Ozaki and Reinhard (2021) projected with a stochastic coupled biogeochemistry-climate model that the mean future lifespan of Earth's atmosphere at oxygen levels above 1% of the present atmospheric level is 1.08 ± 0.14 billion years (1σ), driven by solar brightening and terminal CO2 starvation of the photosynthetic biosphere, with the timing modulated by the net flux of reducing power exchanged between the mantle and the ocean-atmosphere-crust system. The authors explicitly left open how processes excluded or parameterized in that model alter the projection: quantitative temporal constraints on subduction and mantle-degassing fluxes of redox-sensitive species; the net effect of reverse weathering (authigenic silicate formation that releases CO2) on the oxygenated-atmosphere lifespan; and hypothesized organic-haze climate feedbacks that could brake deoxygenation or generate oxygenation/deoxygenation cycles during terminal habitability. Later work through 2026 revised the land-plant survival horizon to roughly 1.6–1.86 billion years and tested seafloor weathering and stochastic outgassing for the plant biosphere, but no study has recomputed the coupled oxygenation projection with these processes, and the mantle redox-flux, reverse-weathering, and haze-oscillation questions remain unanswered. The problem is to quantify these controls and how they alter the projected trajectory of atmospheric O2 through Earth's terminal habitability.

Background

The question of how long Earth will remain habitable originates with Lovelock and Whitfield (1982), who argued that a brightening Sun would eventually sterilize the planet. Caldeira and Kasting (1992) sharpened the mechanism: the carbonate-silicate weathering feedback — the planetary thermostat by which atmospheric CO2 is consumed by the chemical weathering of silicate rocks at a rate that increases with temperature — will draw CO2 down toward the minimum level required by plants within roughly a billion years, so the biosphere dies of CO2 starvation rather than overheating. Mello and Friaça (2019) refined the thermal-limit side of this estimate, and Ozaki and Reinhard (2021) supplied the modern benchmark for the atmosphere itself.

Several specialist terms are needed. PAL denotes the present atmospheric level of O2 (21% by volume). The moist greenhouse is a climate state in which warming lets water vapor penetrate the stratosphere and escape to space, eventually desiccating the planet. Reverse weathering is the formation of authigenic (grown in place) silicate clays in marine sediments, a reaction that consumes dissolved silica and releases CO2 and acidity to the ocean-atmosphere system; Isson and Planavsky (2018) showed it stabilizes seawater pH on geological timescales. Organic haze is a photochemical aerosol formed from methane-derived fragments under low-O2 conditions, as invoked for the Archean Earth (the eon before ~2.4 billion years ago, when atmospheric O2 was vanishingly low); it both scatters sunlight (cooling) and warms via organic greenhouse gases, so its climatic net effect is model-dependent. The reducing-power flux, written Φ(Red) here and F(Red) in the source's Methods, is the signed net input flux of reducing power from the mantle to the exogenic (ocean-atmosphere-crust) system, expressed in Tmol O2-equivalent per year: degassing of reduced volcanic gases (H2S and other reduced gases such as H2) and the subduction of ferric iron add reducing power, while the subduction of organic carbon and pyrite sulfur removes it, so subduction enters with both signs. Positive values denote a net input of reducing power to the surface system; the source's present-day estimate is slightly negative (> -0.16 Tmol O2-equivalent per year from existing empirical estimates, and -0.24 ± 0.27 from its resampled model ensemble). Because these species consume O2, a larger net input shortens the oxygenated lifespan. The source states that relationship (its Fig. 3b) for the lifespan-averaged quantity Φ_1%(Red), defined as the time integral of F(Red) from the present to the future lifespan t, divided by t, where t is the time at which O2 falls below the 1% PAL threshold; the averaging window therefore ends at the lifespan being predicted, and the anti-correlation between reducing power and lifespan refers to this averaged quantity.

Ozaki and Reinhard (2021) coupled a box model — a set of reservoirs ('boxes') for the ocean, atmosphere and crust exchanging material fluxes — of the carbon (C), nitrogen (N), phosphorus (P), oxygen (O) and sulfur (S) cycles and the global redox budget, in the lineage of the COPSE (Carbon–Oxygen–Phosphorus–Sulfur-Evolution) family of Phanerozoic box models, to a zero-dimensional (globally averaged) energy-balance climate, and sampled poorly known geophysical and biological parameters in a Monte Carlo random-sampling ensemble rather than fixing them. The projected sequence is: rising solar luminosity strengthens the weathering feedback, CO2 falls toward the photosynthetic compensation point (the CO2 level at which photosynthesis just balances plant respiration), net primary productivity collapses, and with it the only significant O2 source, so atmospheric O2 crashes to the low levels of the Archean; the mean time at which O2 drops below 1% PAL is 1.08 ± 0.14 billion years (1σ), before moist-greenhouse water loss begins. The study identified the controls that its parameterized framework could not resolve: the magnitude and temporal evolution of the subduction and mantle-degassing redox fluxes that set Φ(Red) (compare Kadoya et al. 2020, who used mantle chemistry to argue volcanic gases became less reducing through time); the ambiguous net effect of reverse weathering, which prolongs CO2 availability while raising temperature under a brightening Sun; and organic haze, hypothesized to brake the magnitude of terminal deoxygenation or to produce oscillating oxygenation/deoxygenation cycles in the final habitable phase — a mechanism never simulated in a self-consistent coupled model. The model also used a 0-D climate (no explicit clouds or three-dimensional dynamics), which the authors regard as a defensible approximation of planetary climate on the million-to-billion-year timescales of the projection given its quantitative consistency with recent 3-D climate models, while noting that uncertain cloud feedbacks and continental configurations will modulate future projections; its land-plant CO2 minimum, UV sensitivity, and redox-dependent phosphorus recycling were sampled rather than mechanistically constrained.

Problem Statement

Determine, within a coupled biogeochemistry–climate framework, how the processes excluded or parameterized in the 1.08 ± 0.14 Gyr stochastic deoxygenation projection of Ozaki & Reinhard (2021) modify the timing, magnitude, and mode of Earth's terminal atmospheric deoxygenation — the point at which atmospheric O2 falls below 1% PAL. Concretely: (1) provide quantitative, temporally resolved constraints on the subduction and mantle-degassing fluxes of reducing and oxidizing species — the net reducing-power flux Φ(Red) — and their effect on the remaining lifespan of oxygenated atmospheric conditions; (2) resolve the net effect of reverse weathering, which prolongs atmospheric CO2 availability while elevating surface temperature under a brightening Sun, on the oxygenated-atmosphere lifespan; and (3) test whether organic-haze formation and its climate feedback brake the magnitude of terminal deoxygenation or produce oxygenation/deoxygenation cycles during terminal habitability, as hypothesized but never simulated in a self-consistent coupled model. In each case the question is how the control changes the projected evolution of atmospheric O2, with co-evolving CO2 and CH4, and hence the timing, magnitude, and mode of terminal deoxygenation relative to the 1.08 ± 0.14 Gyr benchmark; the source itself calls for evaluating these factors using more sophisticated biogeochemistry and climate models, while regarding its own 0-D energy-balance climate as a defensible approximation of planetary climate. Evaluate all three controls (1)–(3) within the same coupled biogeochemistry–climate framework and relate each to the 1.08 ± 0.14 Gyr benchmark. The demanded attributes of the deoxygenation target are: timing, the time at which atmospheric O2 falls below 1% PAL; magnitude, the depth of the terminal O2 decline (the minimum atmospheric O2 level reached, in PAL); and mode, the character of the decline — a single monotonic crash versus an oscillatory oxygenation/deoxygenation decline.

References

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