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The low O2 content of the Archean atmosphere implies that methane should have been present at levels approximately 10(2) to 10(3) parts per million volume (ppmv) (compared with 1.7 ppmv today) given a plausible biogenic source. CH4 is favored as the greenhouse gas that countered the lower luminosity of the early Sun. But abundant CH4 implies that hydrogen escapes to space (upward arrow space) orders of magnitude faster than today. Such reductant loss oxidizes the Earth. Photosynthesis splits water into O2 and H, and methanogenesis transfers the H into CH4. Hydrogen escape after CH4 photolysis, therefore, causes a net gain of oxygen CO2 + 2H2O --> CH4 + 2O2 --> CO2 + O2 + 4H(upward arrow space). Expected irreversible oxidation (approximately 10(12) to 10(13) moles oxygen per year) may help explain how Earth's surface environment became irreversibly oxidized.
Catling et al. (Fri,) studied this question.