Evolution of Earth-like Extrasolar Planetary Atmospheres: Assessing the Atmospheres and Biospheres of Early Earth Analog Planets with a Coupled Atmosphere Biogeochemical Model

1.1. O₂ in modern Earth's atmosphere

The present-day atmosphere contains about 1.2·10²¹ g = 3.75·10¹⁹ mol of O₂ (Lasaga and Ohmoto, 2002). Its abundance is regulated by the established sources and sinks of the oxygen cycle. About 99% of photosynthetically produced organic carbon is approximately in balance with the reverse process, namely, respiration (Prentice et al., 2001), which results in a net primary productivity (NPP) of about 45 petagrams (10¹⁵ g) C per year (Prentice et al., 2001). A small amount of the remaining organic carbon (about 0.2%, Prentice et al., 2001) escapes oxidation during aerobic respiration via sedimental burial at the ocean floor, and the O₂ that remains is then liberated into the atmosphere (1 mol of organic carbon corresponds to 1 mol of O₂). This process constitutes the major source of atmospheric O₂. There is an additional source from the burial of other redox-sensitive chemical compounds like pyrite (FeS₂) and ferrous iron (FeO), whereas the burial of sulfate minerals in sediments removes a small portion of O₂. Sedimental burial is estimated to account for 0.3–0.8 Pg O₂/yr (Holland, 2002); this process would require 1.5–4 million years to produce the present mass of atmospheric O₂. There also exists a much smaller modern-day source of ∼0.4·10⁻³ Pg/yr (Jacob, 1999), which arises via H₂O photolysis followed by escape of atomic hydrogen from the atmosphere. Although this is only a minor source in the modern atmosphere, it might have been much faster for early Earth (Kasting and Catling, 2003). The main O₂ atmospheric modern-day sinks include the following: (1) weathering, estimated to remove ∼0.5 Pg/yr (Holland, 2002); (2) metamorphic reactions that occur on hot volcanic rock, estimated to account for ∼0.08 Pg/yr (Catling and Claire, 2005); and (3) reactions with reduced gases in the atmosphere, estimated to remove about 0.03–0.06 Pg/yr, although this value is highly uncertain (Catling and Claire, 2005).

1.2. Atmospheric O₂ in Earth's history

The O₂ concentration has risen from its prebiotic abundance of less than 10⁻¹³ present atmospheric level (PAL) (Kasting and Donahue, 1981) during the Archean eon ² up to about 1% PAL by about 2.3 Gyr ago and may have exceeded 15% PAL by about 2.1 Gyr (e.g., Knoll and Holland, 1995; Holland and Yang, 2001) (see Fig. 3). Realizing the nature of the Great Oxidation Event (GOE) is central to understanding the development of life on Earth and, hence, atmospheric biosignatures on Earth-like, potentially habitable extrasolar planets. Geological indices that imply an anoxic Archean atmosphere include the mass-independent fractionation (MIF) of sulfur isotopes (e.g., Farquhar et al., 2000; Pavlov and Kasting, 2002) and the existence of banded iron formations (BIFs) (e.g., Cloud, 1968; Holland, 1984; Isley and Abbott, 1999). On the other hand, an oxidized Archean scenario was proposed, for example, by Ohmoto (1997) based on paleosol data. Although cyanobacteria were already present on Earth by about 2.5 Gyr (Summons et al., 1999), for reasons not clear the recorded rise in O₂ took place at least 200 million years later. The O₂ rise may also have changed Earth's climate, triggering a so-called snowball Earth (Kopp et al., 2005) possibly due to responses in the photochemistry and/or negative impacts on methanogenic bacteria leading to a decrease in the warming due to CH₄ (e.g., Zahnle et al., 2006). Note, however, that there are additional possible cooling mechanisms, for example, a change in volcanic gases (see e.g., Catling and Claire, 2005). Canfield (2005) and Holland (2006) reviewed the geological evidence and current understanding of oxidative transitions in Earth's atmosphere. Typically, Earth-system box models (without detailed atmospheric photochemistry and climate calculations) are applied to investigate the rise in O₂. For example, Kump et al. (2001) suggested that oxidation events in the Paleoproterozoic corresponded to a mantle overturning event, where previously oxidized mantle was brought to the surface. This would lead to less-reduced gases being emitted by volcanoes and allow atmospheric O₂ to rise. Lasaga and Ohmoto (2002) applied a box model to investigate negative feedbacks of atmospheric O₂, which may account for its reasonably constant abundance since the Phanerozoic era. For example, lowering O₂, according to their results, would (1) strongly lower the weathering rate and (2) increase oceanic anoxicity and, hence, increase organic carbon burial via less oxidation of organic carbon in the ocean column. Effects (1) and (2) are both negative feedbacks that would stabilize O₂ in the atmosphere. Holland (2003), however, questioned their model assumptions, for example, in deriving the dependence of burial rates on oxygen abundance in seawater. Catling and Claire (2005) summarized the various theories proposed to account for the rise in O₂. Briefly, these include (1) an increase in the burial rate of organic carbon and other redox-sensitive compounds, (2) an increased supply of nutrients that stimulate photosynthesis, (3) a change in volcanic gas composition, or (4) a higher hydrogen escape rate from the top of the atmosphere. Claire et al. (2006) applied a zero-dimensional (0-D) box model to calculate the GOE and suggested a lowering in CH₄ as O₂ increases, whereas Goldblatt et al. (2006) suggested a bistable state (oxic and non-oxic) of the atmosphere whereby O₂ abundances would respond very strongly to small changes in surface fluxes of O₂. To explain this behavior, they proposed a positive feedback mechanism in which an initial increase in O₂ abundances leads to more O₃ and, hence, stronger UV shielding that reduces the O₂ photolytic sink and allows O₂ to build up.

1.3. Contribution of this work

Until now, 0-D box models were used to model Earth's atmospheric O₂ evolution by evaluating the important biogeochemical processes. In these studies, the atmosphere was included in a simplified way in order to investigate CH₄ oxidation as in the works of, for example, Claire et al. (2006) and Goldblatt et al. (2006). On the contrary, there are numerical studies in which the atmospheres of early Earth and Earth-like extrasolar planets have been assessed at different time epochs by applying both one-dimensional (1-D) global mean atmospheric column models as well as three-dimensional (3-D) general circulation models (see, e.g., Kienert et al., 2012; Charnay et al., 2013; Leconte et al., 2013; Wolf and Toon, 2013, 2014; Kunze et al., 2014; Wordsworth et al., 2011).

In the case of the 1-D global mean atmospheric column models, investigations were performed by using either climate (see, e.g., Kasting et al., 1993; von Paris et al., 2008; Goldblatt et al., 2009; Kitzmann et al., 2010, 2011a, 2011b; Wordsworth et al., 2010; Wordsworth and Pierrehumbert, 2013), photochemistry (see, e.g., Kasting et al., 1997; Zahnle et al., 2006; Segura et al., 2007; Haqq-Misra et al., 2011), or coupled climate-photochemistry calculations (see, e.g., Kasting et al., 1984; Pavlov et al., 2001, 2003; Segura et al., 2003, 2005; Grenfell et al., 2007a, 2007b; Kaltenegger and Sasselov, 2010; Grenfell et al., 2011, 2012; Rauer et al., 2011; Roberson et al., 2011), thereby neglecting biogeochemical cycles. However, since biogeochemical processes strongly influence the abundance of atmospheric constituents such as O₂ and CO₂, it is important to add these processes. Additionally, performing time-dependent integrations is a central scientific goal. However, this is currently only achievable for box-model studies (e.g., Claire et al., 2006; Goldblatt et al., 2006). Unfortunately, performing long integrations over millennia with state-of-the-art column models such as our scheme is not possible.

In this study, we therefore developed a Coupled Atmosphere Biogeochemical (CAB) model with detailed photochemistry and climate calculations as well as biogeochemical surface processes that have an impact on atmospheric O₂. Therefore, the approach in our article, which is similar to other atmospheric model studies (e.g., Kaltenegger and Sasselov, 2010; Roberson et al., 2011), is to “insert” Earth's evolution, for example, via O₂ surface concentrations from proxy data and via solar luminosity changes, as a boundary condition in the CAB model. Our main motivation thereby is to focus on understanding the associated atmospheric climatological, chemical, and biological responses. Thus, we model the atmosphere and biosphere of early Earth analog planets consistently by including the effect of the fainter Sun, increased volcanic and metamorphic outgassing, and the impact of the biosphere on the atmosphere. The photochemistry atmosphere module calculates atmospheric O₂, CO₂, and molecular nitrogen (N₂) abundances self-consistently by accounting for their in situ atmospheric sources and sinks. For early Earth analog planetary atmosphere scenarios, we apply a snapshot-like procedure by using the Earth system as a reference. We are able to reproduce the modern Earth atmospheric composition and temperature structure. We further calculate atmospheric surface fluxes required to maintain specified O₂, CO₂, and N₂ abundances in the modern-day atmosphere. For these surface fluxes, we calculate with the biogeochemical module the corresponding NPP of the biospheres, which are needed to maintain the specified O₂ surface volume, vmrs.

As a case study, we investigated atmospheric chemical responses of O₂ in an early Earth analog atmosphere at 10⁻⁶ PAL O₂ by applying the Pathway Analysis Program (PAP) developed by Lehmann (2004).

In the following sections, the CAB model (Section 2) and the PAP algorithm (Section 3) are described in detail. The CAB model is validated in Section 4. Section 5 gives an overview of the simulated early Earth analog planet scenarios, whereas in Section 6 the results are presented and discussed. Section 7 gives an overview of the sensitivity studies performed with the CAB model. We present our main conclusions in Section 8.

2.1. Atmosphere module description

The “variable” ³ 1-D global mean cloud-free, steady-state atmospheric column module is based on the 1-D model, which was described in detail by Kasting et al. (1984), Segura et al. (2003), Grenfell et al. (2007a, 2007b), Rauer et al. (2011), and Grenfell et al. (2011).

The climate module calculates temperature and water profiles from the planetary surface up to the lower mesosphere by solving the radiative transfer equation. Convective adjustment is applied as a common procedure (see, e.g., Manabe and Wetherald, 1967; Kasting, 1988; Mischna et al., 2000; Pavlov et al., 2000) if necessary. That is, the radiative temperature gradient, \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$ { \left\vert { { \frac { dT } { dr } } } \right\vert _ { { \rm { rad } } } } $$ \end{document} , is compared to the adiabatic temperature gradient, \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$ { \left\vert { { \frac { dT } { dr } } } \right\vert _ { { \rm { ad } } } } $$ \end{document} , by calculating the convective temperature; and if the Schwarzschild criterion is fulfilled, that is, \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$ { \left\vert { { \frac { dT } { dr } } } \right\vert _ { { \rm { rad } } } } > { \left\vert { { \frac { dT } { dr } } } \right\vert _ { { \rm { ad } } } } $$ \end{document} , then the calculated convective temperature replaces the radiative temperature. In the troposphere, a wet adiabat is calculated. The tropopause is defined as the height where both temperature profiles intersect. For the determination of the water vapor, a relative humidity distribution observed for modern Earth from the work of Manabe and Wetherald (1967) is assumed. The radiative part of the climate module uses a longwave radiation scheme based on the work of Mlawer et al. (1997) (Rapid Radiative Transfer Model—RRTM) and a shortwave code (quadrature-δ-2-stream approximation) based on the work of Toon et al. (1989). To account for the heating and cooling effects of clouds, the model's surface albedo (A _surf) was adjusted to 0.21 so that the converged surface temperature, T _surf, reaches 288.15 K.

The chemistry module features more than 200 chemical reactions and calculates concentration profiles for 54 chemical species including the hydrogen oxide (HO _x ), nitrogen oxide NO _x , and chlorine oxide (ClO _x ) families and sulfur-containing species, and it solves the chemical reaction network as a coupled set of continuity equations by using the backward Euler method to calculate the concentration profiles of chemical species. Below the tropopause, H₂O is given by the climate module, whereas above it is calculated self-consistently by the chemistry module according to its in situ atmospheric sources and sinks. The chemistry module accounts for wet deposition of chemical species as an atmospheric sink in the lower atmosphere by using solubility constants given by Giorgi and Chameides (1985). In the newly developed CAB model, CO₂ is also removed via rainout by introducing an effective Henry's law constant of 3·10⁻² M atm⁻¹ (Jacob, 1999). At the model boundaries, several different boundary conditions are applied. Natural biogenic and source gas emissions of CH₄, chloromethane (CH₃Cl), CO, and nitrous oxide (N₂O) are included at the lower boundary of the model, whereas for all other species (except O₂, CO₂, and N₂, see below) dry deposition is applied. At the upper boundary, an effusion flux for O and CO is used. In the CAB model, the concentrations of O₂, CO₂, and N₂ are now treated as altitude dependent, that is, similar to all other chemical species, and are calculated throughout the atmosphere according to their in situ chemical sources and sinks. For all scenarios, the surface volume mixing ratio (vmr) of these chemical species is held fixed, and their corresponding atmospheric surface fluxes \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$\Phi _i^{{ \rm{atm}}}$$ \end{document} are calculated. In this work, material surface fluxes are reported as globally averaged emission rates in grams per year. After consistent calculations of gas-phase chemical vertical profiles for O₂, CO₂, and N₂ throughout the atmosphere, these profiles are transferred to the climate part where they are interpolated to the climate grid as is already done for O₃, CH₄, H₂O, and N₂O. In the new variable model version, the steady-state assumption is now applied for only two chemical species, namely, atomic nitrogen (N) and excited methylene (¹CH₂), unlike previous chemistry versions of the model, which assumed steady state for 16 species. These two species have extremely short lifetimes, so they require the steady-state assumption in order to avoid numerical problems.

We have introduced further boundary conditions and input parameters that will be described in more detail in the following sections.

2.2. Biogeochemical module description

The biogeochemical module applied here is based on the approach of Goldblatt et al. (2006). Therefore, we only briefly describe the main components and processes considered. Goldblatt et al. (2006) considered the atmosphere to be part of the atmosphere-ocean system and did not perform climate and photochemistry calculations. Regarding atmospheric processes, they took into account hydrogen escape and a parameterization of CH₄ oxidation. All atmospheric processes in their work are treated without a temperature dependence as atmospheric temperature is not calculated. Since CH₄ oxidation and hydrogen escape are already included in our 1-D global mean atmospheric column module described in Section 2.1, they are explicitly excluded from the biogeochemical modeling described here. We furthermore split the atmosphere-ocean system used by Goldblatt et al. (2006) into the atmosphere and the ocean systems. In addition to our detailed atmosphere module, described in Section 2.1, we focus on the marine environment in our biogeochemical module. This constitutes the strongest long-term source for atmospheric O₂ due to the burial of organic carbon in the ocean (continental biomass contributes only on the short-term scale and, therefore, can be neglected for long-term processes).

For the biogeochemical module, we consider two reservoirs, namely, molecular oxygen ([O₂]) and buried organic carbon ([C^org]). The reservoirs are quantified in units of moles. The exchange of material fluxes between theses reservoirs is given in moles per year and represents sources (F _sources) or sinks (F _sinks) for the respective reservoirs. The summation of those fluxes yields a differential equation for each reservoir according to \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ \frac { d \left[ { { C_i } } \right] } { dt } } = F_i^ { { \rm { sources } } } - F_i^ { { \rm { sinks } } } \tag { 6 } \end{align*} \end{document}

where [C_i ] represents the considered reservoir (or chemical species).

Several biological and nonbiological processes have an effect on the O₂ reservoir, and these are described in the following text. The biological processes are summarized in Table 2. In our model, there are two types of photosynthesis—oxygenic and oxygenic whereby organic carbon is produced without the production of oxygen. Overall, the main context is as follows: Organic carbon produced from the different types of photosynthesis descends through the ocean column, and thereby different processes remove different fractions of the descending carbon that is finally incorporated into the ocean floor. The above is the theoretical foundation upon which the equations of Goldblatt et al. (2006) are based, and this can be described in more detail as follows: The NPP of the biosphere is described by the NPP from oxygenic photosynthesis, N (mol O₂/yr), plus the additional input of inorganic reductants for anoxygenic photosynthesis, r (mol O₂ equivalent/yr), which is represented by ferrous iron, Fe²⁺. Therefore, the rate of total organic carbon produced by oxygenic and anoxygenic photosynthesizers in the ocean system is (N + r) (see Table 2). From the available organic carbon, an assumed amount β = 0.002 (Betts and Holland, 1991; Prentice et al., 2001) is buried in sediments at the ocean floor, namely, β·(N + r), where β is the burial efficiency. Heterotrophic aerobic respirers then use a fraction of organic carbon remaining, namely, γ = [O₂]/(d _γ + [O₂]) [where d _γ = 3.7·10¹⁷ mol corresponding to the inhibition of aerobic respiration at the Pasteur point, ∼0.01 PAL (Engelhardt, 1974)]. Afterward, the remaining organic carbon is used by fermenters and acetotrophic methanogens that produce CH₄ and CO₂. From the CH₄ produced, a certain fraction, namely, δ = [O₂]/(d _δ + [O₂]), is oxidized by methanotrophs depending on the available O₂ concentration where d _δ = 2.7·10¹⁷ mol, which is equivalent to [O₂] = 2 μM (Ren et al., 1997). M is equivalent to moles per liter. Below the critical dissolved O₂ concentration of 2 μM, the rate of methane oxidation is inhibited.

In summary, Fig. 2 shows the total effect of the biosphere on the O₂ concentration, which can be written as \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \begin{split}{\frac d {dt}}{ \left[ {{{ \rm{O}}_2}} \right] ^{{ \rm{Bio}}}} = & \Omega \left( { \left[ {{{ \rm{O}}_2}} \right] } \right) N - \left( {1 - \Omega \left( { \left[ {{{ \rm{O}}_2}} \right] } \right) } \right) r \\\quad & + \beta \left( {1 - \Omega \left( { \left[ {{{ \rm{O}}_2}} \right] } \right) } \right) \left( {N + r} \right)\end{split} \tag{7} \end{align*} \end{document}

where \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$\Omega \left( { \left[ { { { \rm { O } } _2 } } \right] } \right) = \left( { 1 - \gamma } \right) \left( { 1 - \delta } \right) = \Big( { 1 - { \frac { \left[ { { { \rm { O } } _2 } } \right] } { \left( { { d_ \gamma } + \left[ { { { \rm { O } } _2 } } \right] } \right) } } } \Big ) \Big ( { 1 - { \frac { \left[ { { { \rm { O } } _2 } } \right] } { \left( { { d_ \delta } + \left[ { { { \rm { O } } _2 } } \right] } \right) } } } \Big )$$ \end{document} of the organic carbon available to decomposers. For a complete derivation of this equation, we refer the reader to the work by Goldblatt et al. (2006).

OPEN IN VIEWER

FIG. 2.

Processes in the marine biosphere after Goldblatt et al. (2006). N (mol O₂/yr) is the NPP from oxygenic photosynthesis; r (mol O₂ equivalent/yr) represents the input from anoxygenic photosynthesis. β is the fraction of buried organic carbon. γ resembles the fraction of aerobically respired organic carbon. δ depicts the fraction of CH₄ that is oxidized by methanotrophs.

Buried organic carbon is assumed to be weathered at a rate that is determined by the rate of mechanical uplift and weathering. As in the work of Goldblatt et al. (2006), it is assumed that all organic carbon exposed by weathering is consumed by decomposers described above. The rate of weathering [C^org] is w[C^org]. The total effect of weathering of organic carbon for [O₂] is given according to Goldblatt et al. (2006) by \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \frac { d } { { dt } } { \left[ { { { \rm { O } } _2 } } \right] ^ { { \rm { Cw } } } } = - \left( { 1 - \Omega \left( { \left[ { { { \rm { O } } _2 } } \right] } \right) } \right) w \left[ { { { \rm { C } } ^ { { \rm { org } } } } } \right] \tag { 8 } \end{align*} \end{document}

For the evolution of the O₂ reservoir in the surface ocean, Eqs. 7 and 8 are summed up to yield \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \begin{split}{\frac d {dt}} \left[ {{{ \rm{O}}_2}} \right] =& \Omega \left( { \left[ {{{ \rm{O}}_2}} \right] } \right) N - \left( {1 - \Omega \left( { \left[ {{{ \rm{O}}_2}} \right] } \right) } \right) r \\\quad & + \left( {1 - \Omega \left( { \left[{{{ \rm{O}}_2}} \right] } \right) } \right) \left( { \beta \left({N + r} \right) - w \left[ {{{ \rm{C}}^{{ \rm{org}}}}} \right] } \right)\end{split} \tag{9} \end{align*} \end{document}

In the same manner, we can find a differential equation for the buried organic carbon reservoir \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \frac { d } { { dt } } \left[ { { { \rm { C } } ^ { { \rm { org } } } } } \right] = \beta \left( { N + r } \right) - w \left[ { { { \rm { C } } ^ { { \rm { org } } } } } \right] \tag { 10 } \end{align*} \end{document}

If we now consider steady-state conditions for the atmosphere module, then the left-hand side of Eqs. 9 and 10 is set to zero, yielding a more simplified equation, namely, \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} 0 = \Omega \left( { \left[ {{{ \rm{O}}_2}} \right] } \right) N - \left( {1 - \Omega \left( { \left[ {{{ \rm{O}}_2}} \right] } \right) } \right) r \tag{11} \end{align*} \end{document}

This equation is then solved for [O₂] using the Van Wijngaarden–Dekker–Brent root search method (Brent, 1971; Press et al., 1993) (also called Brent's method) yielding the number of moles of O₂ depending on the input from oxygenic and anoxygenic photosynthesis N and r (see Section 2.3). This method combines linear interpolation and inverse quadratic interpolation with bisection in order to obtain the root of Eq. 11 efficiently. To derive the aqueous O₂ concentration, we calculate according to Goldblatt et al. (2006) \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ \left[ { { { \rm { O } } _2 } } \right] ^ { { \rm { aq } } } } = \frac { { { H_ { \left[ { { { \rm { O } } _2 } } \right] } } } } { \mu } \left[ { { { \rm { O } } _2 } } \right] \tag { 12 } \end{align*} \end{document}

where μ = 1.773·10²⁰ mol is the number of moles in the present atmosphere (Goldblatt et al., 2006) and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${H_{{{ \rm{O}}_2}}}$$ \end{document}  = 0.0013 M/atm (Lide, 1995) is the solubility constant of O₂ (in H₂O).

Note that since we set Eqs. 9 and 10 to zero, the burial and weathering of buried organic carbon drop out of the calculations presented. To address these processes and their impact, however, the carbon cycle also has to be implemented, which will be part of future work.

2.3. Coupling of the atmosphere and biogeochemical module

The atmosphere and biogeochemical modules are coupled via a so-called stagnant boundary layer model (Liss and Slater, 1974; Kharecha et al., 2005). It calculates the biogeochemical O₂ flux, \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$\Phi _{{{ \rm{O}}_2}}^{{ \rm{bgc}}}$$ \end{document} , defined by the different processes in Section 2.2 \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \Phi _{{{ \rm{O}}_2}}^{{ \rm{bgc}}} = {v_{ \rm{p}}} \left( {{{ \rm{O}}_2}} \right) \left( {{{ \left[ {{{ \rm{O}}_2}} \right] }^{{ \rm{aq}}}} - {H_{{{ \rm{O}}_2}}}{p_{{{ \rm{O}}_2}}}} \right) C \tag{13} \end{align*} \end{document}

where v _p(O₂) is the piston velocity of O₂, \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${p_{{{ \rm{O}}_2}}}$$ \end{document} is the atmospheric partial pressure of O₂, and C = 6.02·10²⁰ molecules cm⁻³/mol L⁻¹ is a unit conversion factor. The piston velocity is a measure of the diffusivity of a certain chemical species through a stagnant layer. For a chemical species i, it is defined as v _p(i) = K _diff(i)/z _film with the thermal diffusivity, K _diff(i), and the thickness of the stagnant layer, z _film [here ≈40 μm as in the work of Kharecha et al. (2005)]. For O₂, v _p(O₂) is derived according to Wilke and Chang (1955), resulting in a value of v _p(O₂) ≈ 5.7·10⁻³ cm s⁻¹ at 25°C. A solution of the whole CAB model is found if \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \Phi _{{{ \rm{O}}_2}}^{{ \rm{atm}}} - \Phi _{{{ \rm{O}}_2}}^{{ \rm{bgc}}} = 0 \tag{14} \end{align*} \end{document}

where \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$\Phi _{{{ \rm{O}}_2}}^{{ \rm{atm}}}$$ \end{document} is calculated by the atmosphere module for a given surface vmr. Equation 14 is also solved by applying the Van Wijngaarden–Dekker–Brent root search method. In this work, r is held constant at the modern-day input of reductants into the ocean, and N is varied stepwise according to the applied root search method between N _low = 1 mol O₂/yr and N _up = 1·10²⁵ mol O₂/yr in order to determine the input from oxygenic photosynthesis N into the atmosphere that is required to maintain the prescribed atmospheric conditions.

4.1. Atmosphere module

The CAB model was applied to modern Earth conditions to compare the modified atmosphere module presented in this work to the previous atmosphere model version discussed by Rauer et al. (2011) (denoted as RG2011), which was validated against modern Earth. Results suggest that over the calculated pressure (altitude) range a maximum relative change of the temperature profile against RG2011 between −0.5% and 0.1% is observed. The surface temperatures deviate by 0.02 K. Hence, an overall good agreement of the temperature profiles between both models was obtained.

Table 3 shows the maximum relative change in the atmosphere of relevant chemical species vmr profiles against RG2011 over altitude for O₃, H₂O, CH₄, N₂O, CH₃Cl, and CO₂. For O₂ and N₂ only small deviations are obtained. Due to the introduced hydrogen escape at the upper boundary, a maximum relative change of −90% for H₂ is found (not shown) at the TOA, whereas below 40 km the change is negligible. Quite strong changes occur for sulfur-bearing species, for example, H₂S (−64%), SO₂ (−73%), SO (−72%) (not shown), because updated volcanic SO₂ and H₂S emissions were implemented, and furthermore, new volcanic emissions for H₂, CO, CH₄, and CO₂ were introduced into the CAB model (see Table 1). Despite these changes, the biosignature species, O₃ and N₂O, and biosignature-related compounds, CH₄ and H₂O, compare very well with the previous global atmospheric column model used by RG2011, which is shown in Table 4.

4.2. Biogeochemical module

For modern Earth conditions and the present input of inorganic reductants (Fe²⁺) into the ocean of r = r ₀ = 3·10¹¹ mol Fe/yr (Holland, 2006), which is equal to r ₀ = 7.5·10¹⁰ mol O₂ equivalent/yr, the CAB model calculates a global NPP from oxygenic photosynthesis of N = 1.05 petamoles (10¹⁵ mol) O₂ per year, which is of the same magnitude as the present observed value of N ₀ ≈ 3.75 Pmol O₂/yr (Prentice et al., 2001). The range of observed oceanic NPP varies from 2.067 to 4.167 Pmol/yr (Woodwell et al., 1978; Longhurst et al., 1995; Antoine et al., 1996), hence the lower value matches our model value within a factor of 2. The burial rate of organic carbon, β(N + r) (see Fig. 2), calculated by the CAB model is 2.1 Tmol/yr. This value is in the range of the observed value of 10 ± 3.3 Tmol/yr (Holland, 1978). Global mean burial rates are not well known, being based on measurements at individual sites. It is particularly challenging to estimate associated uncertainties; for example, the proxy data is severely limited in time and space and, hence, difficult to estimate in a global model.

6.1. Atmosphere modeling

6.1.1. Climate responses

Figure 4 shows the temperature profiles of a selected number of calculated early Earth analog atmosphere runs in comparison to the modern Earth profile calculated by the CAB model. For the modern Earth p-T profile (t _geo = 0 Gyr, solid black), the temperature decreases with decreasing pressure from T _surf = 288 K at the surface to about T ≈ 212 K at the tropopause at p ≈ 0.1 bar. The distinct temperature maximum at the stratopause is caused by radiative heating due to the absorption of UV radiation by O₃. At the stratopause with a pressure of p ≈ 10⁻³ bar, a maximum temperature of T ≈ 262 K is reached.

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FIG. 4.

Selected p-T profiles of early Earth analog atmosphere control scenario runs calculated by the CAB model. Notation is as follows: solid black: 1 PAL O₂ (modern Earth), dotted: 2.5·10⁻¹ PAL (t _geo = 0.82 Gyr), short dashed: 10⁻¹ PAL (t _geo = 2.18 Gyr), dash-dot: 2.5·10⁻² PAL (t _geo = 2.22 Gyr), dash-dot-dot-dot: 10⁻² PAL (t _geo = 2.22 Gyr), long dashed: 2.5·10⁻³ PAL (t _geo = 2.23 Gyr), red: 10⁻³ PAL (t _geo = 2.24 Gyr), green: 2.5·10⁻⁴ PAL (t _geo = 2.25 Gyr), blue: 10⁻⁴ PAL (t _geo = 2.28 Gyr), magenta: 10⁻⁵ PAL (t _geo = 2.59 Gyr), yellow: 10⁻⁶ PAL (t _geo = 2.69 Gyr). (Color graphics available at www.liebertonline.com/ast)

Going forward in geological time t _geo, the O₂ content, thereby also O₃, and the solar radiation input at the TOA increase. For the 10⁻⁶ PAL O₂ atmosphere run at t _geo = 2.689 Gyr ago, the solar flux incident at the TOA was decreased to about 81% of the modern Earth value (“faint young Sun”). Furthermore, in the low O₂ atmosphere the incoming radiation is less absorbed by molecules such as O₃ (total column: 15.8% of downward shortwave radiation is absorbed compared to 25.5% for modern Earth) due to smaller atmospheric chemical abundances of O₃ (see Fig. 7) and other greenhouse gases. A diminishing of the temperature inversion is observed for the low O₂ atmosphere runs as a result of the low O₃ concentrations (see Fig. 7). Altogether, this leads to a increase in surface temperature (see Fig. 5) by 24 K (2.689 Gyr ago at 10⁻⁶ PAL O₂: T _surf = 264 K, today at 1 PAL O₂: T _surf = 288 K).

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FIG. 5.

Surface temperature for calculated Earth-in-time atmosphere runs. Additionally indicated as a horizontal line is the freezing temperature of H₂O of T = 273.15 K. The beginning of the GOE at t _geo = 2.3 Gyr is indicated as a vertical dashed line.

Note that in the case of the low O₂ atmosphere runs before 1.85 Gyr ago, global surface temperatures are below 0°C, implying no habitable surface conditions. Results in Fig. 4 are only applicable for modern Earth CO₂ concentrations since we have kept CO₂ at modern Earth concentrations in order to analyze the atmospheric responses on reducing surface O₂ concentrations firstly. However, see also sensitivity run G in Section 7 with 5 PAL CO₂. Further note, however, that it was recently shown by 3-D general circulation models used to investigate early Earth—for example, in the works of Wolf and Toon (2013) and Kunze et al. (2014)—that, even with global mean surface temperatures below the freezing point of water, areas with liquid surface ocean water could still exist, which implies habitable conditions.

Since the thermal radiation scheme RRTM is only valid for atmospheres that are quite close to modern Earth conditions (see, e.g., Segura et al., 2003; von Paris et al., 2008; Rauer et al., 2011), we compared the thermal fluxes of RRTM with thermal fluxes computed by the line-by-line radiative transfer code SQuIRRL (Schwarzschild Quadrature InfraRed Radiation Line-by-line, Schreier and Schimpf, 2001; Schreier and Böttger, 2003). For all runs considered, the maximum relative change of net TOA fluxes calculated by RRTM versus SQuIRRL amounted to a maximum value of −1.4%.

6.1.2. Photochemistry responses

UV environment

To a large extent, atmospheric chemistry is driven by the incoming TOA UV fluxes. To understand the absorbing nature of the atmosphere, UVA (315–400 nm), UVB (280–315 nm) and UVC (176–280 nm) radiation was calculated at the surface for reduced O₂ concentration and incoming TOA solar flux. UVA and UVB wavelength ranges are taken from the International Standard (ISO 21348) 2007. Note that in the photochemistry module the term “surface” denotes the lowermost layer at a height of about 500 m for modern Earth. In the case of the 10⁻⁶ PAL O₂ atmosphere, the lowermost layer sinks to a height of z ₁ = 375 m. UVA radiation at the surface stays more or less constant for atmospheres before 2.18 Gyr. It increases from about 75 W m⁻² at t _geo = 2.18 Gyr ago (0.1 PAL O₂) to about 90 W m⁻² for modern Earth. For the considered runs, a steady decrease from more than 12 W m⁻² to 2.3 W m⁻² is observed for surface UVB radiation before the GOE and after the GOE, respectively. The modern Earth control run exhibits a surface UVB radiation of 2.3 W m⁻², which is broadly similar to the observed value for cloud-free conditions of 1.4 W m⁻² (Wang et al., 2000). Going forward in geological time, UVC radiation decreases from 2.8 W m⁻² before 2.7 Gyr to virtually zero t _geo = 2.25 Gyr ago. This behavior is due to increasing O₂ and, hence, O₃ and H₂O concentrations that result in more absorption of photons in the atmosphere and more shielding of the surface from UV radiation. The impact on UVC is directly correlated with the increase in O₃, whereas UVB is affected by O₃ and H₂O together.

Figure 6 shows the ratio surface/TOA radiation, R _UV, as a measure of the radiation shielding efficiency of an atmosphere for UVA, UVB, and UVC radiation on going forward in geological time. For high R _UV values, the radiation passes efficiently through the atmosphere, whereas for R _UV = 0 it is totally blocked. UVA radiation passes efficiently through the atmosphere for all calculated runs. With the beginning of the GOE, UVB radiation is blocked rather strongly by the atmosphere, whereas UVC radiation is already starting to be blocked 2.6 Gyr ago. After the GOE, the atmosphere is totally opaque for UVC radiation. Possible negative impacts on organisms in the marine environment before the GOE might have been reduced due to the Urey effect (Urey, 1959), where a small quantity of O₂ produced during photosynthesis of H₂O absorbs a considerable amount of UV radiation. For modern Earth, UVB radiation is almost totally blocked by the atmosphere.

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FIG. 6.

Ratio (surface/TOA) radiation fluxes, R _UV, for UVA (red), UVB (magenta), and UVC (cyan) as a function of geological time t _geo. The beginning of the GOE at t _geo = 2.3 Gyr is indicated as a vertical dashed line.

In the following photochemical analysis, we only focus on the impact on important atmospheric constituents such as biosignatures (O₃, N₂O, O₂) and related bioindicators (CH₄, H₂O) as well as CO₂. “Bioindicators” are indicative of biological processes but can also be produced abiotically.

Ozone—O₃

O₃ is suggested to be a biosignature because it is formed in the stratosphere mainly from molecular oxygen ⁵ via the Chapman mechanism (Chapman, 1930), which is initiated by the photolysis of mostly biogenic O₂. In the troposphere, O₃ is produced via the smog mechanism (Haagen-Smit, 1952), which requires O₂, volatile organic compounds, nitrogen oxides, and UV radiation. The destruction of O₃ in the stratosphere proceeds via catalytic cycles that involve, for example, HO _x , NO _x , or ClO _x (e.g., Bates and Nicolet, 1950; Crutzen, 1970), which are stored in reservoir species and can be activated by changes in, for example, temperature or UV radiation. In the troposphere, O₃ is removed via wet/dry deposition, photolysis, or reactions with NO _x , HO _x , and unsaturated hydrocarbons.

Figure 7 shows the O₃ vmr profiles for reduced O₂ content of the atmosphere. Modern Earth's O₃ layer (solid black) exhibits a distinct maximum at about 0.01 bar due to the mechanisms described above. Figure 7 suggests that, for reduced O₂ concentrations, the O₃ layer moves to higher pressures (lower altitudes), for example, for 10⁻⁵ PAL to 0.2 bar, because in consequence of a lower O₂ concentration, less O₃ is produced at the same altitude. This results in increased UV radiation in atmospheric layers directly below, which stimulates the Chapman mechanism and produces more O₃; hence the peak of the O₃ layer moves to lower altitudes. However, if O₂ concentrations fall below those of CO₂ ( = 3.6·10⁻⁴, left of the green line), results are consistent with CO₂ photolysis now being the major source for atomic oxygen (O) and, hence, O₃. The O₃ peak moves upward where CO₂ is photolyzed more easily. Additionally, in the upper atmosphere a second O₃ maximum becomes visible, which is related to an increase in O₂ vmr toward lower pressures (see Fig. 16). Note that for modern Earth this secondary O₃ maximum lies in the vicinity of the mesopause (see e.g., Evans et al., 1968; Hays and Roble, 1973; Smith and Marsh, 2005) and arises due to the interplay between active-hydrogen and active-oxygen chemistry, relatively low temperatures, and a local maximum of O (Allen et al., 1984; Smith and Marsh, 2005).

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FIG. 7.

O₃ profiles of Earth-in-time atmosphere runs calculated by the CAB model. Notation as in Fig. 4.

The change in overall O₃ column amount on going forward in geological time is shown in Fig. 8. It increases from zero before the GOE to 296 Dobson units (DU) after the GOE. At about 0.8 Gyr ago, a Second Oxidation Event occurred, resulting in an increase of the O₃ column amount to 325 DU. Afterward, it decreases to the modern Earth value of 305 DU. To illustrate this decrease in O₃, we have included Fig. 9, in which it can be seen that the troposphere becomes damper (going forward in time) due to evaporation because of increasing surface temperatures. However, in the stratosphere this is not always the case (compare the solid black line with the short-dashed and dotted line). A dryer stratosphere leads to less HO _x and, hence, enhanced NO _x , resulting in an increase in catalytic O₃ loss. The dryer stratosphere is a result of a decrease in CH₄ (see Fig. 13) that is driven by OH, which has a complex photochemistry. Berkner and Marshall (1965) estimated that effective UV shielding would be provided by a column amount of 200 DU, which is reached in this work at t _geo = 2.22 Gyr ago (0.025 PAL O₂), whereas Ratner and Walker (1972) adopted a more stringent lower limit on the O₃ column amount of 259 DU [reached in this work at t _geo = 2.19 Gyr ago (0.1 PAL O₂)].

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FIG. 8.

O₃ column (DU) amount as a function of geological time t _geo for considered Earth-in-time atmosphere runs. The beginning of the GOE at t _geo = 2.3 Gyr is indicated as a vertical dashed line.

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FIG. 9.

H₂O profiles of Earth-in-time atmosphere runs calculated by the CAB model. Notation as in Fig. 4.

Water—H₂O

In the case of modern Earth, the water vapor vmr in the troposphere is chemically inert and subject to the hydrological cycle. Above the tropopause, however, the H₂O vapor concentration is determined by its chemical sources (here, CH₄ oxidation) and sinks as well as transport from the troposphere and approaches an isoprofile for modern Earth.

Figure 9 shows the H₂O vapor vmr profiles on decreasing ground-level O₂ concentrations on going back in time. The solar flux incident at the TOA decreases, which results in a decrease in surface temperature and, hence, condensation of H₂O in the troposphere. The atmosphere becomes dryer due to decreasing surface temperatures. The stratospheric H₂O profile deviates from the isoprofile (found for modern Earth), and a distinct maximum develops in the early Earth analog runs. In this region, H₂O is primarily produced from O₂ (which increases in this region—see later) via the net reaction CH₄ + O₂ → H₂O + H₂ + CO, which is initiated by the photolysis of CH₄. Furthermore, H₂O is predominantly destroyed via photolysis in the low O₂ atmosphere due to enhanced UV radiation resulting in the formation of H₂ and CO₂.

The overall H₂O column amount increases on going forward in geological time as shown in Fig. 10, which can be attributed directly to the temperature behavior shown in Fig. 5. There is the caveat, however, that there could be deviations in our temperature behavior in comparison to the geological record.

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FIG. 10.

H₂O column amount (DU) as a function of geological time t _geo for Earth-in-time atmosphere runs considered. The beginning of the GOE at t _geo = 2.3 Gyr is indicated as a vertical dashed line.

Nitrous oxide—N₂O

N₂O is an important biosignature. For modern Earth, it is almost exclusively produced by bacteria as part of the (de)nitrifying cycle (IPCC, 2001). It is destroyed mainly in the stratosphere via photolysis or via the reaction with excited oxygen (O(¹D)).

Figure 11 shows the N₂O vmr profiles for decreased ground-level O₂ concentrations. N₂O destruction via photolysis becomes more efficient in the atmosphere due to increased UV radiation for atmospheres with lower O₂ surface vmrs. This results in decreased N₂O concentrations and, hence, lower column amounts (shown in Fig. 12) in the geological past. In situ inorganic production of N₂O is negligibly small.

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FIG. 11.

N₂O profiles of Earth-in-time atmosphere runs calculated by the CAB model. Notation as in Fig. 4.

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FIG. 12.

N₂O column amount (DU) as a function of geological time t _geo for Earth-in-time atmosphere runs considered. The beginning of the GOE at t _geo = 2.3 Gyr is indicated as a vertical dashed line.

Methane—CH₄

Atmospheric CH₄ is a bioindicator since in addition to biogenic sources some geological sources exist. CH₄ is destroyed in the atmosphere mainly by the reaction with hydroxyl (OH) and in the upper stratosphere by photolysis.

Figure 13 shows the CH₄ profiles for reduced ground-level O₂ concentration. Note, however, that we fixed the biological surface flux for all scenarios considered. But see also sensitivity run H in Section 7, which considers a doubled flux. For increasing O₂ concentrations, CH₄ increases as well, reaches a maximum at 0.1 PAL O₂, and then decreases toward higher O₂ values. The corresponding column amounts are given in Fig. 14. The maximum in CH₄ column amount at t _geo = 2.18 Gyr (0.1 PAL O₂ vmr) is directly linked with a minimum concentration of OH and, hence, minimum destruction of CH₄ at the same geological time. For modern Earth, standard OH sources are, for example, H₂O + O(¹D) → OH + OH [where O(¹D) arises mainly from O₃ photolysis]; and sinks are, for example, CO + OH → CO₂ + H and OH + HO₂ → H₂O + O₂. Note that the first sink reaction allegedly destroys OH. Most of the H atoms formed react quickly via the reaction H + O₂ + M → HO₂ + M followed by, for example, HO₂ + O₃ → OH + 2O₂, which reforms OH; thus the reaction between CO and OH does not lead to an efficient OH loss. The second loss reaction is a more permanent sink for OH. The main source of OH switches to H₂O + hν → H + OH for the low O₂ atmospheric run due to higher UV.

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FIG. 13.

CH₄ profiles of Earth-in-time atmosphere runs calculated by the CAB model. Notation as in Fig. 4.

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FIG. 14.

CH₄ column amount (DU) (red) and surface OH vmr (black) as a function of geological time t _geo for Earth-in-time atmosphere runs considered. The beginning of the GOE at t _geo = 2.3 Gyr is indicated as a vertical dashed line.

Figure 14 illustrates an important result of our work; that is, we calculate an increase in CH₄ concentration with increasing O₂ vmrs at the GOE. Previous works (e.g., Claire et al., 2006; Zahnle et al., 2006) with much simpler chemical schemes, however, suggest the opposite effect, namely, that increasing O₂ (more oxidizing conditions) would lead to stronger CH₄ oxidation (into CO₂ and H₂O) and, hence, a reduction in CH₄. This behavior is hypothesized by the authors to lead to a snowball Earth. CH₄ oxidation is a complex multireaction process that usually begins by attacking OH on CH₄. OH is photolytically produced, which (generally) means high OH abundances in high-UV atmospheres, all else being equal. In our study, an increase in O₂ leads to an increase in O₃, which blocks UV. This leads to less OH and, hence, more CH₄. Our work suggests that more investigations are required in the chemical feedbacks between CH₄ and O₂ on early Earth. After the GOE, O₂ further increases, and CH₄ is more and more destroyed via the reaction with OH, which then increases because of higher production via, for example, H₂O + O(¹D) → 2OH (since H₂O increases as discussed). Note that in our study we assume a constant biogenic input of CH₄ of 474 Tg/yr at the surface for every run considered. This value could be rather weak for early Earth (see Claire et al., 2006). Also, due to the toxic nature of O₂ to CH₄-producing microorganisms, the rise in O₂ likely had a severe impact on the biological activity and produced atmospheric CH₄, therefore resulting in a dramatic decrease in biotic CH₄ production. This mechanism is not included in the CAB model and is beyond the scope of this article.

Carbon dioxide—CO₂

CO₂ is an important greenhouse gas that is generally well mixed in the modern Earth atmosphere.

Figure 15 shows how the CO₂ vmr profiles change on decreasing the ground-level O₂ concentrations. For decreases down to 0.1 PAL O₂, CO₂ increases in the stratosphere mainly due to the HO _x catalyzed net reaction O₃ + 3CO → 3CO₂, which is initialized by the catalyzed photolysis of O₃ and O₂. For further decreases in O₂, stronger photolysis of CO₂ leads to decreased vmrs in the stratosphere. This implies that CO₂ does not exhibit an isoprofile throughout the atmosphere for low O₂ concentrations. In the case of 10⁻⁶ PAL O₂, the TOA vmr of CO₂ is 334 ppm in comparison to the surface vmr of 355 ppm. There is a caveat, however: CO₂ profiles could depend on the rather unconstrained value of the eddy diffusion profile K(z).

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FIG. 15.

CO₂ profiles of Earth-in-time atmosphere runs calculated by the CAB model. Notation as in Fig. 4.

Molecular oxygen—O₂

Figure 16 shows that O₂ exhibits an isoprofile behavior for atmosphere runs with ground-level O₂ concentrations above 10⁻⁴ PAL O₂, which implies that its concentration is dominated by transport processes rather than chemical production (P) and destruction (L). For the atmosphere runs with surface O₂ concentrations below 10⁻⁴ PAL O₂, an anticorrelation between the vertical CO₂ and O₂ profiles becomes visible, implying that the destruction of CO₂ provides a source of atmospheric O₂ in the upper stratosphere. A detailed chemical analysis will be presented in Section 6.1.3 to gain detailed insight into the rather complex production (and destruction) processes for O₂.

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FIG. 16.

O₂ profiles of Earth-in-time atmosphere runs calculated by the CAB model. Notation as in Fig. 4.

Figure 17 compares the net chemical change \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ \left( { \Delta {n_i}} \right) _{{ \rm{chem}}}} = {P_i} - {L_i} \tag{15} \end{align*} \end{document}

of i = O₂ in the atmosphere for modern Earth and low O₂ atmospheres. Thereby, n_i is the number density of the chemical compound i. For modern Earth, O₂ is only produced immediately below and above the O₃ layer maximum in the stratosphere. In general, O₂ is mostly destroyed in the atmosphere except for the lowermost atmospheric layers of atmospheres with ground-level concentrations between 10⁻² and 10⁻³ PAL. For very low O₂ atmospheres, there is a net production at the uppermost layers, which is a result of increased CO₂ photolysis as mentioned above.

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FIG. 17.

Atmospheric net (P − L) chemical change of O₂ calculated by the CAB model for modern Earth and low O₂ atmospheres. Notation is as follows: solid red: 1 PAL O₂ (modern Earth), dashed green: 10⁻¹ PAL (t _geo = 2.18 Gyr), dotted dark blue: 10⁻² PAL (t _geo = 2.22 Gyr), dotted purple: 10⁻³ PAL (t _geo = 2.24 Gyr), dot-dashed cyan: 10⁻⁴ PAL (t _geo = 2.28 Gyr), dot-dashed yellow: 10⁻⁵ PAL (t _geo = 2.59 Gyr), dot-dot black: 10⁻⁶ PAL (t _geo = 2.69 Gyr). (Color graphics available at www.liebertonline.com/ast)

Figure 18 depicts the net column-integrated (global mean) (P − L) chemical change of O₂ calculated by the CAB model on going forward in geological time. Additionally, in the upper right of Fig. 18 the column-integrated production and destruction rates of O₂ are shown for comparison. This illustrates that O₂ is generally destroyed within the atmosphere for all runs considered. Hence, this indicates that a positive O₂ flux of the same amount into the atmosphere is required in order to achieve steady state and maintain O₂ levels above zero. It is striking that, although the surface O₂ concentration varies by several orders of magnitude, the associated O₂ surface flux, \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$\Phi _{{{ \rm{O}}_2}}^{{ \rm{atm}}}$$ \end{document} , into the atmosphere varies between about 3300 and 4000 Tg/yr by only about 20%. Before the GOE it exhibits an almost constant behavior. In this atmosphere regime, small changes in the O₂ surface flux can support a wide range of different surface O₂ vmrs (not shown). Then, \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$\Phi _{{{ \rm{O}}_2}}^{{ \rm{atm}}}$$ \end{document} increases sharply during the GOE as surface O₂ concentrations increase strongly. After the GOE, \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$\Phi _{{{ \rm{O}}_2}}^{{ \rm{atm}}}$$ \end{document} decreases, followed by a sharp increase at the Second Oxidation Event at 0.8 Gyr ago, and then decreases again. Generally, one recognizes that the mathematical solution is not unique; that is, for one atmospheric O₂ surface flux there are multiple surface O₂ vmrs regarding the different boundary conditions. This means that the same magnitude of O₂ surface flux (which is a measure of the strength of the chemical production and destruction of O₂ in the whole atmosphere) can support either (a) an anoxic atmosphere or (b) a rather oxic atmosphere [which in turn depends on other established factors known to affect O₂(g) such as irradiation and volcanic/metamorphic outgassing]. The biosphere productivity that corresponds to the O₂ surface flux at different ground-level O₂ concentrations is investigated in Section 6.2.

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FIG. 18.

Column-integrated net (P − L) chemical change of atmospheric O₂ calculated by the CAB model as a function of geological time t _geo for Earth-in-time atmosphere runs considered. The beginning of the GOE at t _geo = 2.3 Gyr is indicated as a vertical dashed line. In the upper right panel the column-integrated P (green) and L (red) rates are given as a function of geological time t _geo for comparison. (Color graphics available at www.liebertonline.com/ast)

Comparison to previous work

Generally, it is not easy to compare results with those of previous works in the literature regarding early Earth since either, for example, only stand-alone photochemical models (i.e., without coupled climate calculations) have been presented (e.g., Kasting and Donahue, 1980; Kasting, 1982; Kasting et al., 1985; Zahnle et al., 2006) or coupled climate-chemistry calculations performed using an isoprofile assumption for O₂, CO₂, and N₂ (e.g., Segura et al., 2003 ⁶ ). Furthermore, previous workers have assumed increased CO₂ vmrs (see, e.g., Kasting et al., 1984) and CH₄ surface fluxes (see e.g., Pavlov et al., 2003) to be present in the early Earth atmosphere.

Some key chemical reactions resulting in the production and destruction of O₂ have, however, also been identified, for example, in Kasting et al. (1984), although calculated O₂ profiles differ from this work. Focusing on atmospheric O₃, Fig. 19 shows a comparison of the O₃ column depth calculated by this study with those of Segura et al. (2003) and Kasting and Donahue (1980). To compare with the work of Segura et al. (2003), additional runs were performed with the CAB model (“Segura comp.” shown in dark green) with the initial atmospheric conditions as in the Segura et al. (2003) study. A further important result of this work is shown in Fig. 19, where it can be seen that, due to our atmosphere model improvements, we calculate a consistently enhanced O₃ column amount compared to previous works in the literature. This difference calculated in O₃ occurs, for example, due to an increased photolytic destruction of CO₂ in the runs of this work leading to production of O₂ and, hence, O₃. Comparing results of the Segura comp. runs with the results of Segura et al. (2003) suggests, for example, a maximum relative change in the O₃ column amount of 82% at t _geo = 2.28 Gyr (10⁻⁴ PAL O₂). For H₂O, N₂O, and CH₄, qualitatively similar results were found.

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FIG. 19.

Column amount of atmospheric O₃ in DU as a function of geological time t _geo for Earth-in-time atmosphere runs considered in comparison to previous work. The beginning of the GOE at t _geo = 2.3 Gyr is indicated as a vertical dashed line. (Color graphics available at www.liebertonline.com/ast)

6.1.3. Pathway analysis with respect to O₂

For the early Earth analog runs, model calculations generally predict an increase of the O₂ vmr with increasing atmospheric height, which implies an in situ atmospheric source of O₂ (see Fig. 16). Furthermore, it can be seen that the CO₂ profile is anticorrelated with the O₂ profile in the low O₂ Earth-in-time atmosphere runs (see Fig. 15). This might imply that CO₂ serves as a source species for O₂. Our goal is to identify how O₂ is produced from CO₂ in the presence of highly reactive radicals such as OH. We further focus on the O₂ destruction pathways to identify the dominant reduced chemical species that are responsible for the consumption of O₂. Therefore, PAP (for details, see Section 3) is applied for an atmosphere with a surface O₂ vmr of 10⁻⁶ PAL O₂ (t _geo = 2.688 Gyr). Our study represents the first application of PAP in the context of early Earth. We consider only pathways with an individual contribution larger than 1.5% of the total production (or destruction) of O₂.

In the analysis, we firstly considered all chemical species with an in situ chemical lifetime smaller than that of O₂ as a branching point as described in Section 3. It turned out that CO is part of the net reactions of the dominant O₂ production and destruction pathways, respectively. This indicates that, for the rates of O₂ production and destruction pathways, it is relevant whether CO is treated as a branching point or not (if it is, all CO production and destruction pathways will be combined as far as possible to yield null cycles, i.e., pathways that do not have a net effect on CO; if it is not, CO production and destruction pathways are not combined). For about 40% of the atmospheric layers considered, CO was used as a branching point. To ensure a consistent treatment of all O₂ production and destruction pathways at every atmospheric height, we repeated the analysis by excluding CO as a branching point.

Production pathways and their altitude dependence

Table 6 summarizes the major column-integrated chemical production pathways, P1–P7, found by PAP and their percentage contributions to the total column-integrated O₂ production rate for an atmosphere with a surface O₂ vmr of 10⁻⁶ PAL O₂.

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Table 6.

Summary of Dominant Chemical Production (P) Pathways of O ₂ Found by PAP and Their Percentage Contribution to the Total Column-Integrated O ₂ Production Rate for an Earth-like Atmosphere with a Surface O ₂ vmr of 10 ⁻⁶ PAL O ₂

Class	Subclass	Pathway number	Contribution (%)	Pathway
PA	PA1	P1	28.4	2·(CO2 + hν → CO + O(1D))
				2·(O(1D) + N2 → O + N2)
				HO2 + O → OH + O2
				OH + O → H + O2
				H + O2 + M → HO2 + M
				net: 2CO2 → O2 + 2CO
	PA1	P2	28.1	2·(CO2 + hν → CO + O)
				HO2 + O → OH + O2
				OH + O → H + O2
				H + O2 + M → HO2 + M
				net: 2CO2 → O2 + 2CO
	PA1	P7	2.3	2·(CO2 + hν → CO + O(1D))
				2·(O(1D) + N2 → O + N2)
				O + O2 + M → O3 + M
				OH + O → H + O2
				H + O3 → OH + O2
				net: 2CO2 → O2 + 2CO
	PA2	P3	20.7	2·(CO2 + hν → CO + O(1D))
				2·(O(1D) + N2 → O + N2)
				O + O + M → O2 + M
				net: 2CO2 → O2 + 2CO
	PA2	P4	6.8	2·(CO2 + hν → CO + O)
				O + O + M → O2 + M
				net: 2CO2 → O2 + 2CO
PB	PB1	P6	3.9	OH + O → H + O2
				H + O2 + M → HO2 + M
				HO2 + O → OH + O2
				net: 2O → O2
	PB2	P5	5.3	O + O + M → O2 + M
				net: 2O → O2

Only pathways that contribute >1.5% of the total column-integrated production rate are shown. For explanation of classes and subclasses see text.

The major column-integrated chemical production pathways presented in Table 6 can be categorized into two classes, as follows:

• class PA: O₂ is produced by pathways with the net reaction 2CO₂ → O₂ + 2CO

▪ subclass PA1 (P1, P2, P7): catalyzed by HO _x species

▪ subclass PA2 (P3, P4): without the presence of HO _x

• class PB: O₂ is formed by pathways with the net reaction 2O → O₂

▪ subclass PB1 (P6): catalyzed by HO _x species

▪ subclass PB2 (P5): without the presence of HO _x

The relative contributions of the pathways mentioned above to the total column-integrated production rate are given in Fig. 20. Pathways of subclass PA1 and PA2 are initiated by the photolysis of CO₂, whereas class PB pathways require overall the presence of atomic oxygen. The main source for O originates from the photolysis of CO₂ in the upper stratosphere, producing O(¹D) and hence O, which is then transported downward by eddy diffusion, contributing to enhanced O₂ vmrs in the upper stratosphere. Note that at the upper boundary of the photochemistry part of the atmosphere module an effusion flux for O and CO is implemented in order to simulate this effect from atmospheric layers above the module TOA. Pathway P2 was found by Yung and DeMore (1999) in the context of a pure CO₂-dominated atmosphere.

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FIG. 20.

O₂ production classes (see Table 6) and their contributions to the total column-integrated O₂ production rate via pathways calculated by PAP for an Earth-like atmosphere with a surface O₂ vmr of 10⁻⁶ PAL O₂.

Figure 21 shows the altitude dependence of the production pathways of O₂ for an Earth-like atmosphere with a surface O₂ vmr of 10⁻⁶ PAL O₂, which indicates that the production of O₂ in the atmosphere is strongest in the upper stratosphere. The total production rate due to chemical pathways calculated by PAP is also shown (solid black line). About 98.7% of the total column-integrated O₂ production rate is explicable via pathways found by PAP with individual contributions above 1.5%. The dominant production pathways P1 and P3 (as well as P7), which produce excited oxygen (O(¹D)) from CO₂ photolysis, act in the upper stratosphere where UV radiation is strongest. As the UV radiation passes through the atmosphere, it is absorbed; hence the second dominant pathway P2 (and also P4), which involves ground-state oxygen instead of O(¹D), has its maximum rate at lower altitudes. Due to the enhanced O abundance in the upper stratosphere, which is provided from CO₂ photolysis that produces O(¹D) and is transported downward to the analyzed atmospheric layers, the pathways P5 and P6 have their maximum rate in the upper stratosphere. Note that, except for the photolysis of CO₂, pathways P5 and P6 are equal to P4 and P2.

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FIG. 21.

Altitude dependence of O₂ production pathways P1 to P7 (see Table 6) for an Earth-like atmosphere with a ground-level O₂ concentration of 10⁻⁶ PAL.

Destruction pathways and their altitude dependence

Table 7 summarizes the major column-integrated chemical destruction pathways and their percentage contributions to the total column-integrated O₂ destruction rate found by PAP for an atmosphere with a surface O₂ vmr of 10⁻⁶ PAL O₂.

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Table 7.

As for Table 6 but for O₂ Destruction (L) Pathways

Class	Subclass	Pathway number	Contribution (%)	Pathway
LA	LA1	L1	28.5	2·(H + O2 + M → HO2 + M)
				HO2 + HO2 → H2O2 + O2
				H2O2 + hν → OH + OH
				2·(CO + OH → CO2 + H)
				net: O2 + 2CO → 2CO2
	LA1	L2	9.4	2·(H + O2 + M → HO2 + M)
				HO2 + O → OH + O2
				HO2 + hν → OH + O
				2·(CO + OH → CO2 + H)
				net: O2 + 2CO → 2CO2
	LA1	L6	4.4	2·(H + O2 + M → HO2 + M)
				HO2 + O → OH + O2
				NO + HO2 → NO2 + OH
				2·(CO + OH → CO2 + H)
				NO2 + hν → NO + O
				net: O2 + 2CO → 2CO2
	LA1	L8	3.4	H + O2 + M → HO2 + M
				H + HO2 → OH + OH
				2·(CO + OH → CO2 + H)
				net: O2 + 2CO → 2CO2
	LA2	L3	7.4	O2 + hν → O + O
				2·(HO2 + O → OH + O2)
				2·(CO + OH → CO2 + H)
				2·(H + O2 + M → HO2 + M)
				net: O2 + 2CO → 2CO2
	LA2	L5	5.0	O2 + hν → O + O(1D)
				O(1D) + N2 → O + N2
				2·(HO2 + O → OH + O2)
				2·(CO + OH → CO2 + H)
				2·(H + O2 + M → HO2 + M)
				net: O2 + 2CO → 2CO2
LB	LB1	L4	5.4	H2O2 + hν → OH + OH
				2·(CH4 + OH → CH3 + H2O)
				2·(CH3 + O2 + M → CH3O2 + M)
				2·(CH3O2 + HO2 → CH3OOH + O2)
				2·(CH3OOH + hν → H3CO + OH)
				2·(H2CO + OH → H2O + HCO)
				2·(HCO + O2 → HO2 + CO)
				HO2 + HO2 → H2O2 + O2
				2·(H3CO + O2 → H2CO + HO2)
				net: 3O2 + 2CH4 → 4H2O + 2CO
	LB1	L7	4.3	2·(H2CO + OH → H2O + HCO)
				2·(HCO + O2 → HO2 + CO)
				3·(HO2 + HO2 → H2O2 + O2)
				3·(H2O2 + hν → OH + OH)
				2·(CH4 + OH → CH3 + H2O)
				2·(CH3 + O2 + M → CH3O2 + M)
				2·(CH3O2 + OH → H3CO + HO2)
				2·(H3CO + O2 → H2CO + HO2)
				net: 3O2 + 2CH4 → 4H2O + 2CO
	LB2	L10	2.5	CH3OOH + hν → H3CO + OH
				CH4 + OH → CH3 + H2O
				CH3 + O2 + M → CH3O2 + M
				CH3O2 + HO2 → CH3OOH + O2
				H3CO + O2 → H2CO + HO2
				H2CO + hν → H2 + CO
				net: O2 + CH4 → H2O + H2 + CO
LC		L9	3.0	2·(H + O2 + M → HO2 + M)
				HO2 + HO2 → H2O2 + O2
				H2O2 + hν → OH + OH
				2·(H2 + OH → H2O + H)
				net: O2 + 2H2 → 2H2O
LD		L11	1.7	CO + OH → CO2 + H
				H2O + hν → H + OH
				2·(H + O2 + M → HO2 + M)
				HO2 + HO2 → H2O2 + O2
				net: O2 + H2O + CO → H2O2 + CO2

These pathways can be categorized into 4 classes:

• class LA: O₂ is destroyed by pathways with the net reaction O₂ + 2CO → 2CO₂ (CO oxidation), which are catalyzed by HO _x and NO _x species

▪ subclass LA1 (L1, L2, L6, L8): initialized by the oxidation of H

▪ subclass LA2 (L3, L5): initiated by the photolysis of O₂

• class LB: O₂ is consumed by CH₄-oxidation pathways

▪ subclass LB1 (L4, L7): net reaction 3O₂ + 2CH₄ →  4H₂O + 2CO

▪ subclass LB2 (L10): net reaction O₂ + CH₄ →  H₂O + H₂ + CO

• class LC (L9): O₂ is consumed by pathways with the net reaction O₂ + 2H₂ → 2H₂O (H₂ oxidation),

• class LD (L11): O₂ is consumed by pathways with the net reaction O₂ + H₂O + CO → H₂O₂ + CO₂.

Their relative contributions to the total destruction rate via pathways are given in Fig. 22. Generally, O₂ is consumed forming CO₂, CO, H₂, H₂O, and H₂O₂. Pathways of class LA lead to the oxidation of CO mainly via HO _x . Thereby, in the subclass LA2 pathways are initiated by the photolysis of O₂. The complex pathways of the subclasses LB1 and LB2 destroy O₂ via the oxidation of CH₄, whereas class LC leads to the oxidation of H₂. Furthermore, there is a small contribution from class LD that leads to the formation of H₂O₂ via oxidation of CO and H₂O. This is rather surprising since H₂O₂ is a highly reactive (oxidizing) tropospheric species (produced by self-reaction of HO₂ and removed via photolysis and fast surface deposition). H₂O₂ features a lifetime of typically a few hours and is therefore set to be a branching point species throughout the troposphere (see Section 3). Nevertheless, L11 suggests a pathway in which H₂O₂ is overall produced. We interpret this result as follows: PAP was supplied with input from rate data for chemical reactions that occur only (in situ) in the atmosphere. It was not supplied with rates for other processes such as dry and wet deposition. H₂O₂ features a rapid depositional surface sink; therefore to attain an equilibrium concentration for this species in the atmospheric model, there must exist a pathway in the atmosphere that overall forms a net source of H₂O₂, to balance the strong surface depositional sink. It is this net source that PAP has found in the form of L11.

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FIG. 22.

As for Fig. 20 but for destruction (see also Table 7).

Several pathways shown in Table 7 have also been found by previous workers in the context of martian atmospheric chemistry, for example, L1 by Parkinson and Hunten (1973) and Yung and DeMore (1999), L2 by Stock et al. (2012a), L3 by McElroy and Donahue (1972), L6 by Nair et al. (1994) and Yung and DeMore (1999), and L8 by Sonnemann et al. (2006). This implies that pathways that are important for the CO₂-dominated martian atmosphere may also play a key role in an Earth-like atmosphere with low O₂ and 1 PAL CO₂ abundances.

Figure 23 shows the altitude dependence of the O₂-consumption pathways for an Earth-like atmosphere with a surface O₂ vmr of 10⁻⁶ PAL O₂. The total destruction rate due to chemical pathways calculated by PAP is also shown (solid green line). About 84.1% of the total column-integrated O₂ destruction rate is due to pathways with individual contributions above 1.5%. Especially, in the troposphere the destruction of O₂ is composed of a large number of pathways, which individually contribute less than 1.5% to the total column-integrated destruction rate. Figure 23 suggests two regimes for the destruction of O₂ in the atmosphere, as follows:

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FIG. 23.

As for Fig. 21 but for destruction (see also Table 7).

• The main consumption of O₂ in the troposphere occurs via the oxidation of reduced gases such as CO, CH₄, and H₂ [but only to a very small amount (<1.5%) by reduced sulfur such as H₂S] and is composed of a large number of different pathways. The dominant pathway L1 leads to CO-oxidation catalyzed by HO _x (CO is provided by diffusion from the upper atmosphere, where it is strongly produced from CO₂ photolysis), whereas the complex CH₄ oxidation pathways L4, L7, and L10 have smaller contributions. Note that our results may change depending on the CH₄ concentration and, hence, biological CH₄ flux inserted at the surface. The minor pathway L9 results in the oxidation of H₂, which is delivered by volcanic emissions from the surface and via diffusion from the upper atmosphere. H₂ is destroyed in situ in the lower atmosphere. There is an additional small contribution from pathway 11 that results in the oxidation of CO in the presence of H₂O.

• A minor contribution (L3, L5, and L8) to the destruction pathways originates in the stratosphere. At these altitudes O₂ consumption during CO oxidation is most efficient due to a maximum in HO₂ abundance (not shown), whereby pathways L3 and L5 are initiated by the photolysis of O₂.

In summary, for an Earth-like atmosphere with low surface O₂ concentrations (10⁻⁶ PAL O₂), atmospheric O₂ is produced in the upper stratosphere mainly from the in situ photolytic destruction of CO₂ (whereas a small contribution relies on the delivery of O by atmospheric diffusion). O₂ is mainly destroyed in the lower atmosphere by complex pathways resulting mainly in the formation of H₂O and CO₂ via the oxidation of CO, CH₄, and H₂. Thereby, there is a minor contribution from pathways resulting in the formation of H₂ and H₂O₂. In both the production and destruction of O₂, CO plays a key role. Note that the abiotic in situ production rate of O₂ in the atmosphere from CO₂ photolysis as well as the O₂ destruction rate is comparatively smaller than the O₂ flux originating from the surface biosphere.

6.2. Biogeochemical modeling

The CAB model calculates how much input from oxygenic photosynthesis, N (NPP), is needed to maintain the surface flux \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$\Phi _{{{ \rm{O}}_2}}^{{ \rm{atm}}}$$ \end{document} calculated by the atmospheric chemistry module for a given surface vmr of O₂.

Assuming three constant inputs from anoxygenic photosynthesis [r = 7.5·10⁹, 7.5·10¹⁰ (present value, Holland, 2006), and 7.5·10¹¹ mol O₂ equivalent/yr (Archean upper limit, Holland, 2006)], Fig. 24 shows the resulting N as a function of geological time t _geo.

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FIG. 24.

Calculated input from oxygenic photosynthesis, N, in mol O₂ per year for a constant value of anoxygenic photosynthesis, r, as a function of geological time t _geo: r = 7.5·10¹⁰ mol O₂ equivalent/yr is the present value (Holland, 2006) (green); r = 7.5·10¹¹ mol O₂ equivalent/yr is an upper limit for the Archean (Holland, 2006) (blue); and for comparison calculations were performed for a constant value of r = 7.5·10⁹ mol O₂ equivalent/yr (red). The beginning of the GOE at t _geo = 2.3 Gyr is indicated as a vertical dashed line. (Color graphics available at www.liebertonline.com/ast)

Before the GOE at about 2.3 Gyr, N exhibits an almost constant behavior, although O₂ concentrations vary over 2 orders of magnitude (see Table 5). After the GOE, it increases modestly with increasing O₂ concentrations and does not reflect the sometimes oscillating behavior found for the atmospheric O₂ surface flux [see (P − L) chemical change behavior in Section 6.1.2 for comparison]. On inserting Eq. 13 into Eq. 14, one obtains \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \Phi _{{{ \rm{O}}_2}}^{{ \rm{atm}}} = {v_{ \rm{p}}} \left( {{{ \rm{O}}_2}} \right) \left( {{{ \left[ {{{ \rm{O}}_2}} \right] }^{{ \rm{aq}}}} - {H_{{{ \rm{O}}_2}}}{p_{{{ \rm{O}}_2}}}} \right) C \tag{16} \end{align*} \end{document}

Equation 16 can now be rearranged for [O₂]^aq, which is calculated by the biogeochemical module (see Eqs. 11 and 12) and directly depends on N. For N, two regimes can then be identified, as follows:

• Regime I (low O₂ regime before the GOE): \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$ { H_ { { { \rm { O } } _2 } } } { p_ { { { \rm { O } } _2 } } } < < { \frac { \Phi _ { { { \rm { O } } _2 } } ^ { { \rm { atm } } } } { C { v_ { \rm { p } } } \left( { { { \rm { O } } _2 } } \right) } } $$ \end{document} : Eq. 16 simplifies to [O₂]^aq ≃  \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$ { \rm { } } { \frac { \Phi _ { { { \rm { O } } _2 } } ^ { { \rm { atm } } } } { C { v_ { \rm { p } } } \left( { { { \rm { O } } _2 } } \right) } } $$ \end{document} . Since in this regime \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$\Phi _{{{ \rm{O}}_2}}^{{ \rm{atm}}}$$ \end{document}  ≈ const. [O₂]^aq is also approximately constant, N (which determines [O₂]^aq) exhibits a constant behavior as well.

The switch between both regimes can be found where \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$ { H_ { { { \rm { O } } _2 } } } { p_ { { { \rm { O } } _2 } } } = { \frac { \Phi _ { { { \rm { O } } _2 } } ^ { { \rm { atm } } } } { C { v_ { \rm { p } } } \left( { { { \rm { O } } _2 } } \right) } } $$ \end{document} and occurs at about 4·10⁻⁴ PAL O₂, which corresponds to about t _geo = 2.25 Gyr ago.

Results in Fig. 24 can also be plotted over O₂ mixing ratio; see Fig. 25 suggesting that one level of NPP from oxygenic photosynthesis, N, supports only one specific O₂ surface vmr. Please note that the y axis in Fig. 25 is logarithmic and in the case of low O₂ atmospheres changes in N are very small but monotonically increasing.

OPEN IN VIEWER

FIG. 25.

As for Fig. 24 but over O₂ vmr instead of geological time t _geo.