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).

Figure 1: Schematic of the rock cycle and the evolution of controls on atmospheric oxygen. Arrows show fluxes of rock (brown), organic carbon (black), oxygen (green), and other reduced species (red). Dashed circle shows primary negative feedback control on atmospheric oxygen. (a) Modern rock cycle36 fluxes (1018 ton Gyr−1, ‘Met.’=metamorphism, ‘Ero.’=erosion) and masses (1018ton). (b) Archean: organic carbon burial is balanced by metamorphism, with negligible oxidative weathering. Atmospheric oxygen is a minor component with concentration determined by the oxygen sensitivity of reactions with reduced atmospheric gases. (c) Proterozoic: sedimentary organic carbon is partly oxidized but mainly recycled. Atmospheric oxygen is controlled by the oxygen sensitivity of oxidative weathering. (d) Modern: sedimentary organic carbon is oxidized with little recycling. Atmospheric oxygen is controlled by feedbacks on carbon burial. Full size image

Table 1 Potential oxygen sinks based on modern-day fluxes. Full size table

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 × 1012mol yr−1) with a smaller contribution (∼1.25 × 1012mol 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 pO 2 <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.

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 pO 2 , 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 pO 2 =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 pO 2 near ∼1 PAL, but it is fairly weak.

Figure 2: Sensitivity of atmospheric oxygen sinks to oxygen concentration. (a) Oxidative weathering rate for carbon, from the shale reaction-transport model of Bolton et al.32 integrated over a distribution of land-surface erosion rates44, showing contributions to carbon oxidation from bins for erosion rate (cm kyr−1). Dashed line shows pO 2 0.5 dependency45 assumed in some biogeochemical models11,25. (b) Global integrated oxygen consumption from volcanic reduced gases (blue), sedimentary organic carbon oxidation (green) and sedimentary pyrite oxidation (dashed red). The organic carbon and pyrite results are from the modelling herein, whereas the volcanic reduced gas consumption is a schematic curve to show pO 2 sensitivity at pre-Great Oxidation Event levels (≤10−5 PAL) but not at Proterozoic levels40,42 (hence this process cannot help explain Proterozoic atmospheric oxygen regulation). Full size image

As pO 2 declines, the oxidative weathering flux declines and becomes more sensitive to pO 2 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 pO 2 . At pO 2 ∼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 pO 2 . However, as pO 2 declines further, below pO 2 ∼0.03 PAL, although oxidative weathering remains sensitive to pO 2 the potential negative feedback becomes weaker as this sink becomes relatively small (Fig. 2b). Overall a dependency of oxidative weathering on pO 2 0.5 (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 pO 2 =1 PAL and shifts the region of strong negative feedback to somewhat lower pO 2 .

Oxygen regulation

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 pO 2 at levels after the Great Oxidation Event40,42 (Fig. 2b). Including the additional sink from metamorphic/volcanic reduced gases demonstrates the dependence of pO 2 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 pO 2 ∼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 pO 2 to vary by a factor of ∼2, with low global erosion and/or increased shale porosity, and therefore more complete oxidation, producing lower pO 2 (Fig. 3a). Varying organic carbon burial can cause larger variations in pO 2 within the same stable state. However, if organic carbon burial drops below ∼25% of present (∼1.25 × 1012mol C yr−1), corresponding to pO 2 <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.

Figure 3: Dependence of atmospheric pO 2 on organic carbon burial rate. (a) Atmospheric pO 2 level at steady-state for oxidative weathering model and minimum estimate 1.25 × 1012mol O 2 eq yr−1 reduced volatile flux (Table 1). Solid lines show sensitivity to land-surface uplift distribution and shale porosity (see Methods and Fig. 7) with default parameters (blue), and with very low uplift and increased shale porosity (n*=1.5) (red)—both normalized to give the same pO 2 at modern organic carbon burial rates. Vertical dashed lines show modern total and estimated marine (50% of total) organic carbon burial rate. (b) Default parameters as in a, but including a larger reduced atmospheric flux from a methane metamorphic pathway (1.55 × 1012 mol CH 4 yr−1; Table 1) and a corresponding increase in organic carbon burial (to 8.1 × 1012mol C yr−1), with the methane metamorphic pathway assumed to adjust to 38% of the long-term average carbon burial rate (black line). The other lines show the response with a constant metamorphic methane flux, fixed at 38% of initial burial rates of 8.1 × 1012mol C yr−1 (modern; blue), 4 × 1012mol C yr−1 (Proterozoic; green) and 2 × 1012 mol C yr−1 (Great Oxidation Event transition; red). These cases represent the short-term response to perturbations because we presume that on long timescales the metamorphic flux of methane must be proportional to the organic carbon flux previously deposited. Full size image

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 pO 2 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 CO 2 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 (δ13C carb ) record. Conventionally the constancy of δ13C carb 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 pO 2 ). 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 δ13C carb as oxidative weathering exceeds organic carbon burial. However, after ∼10 Myr, atmospheric oxygen and oxidative weathering decrease to a new steady state, leaving δ13C carb 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 δ13C carb and return to its initial value.

Figure 4: Transient response to changes in organic carbon burial flux. Results from the Precambrian COPSE model with perturbation applied to the model steady-state at 1 Ga (see ‘Methods’ section). (a) Phosphorus weathering perturbation via parameter ɛ. (b) Atmosphere/ocean oxygen fluxes: source from marine organic carbon burial (black), sinks from atmospheric reactions with reduced volcanic/metamorphic gases (red), and oxidative weathering (blue). (c) Atmospheric oxygen pO 2 showing decrease and approach to new steady-state at 25 My, where oxidative weathering and volcanic sinks again balance production by carbon burial, followed by return to initial level. (d) Carbon isotope responses of marine carbonate burial δ13C carb (black), input (blue) and output (cyan) to ocean/atmospheric system, with mean of sedimentary carbonate carbon (green) and degassing (red). Oxidative weathering initially exceeds organic carbon burial, resulting in a negative δ13C transient. After ∼10 Myr, atmospheric oxygen and oxidative weathering decrease, leaving δ13C unchanged. Similar behaviour occurs when organic carbon burial is increased again after 25 Myr. Full size image

The long-term steady-state isotopic composition of the ocean and δ13C carb 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 δ13C carb 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).