathering flux which is a strong function of oxygen concentration (Fig. 2a,b), giving the potential to provide strong negative feedback on pO2. However, as pO2 declines further, below pO2 ∼0.03 PAL, although oxidative weathering remains sensitive to pO2 the potential negative feedback becomes weaker as this sink becomes relatively small (Fig. 2b). Overall a dependency of oxidative weathering on pO20.5 (Fig. 2a, dashed line), consistent with coal oxidation kinetics45 and as assumed in some previous biogeochemical models11,25, provides a reasonable fit to the results.
We performed a sensitivity analysis increasing shale oxygen diffusivity (controlled by porosity) and removing the contributions of high-uplift regions to global sediment discharge rates (see ‘Methods’ section). This can weaken the sensitivity of the global oxidative weathering flux to oxygen variation near pO2=1 PAL and shifts the region of strong negative feedback to somewhat lower pO2.
The relative strength of the oxidative weathering feedback is determined by its size relative to other sinks (Table 1), especially atmospheric sinks, which would have been insensitive to pO2 at levels after the Great Oxidation Event40,42 (Fig. 2b). Including the additional sink from metamorphic/volcanic reduced gases demonstrates the dependence of pO2 on organic carbon burial rate (Fig. 3). Here, we first consider parameterizations for the modern Earth and a minimum estimate for atmospheric reductant inputs. Assuming negligible burial of terrestrial organic matter in the Proterozoic, which comprises ∼50% of total burial today11,13,46, and assuming modern ocean nutrient levels, marine organic carbon burial could have been comparable to the modern level of ∼2.5 × 1012 mol C yr−1. Combining this with minimum estimates for volcanic and metamorphic inputs, the model predicts pO2 ∼0.1 PAL (Fig. 3a) with oxygen stabilized by the negative feedback from oxidative weathering. Varying the distribution of continental erosion rates between plausible limits then causes pO2 to vary by a factor of ∼2, with low global erosion and/or increased shale porosity, and therefore more complete oxidation, producing lower pO2 (Fig. 3a). Varying organic carbon burial can cause larger variations in pO2 within the same stable state. However, if organic carbon burial drops below ∼25% of present (∼1.25 × 1012 mol C yr−1), corresponding to pO2<0.01 PAL, this state loses stability and a ‘Great Deoxygenation’ is predicted, because the oxygen source to the atmosphere is insufficient to counterbalance the volcanic input of reduced matter. Conversely, an increase in organic carbon burial from lower values to >25% of present is sufficient to trigger the Great Oxidation Event in the model, as the net biological source of oxygen exceeds the volcanic input of reduced matter.
This means that to increase atmospheric oxygen toward modern levels (∼1 PAL) requires a factor of ∼4 larger increase in organic carbon burial flux than needed for the Great Oxidation Event (Fig. 3a). This second transition is not as abrupt, but still represents a fundamental change in oxygen regulation regime, in which reductant burial exceeds the reductant supply via sediment recycling and the predominant negative feedback control shifts from the oxygen sink to the oxygen source.
A major uncertainty in atmospheric reductant input is the contribution of thermogenic methane from organic carbon metamorphism (Table 1). If this is assumed to be controlled by overall sedimentary organic carbon content independent of organic carbon burial rate, then this provides a large additional oxygen-independent sink (Fig. 3b, blue line), reducing the relative strength of the oxidative-weathering feedback. However, thermogenic methane is more plausibly linked to a low temperature metamorphic pathway primarily associated with relatively recently buried organic carbon (age ≲100 Myr, but longer than the oxygen residence time of ∼10 Myr). In this case it scales with the organic carbon burial rate and hence has a greatly reduced influence in the Precambrian (Fig. 3b, black line), although it still reduces the stability domain of Proterozoic pO2 with respect to short-timescale perturbations (green line).
Secular changes in tectonic (and solar) forcing will modify this picture40. As an illustrative case, an ‘episodic continental growth’ model47 assumes 80% of present continental area at 2.5 Ga, and predicts global heat flux Q∼1.5 of present, and ocean crust formation rate and high-temperature hydrothermal heat loss scaling with Q2∼2.25 of present. Metamorphic fluxes plausibly scale proportional to global heat flux (Q) and continental area, hence would be ∼1.2 of present (increasing both chemical weathering of phosphorus hence oxygen source, and reductant input hence oxygen sink). Mantle inputs scale as Q2 increasing both CO2 input and the seafloor hydrothermal oxygen sink (primarily serpentinisation in the low-sulfate Precambrian48). The overall sign of the combined effect on oxygen level will therefore be model-dependent.
Effects on the carbon isotope record
Our proposed mechanism for Proterozoic oxygen regulation changes the interpretation of the Precambrian carbonate carbon isotope (δ13Ccarb) record. Conventionally the constancy of δ13Ccarb is taken to imply a constant ‘f-ratio’ of ‘new’ organic to inorganic carbon burial49,50,51. However, in an oxidative-weathering-limited regime, persistent changes in organic carbon burial result in large counterbalancing changes in oxidative weathering of organic carbon (via changes in pO2). The detail of the transient adjustment process and return to steady-state for an arbitrary decrease (and later increase) in organic carbon burial is illustrated in Fig. 4. Initially there is a drop in δ13Ccarb as oxidative weathering exceeds organic carbon burial. However, after ∼10 Myr, atmospheric oxygen and oxidative weathering decrease to a new steady state, leaving δ13Ccarb unchanged from its initial value, with both the net input and output fluxes of δ13C to/from the ocean isotopically heavier than they were (because isotopically-light organic carbon input and output fluxes have declined relative to isotopically heavier inorganic carbon fluxes). Similarly, an increase in organic carbon burial results in a transient increase in δ13Ccarb and return to its initial value.
The long-term steady-state isotopic composition of the ocean and δ13Ccarb is therefore independent of the burial rate of ‘new’ organic carbon (Fig. 5a), as oxygen level adjusts such that net input and output fluxes of δ13C to/from the ocean are equal39. Hence, long-term changes in ‘new’ organic carbon burial during the Proterozoic are not expected to show up in the carbon isotope record. Sedimentary recycling of organic carbon during the Archaean and Proterozoic can thus help reconcile increases in oxygen, and presumed associated increases in biological productivity, with the lack of a secular trend in δ13Ccarb until the Phanerozoic17 (where there is a shift from 0 to 2‰ associated with the rise of land plants13). As long as the erosion rate is unchanged, changes in new organic carbon burial change the relative proportion of detrital and new organic carbon being buried (Fig. 5b).
As our focus is on oxygen regulation after the Great Oxidation Event (rather than long-term controls on organic carbon accumulation) we have assumed that the Proterozoic rock cycle was in overall redox balance51 (as in Phanerozoic carbon cycle models including GEOCARB38 and COPSE11). We have also assumed that atmosphere-ocean reduced input flux is dominated by that from metamorphic sedimentary volatiles, as for the modern Earth. Higher inputs of reductant relative to today—either due to higher mantle fluxes52, ongoing crustal oxidation during metamorphism hence more reduced metamorphic fluxes40 or greater submarine volcanism resulting in more reduced volatiles53—would affect the stability of an oxygen-sink-controlled feedback regime. However, we suggest these increased reductant inputs had largely declined by the Great Oxidation Event or at latest the end of the Lomagundi excursion. For example, assuming crust oxidation (resulting in a present Fe3+ excess54 of ≈2 × 1021 mol O2 eq) is linked to continental growth, an ‘episodic continental growth’ model55 with rapid growth from 10 to 80% of present area 3.2–2.5 Ga would imply a net oxidation rate of ≈2 × 1012 mol O2 eq yr−1 (balanced by a combination of hydrogen escape and organic carbon accumulation). This would drop after 2.5 Ga to a net oxidation rate of ≈1.6 × 1011 mol O2 eq yr−1, which is small relative to sediment and metamorphic redox transformations (Table 1). However, the iron oxidation state of shales only changes after the Great Oxidation Event, suggesting significant ongoing oxidization of crustal iron6. We have assumed that any increase in oxygen source triggering the Great Oxidation Event was modest, but if the oxygen source increased a lot, for example, in the Lomagundi event, then the oxidative weathering sink might have been temporarily overwhelmed leading to high oxygen levels2,3,4,5,6,7. Either way by ∼1.85 Ga oxygen levels were low again.
Our proposed Proterozoic oxygen regulation mechanism requires that marine organic carbon burial remained at least ∼25% of today’s total organic carbon burial flux after the Great Oxidation Event. Marine-derived organic carbon is estimated to comprise half11,13 to two-thirds56 of today’s total organic carbon burial flux (the remainder being derived from land plants). Hence, marine organic carbon burial must have remained at least ∼40–50% of its present value since the Great Oxidation Event. This in turn requires at least ∼40–50% of modern ocean nutrient concentrations, or if they were lower, a more efficient biological carbon pump and/or more efficient sedimentary preservation of organic carbon. Several studies have suggested that nutrient levels were low25 or the biological pump was less efficient57 in the Proterozoic. However, if total organic carbon burial was <25% of present, corresponding to pO2 ∼0.01 PAL, our model predicts a reversal of the Great Oxidation Event, because although the oxidative weathering of ancient organic carbon would have become negligible, the oxygen source to the atmosphere would have been insufficient to counterbalance the volcanic/metamorphic input of reduced matter. Atmospheric oxygen then drops until the oxidation of these gases becomes kinetically-limited (that is, oxygen concentration limited) at pO2<10−5 PAL (Fig. 2b). However, the lack of MIF-S1 after 2.32 Ga constrains pO2>10−5 PAL. Therefore, if recent inferences14 of Proterozoic pO2<0.001 PAL are correct, they require an as yet unidentified oxygen regulating mechanism, which operates somewhere in the range 10−5<pO2<10−2 PAL.
The sulfur cycle could not have provided an equivalent negative feedback on pO2 at lower levels, even though oxidation and subsequent reduction of sulfur were more important fluxes in the Proterozoic surface redox budget than they are today15. This is because the Precambrian sulfur cycle was dominated by a reduced sedimentary reservoir (pyrite), which after surface oxidation in weathering was soon reduced again and buried, whereas the carbon cycle consists of a primarily oxidized reservoir that is available for biotic burial of the reduced form. This burial of reduced carbon is nutrient (rather than carbon) limited whereas the burial of reduced sulfur only requires a redox gradient generated by the much larger carbon export production flux.
The oxidative weathering model predicts that beneath the upper soil layers, the weathering environment was essentially anoxic and reducing for Proterozoic oxygen levels pO2<0.1 PAL (for example, Fig. 6). This has important implications for interpreting redox-sensitive proxies, namely that they are controlled by fluvial transport times and corresponding oxygen exposure9, not by time spent in the weathering environment (as has erroneously been assumed in previous simpler models14,58). For pyrite this means oxidation in soils becomes kinetically-limited at pO2<0.1 PAL (Fig. 2b), starting in the most rapidly eroding terrains, and implying a supply of detrital pyrite to fluvial systems. Existing work9 estimates that for rivers with short transport distances, often found in the most rapidly eroding terrains (for example, on volcanic arc islands), some of this pyrite would survive oxidation at pO2<0.05 PAL. Indeed some detrital pyrite survives oxidation today in the most rapidly eroding settings59. Therefore recent inferences14 of pO2<0.001 PAL appear inconsistent (by orders of magnitude) with the absence of detrital pyrite in Proterozoic sediments. Again, the one-box model behind these very low pO2 inferences14 can be questioned because it assumes that manganese can be oxidized in the weathering environment imparting Cr-isotope fractionation above pO2∼0.001 PAL, when instead the soil is predicted to be anoxic and reducing up to pO2∼0.1 PAL (Fig. 6).
Taking into account the incomplete oxidation of organic carbon under low Proterozoic O2, it appears that the lack of a long-term secular trend in δ13Ccarb until the Phanerozoic17 cannot be taken to imply a constant ‘f-ratio’ of new organic to inorganic carbon burial (as is standard practice49,50,51). Instead there could have been large Precambrian changes in new organic carbon burial that may not show up in long-term δ13Ccarb, reopening the possibility that, for example, the Great Oxidation Event was driven by an increase in new organic carbon burial. The conventional interpretation of the long-term carbon isotope record (in terms of changing proportions of new organic to inorganic carbon burial) is only appropriate in a high oxygen world where oxidative weathering of organic carbon is fairly complete, and therefore the δ13C value of carbon inputs remains fairly stable. Even today there is some compensation of changes in new organic carbon burial and pO2 by corresponding changes in the input of ancient organic carbon with the same isotopic composition.
There are of course long-term (>1 Myr) δ13Ccarb excursions in the Precambrian, notably the Lomagundi event3,5,6,7 (∼2.22–2.06 Ga). This can be explained by redox exchanges with sedimentary sulfur and iron reservoirs, shifting electrons from sedimentary sulfide and siderite to reduced organic carbon (and back again) on the sedimentary recycling timescale6,60. Such δ13Ccarb excursions can also arise from changes in the inorganic carbon cycle or in δ13C fractionation. The carbon isotope decoupling observed in the Neoproterozoic δ13C record61 (where δ13Ccarb varies but δ13Corg is near constant) can, as previously proposed49,61,62, be explained by the recycling of detrital organic carbon. Furthermore, the spatially-variable mixing of detrital and marine sources implies that the δ13Corg signature will be location-dependent.
The mechanism we describe provides a potential explanation for the overall stepwise evolution of atmospheric oxygen on Earth. Recycling of sedimentary organic carbon and its kinetically limited oxidation could have sustained low Proterozoic atmospheric oxygen levels—albeit not as low as has recently been inferred14. The rise of oxygen to present levels simply required an increase in organic carbon burial rate, which may have begun in the Neoproterozoic Era10, but in our model was not completed until the mid-Palaeozoic Era with the colonization of the land by plants and fungi, liberating nutrient phosphorus from rocks and producing high C/P material for burial11,13.
Land-surface oxidative weathering model
Oxidative weathering of organic carbon and pyrite was simulated using an existing 1D reaction-transport model32,43 (Table 2), integrated over the observed distribution of uplift rates estimated from river sediment budgets44.
The 1D shale model represents the steady-state balance between downwards oxygen diffusion in a porous shale and reaction with organic carbon and (optionally) pyrite. It thus quantifies the local transition between a supply-limited regime (where a diffusive oxygen supply exceeds reduced matter supply, a reaction front forms in the shale column, and all supplied reduced matter is consumed), and a kinetic-limited regime where reduced material is incompletely oxidized with the remainder eroded. The model has been calibrated against laboratory measurements constraining local kerogen45 and pyrite32,63 oxidation kinetics, and a field study constraining oxygen transport through porous shale43. The shale model was run repeatedly to span the present-day global distribution of erosion rates across the continental surface44 and the results weighted by the observed fractional areal contributions of these different erosion rates to obtain a global oxidative weathering flux. The estimated total oxidative weathering flux was then scaled to the present day value at pO2=1 PAL.
Model parameters (summarized in Table 2) are taken from the default parameter set of Bolton et al.32 (their Table 1 and Figs 3–5), which generate a reaction front at depth ∼10 m for oxidative weathering of organic carbon at global-mean values for TOC (1 wt%) and erosion rate (5 cm kyr−1) (Fig. 6). For given shale properties (organic matter content, porosity, temperature) the reaction front depth is proportional to atmospheric oxygen level and inversely proportional to supply rate (=erosion rate). If the reaction front reaches the surface, organic matter oxidation is incomplete and detrital organic matter is eroded.
The dependency of the land-surface integrated oxidation rate on pO2 is therefore sensitive to oxygen transport, controlled by shale porosity (n*), and reduced matter supply, controlled by organic carbon and pyrite content and the distribution of uplift rates (Fig. 7). As demonstrated by Bolton et al.32, at pO2∼1 PAL organic carbon is completely oxidized for uplift rates <10 cm kyr−1 and even conservative (low porosity; n*=2) shale parameters. However, integration over a distribution of uplift rates results in a land-surface average with incomplete oxidation in high-uplift regions, which is very different to that of a homogeneous surface with mean uplift rate (∼5 cm kyr−1).
In a sensitivity analysis (Fig. 7) we examined how the oxygen dependence of global organic carbon oxidation varied with removing the contribution to global sediment discharge rates44 of regions with the highest uplift (oceanic islands), or those plus the next highest uplift regions (SE Asia and the Himalayas), and with increasing shale oxygen diffusivity (n*=1.5). These changes were designed to maximize O2 uptake and thus establish a lower limit at which this mechanism could regulate atmospheric O2.
Precambrian COPSE model
We parameterize the COPSE model11 for the Precambrian64 (sufficient to represent the oxygen controls and carbon isotope response discussed in the main text) with the following minimum set of changes from the original model11 to represent a high-CO2 system with no land biota and reduced solar forcing:
The rates of organic carbon burial and oxidation were set as discussed in the main text (organic carbon burial 5 × 1012 mol C yr−1, oxidative weathering 3.75 × 1012 mol C yr−1, metamorphic/volcanic reductant input 1.25 × 1012 mol C yr−1), to be consistent with estimates from sediment erosion rates, with carbon to sulfur ratios, and with arguments for the relative sizes of the organic carbon metamorphic and weathering sinks. Rates are comparable to those in the GEOCARB series of models38 and are reduced by approximately a factor-of-two relative to the original COPSE model11.
The (pO2)1/2 dependency of oxidative weathering on atmospheric oxygen level in the original version of the COPSE model was replaced with the Earth-surface integrated oxidative weathering rate calculated above from the oxidative weathering model, rescaled to give oxidative weathering of koxidw=3.75 × 1012 mol C yr−1 at pO2=1 PAL.
The COPSE land biota (and accompanying weathering enhancement and organic carbon burial) was removed, and solar luminosity was set at 92% of present to generate a steady-state appropriate to 1 Ga, with resulting pCO2 of 26.8 PAL.
A forcing parameter ɛ was added representing the secular evolution of mechanisms (biological or abiotic) enhancing phosphorus weathering and bioavailability, and thus controlling marine organic carbon burial. The anoxia dependence of marine organic C/P burial ratio was also switched on (as in run 2 of the original paper11).
The sulfur cycle was removed, consistent with the assumption discussed in the main text that sulfur was predominantly in reduced form during the Precambrian.
Atmospheric CO2 was made proportional to the square of the total amount of carbon in the ocean and atmosphere. Long-timescale results of interest here are insensitive to the detailed form of this partitioning.
The code for the oxidative weathering model and the code for the Precambrian COPSE model (both in MATLAB) are available from S.J.D. on request (S.Daines@exeter.ac.uk). The authors are in the process of developing a new, release version of the COPSE model, details of which are available from the corresponding author (T.M.L.).
The data that support the findings of this study are the input assumptions of the models (detailed in the ‘Methods’ section) and the model output (shown in the Figures). These are available from S.J.D. (S.Daines@exeter.ac.uk) or the corresponding author (T.M.L.) on request.
How to cite this article: Daines, S. J. et al. Atmospheric oxygen regulation at low Proterozoic levels by incomplete oxidative weathering of sedimentary organic carbon. Nat. Commun. 8, 14379 doi: 10.1038/ncomms14379 (2017).
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This work was supported by the Leverhulme Trust (RPG-2013-106) and the Natural Environment Research Council (NE/N018508/1). We thank Andrey Bekker, Jim Kasting and Tom Laakso for thorough reviews that helped improve the paper.