Mechanistic links between intense volcanism and the transient oxygenation of the Archean atmosphere

Biogeochemical box model

We developed a biogeochemical box model that considers the biogeochemical cycles of C, P, S, Fe, O₂, and Ca in the ocean–atmosphere system, which is an improved version of the previous study⁴⁴. More specifically, the original model was improved by including the dynamical S cycles and C and S isotopes (δ¹³C and δ³⁴S). The new model considers the dynamical responses of atmospheric CO₂, CH₄, and O₂ concentrations, oceanic levels of DIC, carbonate alkalinity (Alk_c), [PO₄^3–], [SO₄^2–], [Fe²⁺], [Ca²⁺], dissolved O₂, and dissolved CH₄, and DIC, Alk_c, and [Ca²⁺] in the pore spaces of oceanic crust. Atmospheric budgets of O₂, CH₄, and CO₂ via photochemical reactions are calculated using a parameterization created in the previous study⁴⁷. The surface temperature is calculated using the temperature parameterization of Watanabe and Tajika⁶⁴, which accounts for the greenhouse effects of CO₂, H₂O, CH₄, and C₂H₆ based on the results of the radiative-convective climate models^100,101. The atmospheric CO₂ is removed via the weathering of the continental crust and the gas exchange with the ocean⁴⁴.

The ocean is divided into a low-latitude surface ocean box (<100 m depth and 90% of the oceanic area), a high-latitude surface ocean box (<400 m depth and 10% of the oceanic area), an intermediate ocean box (100–1500 m depth below the low-latitude surface ocean box), and a deep ocean box⁴⁴. The oceanic DIC is removed via the deposition of organic matter in the sediments and calcium carbonate in sediments and in the pore spaces of the oceanic crust. Marine phosphate is supplied via rivers and removed from the ocean via the deposition of organic matter and adsorption to Fe-bearing minerals and Ca-bound P burial. Marine Fe(II) is supplied via rivers and hydrothermal systems and removed from the ocean via the deposition of Fe(III) hydroxide and pyrite in sediments. The primary production in the ocean is driven by OP and Fe-(II)-based anoxygenic photoautotrophs (AP). O₂ is produced in surface oceans by OPs and is partly consumed by methanotrophs and the oxidation of Fe(II), with the remaining O₂ being outgassed into the atmosphere. CH₄ is generated by the decomposition of organic matter through methanogenesis and is partly consumed by methanotrophs, with the remainder outgassed into the atmosphere. In this model, the activities of H₂-based photoautotrophs and/or H₂-/CO-consuming chemoautotrophs are not considered. Their activities would increase the primary productivity of APs under low atmospheric pO₂ conditions^48,102,103. If their activities are considered, the atmospheric pCH₄ and the surface temperature under Archean-like low atmospheric pO₂ conditions would likely increase. However, this would not strongly alter the fundamental behavior of the atmosphere–biosphere interactions after the eruption of LIPs and whiffs.

Carbon isotopes

The budget of ¹³C of the atmospheric CO₂ and CH₄ are represented as follows:

where μ is the number of moles in the present atmosphere (μ = 1.773 × 10²⁰ mol); f₁₃ represents the abundance of ¹³C relative to total C; f_13,vc is f₁₃ of the CO₂ outgassing from the interior of the Earth; f_13,wog is f₁₃ of the sedimentary organic matter; the subscripts ↑ and ↓ represent the upward and downward counterpart, respectively; F_oa,co2 is the gas exchange rate between the ocean and atmosphere; F_vc is the volcanic outgassing rate of CO₂; F_wog is the oxidative weathering rate of sedimentary organic matters; F_oxi is the oxidation rate of atmospheric CH₄ to form CO₂; F_esc is the consumption rate of atmospheric CH₄ via H₂ escape; and F_ws and F_wc are the terrestrial continental weathering rate of silicates and carbonates. The budgets of ¹³C of the oceanic and pore-space DIC are represented as follows:

where the subscripts → and ← represent the fluxes from the low-latitude surface ocean box to the high-latitude surface ocean box and vice versa, respectively; f_area is the areal fraction of the surface ocean box in total oceanic area; V is the volume of each ocean box; f_13,borg and f_13,pc are f₁₃ of the organic matter and carbonate depositing in the ocean, respectively; f_13,sedc is f₁₃ of the terrestrial carbonates; f_13,methano is f₁₃ of CH₄ produced via fermentation and methanogenesis; f_13,bpyrsdc is f₁₃ of the OC decomposed during the formation of pyrite in sediments; α_m and α_sd is the transfer efficiency of organic matter in the intermediate water box and deep ocean box below the low-latitude surface ocean box, respectively; F_dif and F_adv are the water exchange rate between ocean boxes via diffusion and advection; F_met is the oxidation rate of CH₄ by methanotrophs; F_dgc is the decomposition rate of organic matter in each ocean box; F_pc and F_dc are the formation and dissolution rates of CaCO₃ in each ocean box; F_po is the export production rate; F_bo is the burial rate of organic matter from each ocean box; F_AOM is the abiotic oxidation rate of methane by marine sulfate; F_bpyr,sd,c is the rate of OC decomposition during the formation of pyrite in sediments. The budgets of ¹³C of the oceanic CH₄ are represented as follows:

where F_dgch4 is the production rate of CH₄ by methanogenesis.

Global sulfur cycle

We introduced the dynamical S cycle to the biogeochemical box model. The budgets of marine sulfate (SO₄^2–), marine hydrogen sulfide (ΣH₂S), crustal pyrite (S_pyr), and crustal gypsum (S_gyp) are represented as follows:

where F_dpyr and F_dgyp are the outgassing rates of S from volcanos via metamorphic decompositions of pyrite and gypsum, respectively; F_wpyr is the oxidative weathering rate of sedimentary pyrite; F_wgyp is the weathering rate of sedimentary gypsum; F_dg,S is the decomposition rate of organic C by marine sulfate; F_AOM is the rate of abiotic oxidation of methane (AOM) by marine sulfate; F_oxhs is the oxidation rate of ΣH₂S; F_bgyp and F_bpyr are the gypsum and pyrite burial fluxes from the ocean, respectively. The budgets of ³⁴S are represented as follows:

where f₃₄ represents the abundance of ³⁴S relative to total S; and f_34,bpyr represents f₃₄ of pyrite formed in the ocean, respectively.

The burial of gypsum from the water column is assumed to occur in the low-latitude surface ocean box, as follows^104,105,106:

where [SO₄^2–]₀ and [Ca²⁺]₀ are the present oceanic concentration of sulfate and calcium ions, respectively, and k_bgyp,0 is the rate constant for the burial of sedimentary gypsum. The buried gypsum enters the sedimentary gypsum reservoir. The sedimentary gypsum experiences metamorphism volcanism and provides S to the ocean–atmosphere system:

where r_sp is the seafloor spreading rate relative to present, and k_dgyp is the rate constant for the pyrite degassing. The weathering rate of sedimentary gypsum is represented as follows:

where F_wgyp,0 and F_ws,0 are the present sedimentary gypsum and continental silicate weathering fluxes, and S_gyp,0 is the present sedimentary gypsum reservoir size.

The burial of pyrite is assumed to occur in the water column (F_bpyr,wc) and sediment (F_bpyr,sd):

The stoichiometric reaction for the pyrite formation in the water column is represented as follows:

The burial of pyrite from the water column (F_bpyr,wc) is estimated as follows¹⁰⁷:

where k_bpyr,wc is the rate constant for the burial of pyrite from the water column. For pyrite burial in sediments, on the other hand, we assumed that part of H₂S originating from MSR in sediments deposits is pyrite. The stoichiometric reaction for pyrite formation in sediments is represented as follows:

The burial of pyrite in sediments is represented as follows:

where k_bpyr,sd is the rate constant for the burial of pyrite in sediments and K_MSR is the half-saturation constant for MSR. The net production rate of O₂ via deposition of pyrite in the water column and sediments via the production of H₂ can be represented in terms of the budget of O₂ as follows:

where the first term of the right-hand side represents the net consumption of O₂ via H₂ produced by the production of pyrite in the water column via Eq. 24 and the second term represents the production of H₂ in sediments via Eq. 26.

The buried pyrite enters the sedimentary pyrite reservoir. The sedimentary pyrite experiences metamorphism volcanism and oxidative weathering, whose rates are given as follows, respectively¹⁰⁸:

where k_dpyr is the rate constant for pyrite degassing, F_wpyr,0 is the present oxidative weathering flux of sedimentary pyrite, and S_pyr,0 is the present sedimentary pyrite reservoir size. The stoichiometric reaction for pyrite degassing and oxidative weathering of pyrite is represented as follows:

The net effect of the metamorphic volcanism and oxidative weathering of pyrite on the global redox budget can be represented in terms of the consumption of O₂, as follows:

LIP eruption scenario

For the standard scenario of volcanism after an eruption of LIPs, we assumed an eruption scenario of the Ontong Java Plateau that caused the deoxygenation of the ocean, the so-called ocean anoxic event 1a at ~120 Ma. For this standard scenario, we assumed a period of intense volcanisms of 400 kyr³⁶ and a total C influx of 10²¹ g CO₂ (~2.7 × 10⁵ GtC) which is an estimated maximum value for the eruption of the Ontong Java Plateau⁴⁵. The volcanic gases are supplied to the atmosphere at a constant rate over the period of the eruption of LIP, assuming the emplacement of LIP on continents. In reality, it is likely that the emplacement on the oceanic crust was more frequent than on continents considering the small mass of the continental crust. Nevertheless, this treatment would be sufficient for representing the response of the system at a timescale longer than the gas exchange between the atmosphere and the ocean. We assumed that the supply rate of reducing gas (represented by H₂) relative to C from LIP volcanism (f_red,lip) is constant throughout the LIP emplacement. Despite the uncertainty in f_red,lip^109,110, we set f_red,lip to 0.36, which is equal to the relative supply rate of C and H₂ in the background steady state of the model⁴⁴. However, it has been discussed that the different pressure conditions owing to the different locations of the LIP emplacement result in different values of f_red,lip^43,111,112. The impact of the choice of f_red,lip was investigated in Fig. S5 and S6. The supply of Fe(II) from the erupted silicate minerals on continents is not considered because we assumed a continental LIP eruption. Note that the supply of Fe(II) would affect the conditions for the occurrence of LIPs in the case of the marine LIP: however, it is beyond the scope of this study.

Using this model, we estimated the response of the global C–P–S–Fe–O₂–Ca biogeochemical cycles to the intense volcanism after the eruption of LIPs under the reducing conditions during the late Archean. We first obtain the Archean-like background steady-state using the set of the standard parameters listed in Table 1. Starting from this background state, we investigate the response of the system to the volcanism assuming the eruption of LIPs. We simulate the response with respect to different background hydrothermal Fe(II) supply rates, f_a, background reducing gas outgassing rate, reducing gas outgassing rate from LIPs, total C influx, and duration of LIP (Table S5).