Understanding the evolution of Earth and potentially habitable Earth-like worlds is essential to fathom our origin in the Universe. The search for Earth-like planets in the habitable zone and investigation of their atmospheres with climate and photochemical models is a central focus in exoplanetary science. Taking the evolution of Earth as a reference for Earth-like planets, a central scientific goal is to understand what the interactions were between atmosphere, geology, and biology on early Earth. The Great Oxidation Event (GOE) in Earths history was certainly caused by their interplay, but the origin and controlling processes of this occurrence are not well understood, the study of which will require interdisciplinary, coupled models. In this work, we present results from our newly developed Coupled Atmosphere Biogeochemistry model in which atmospheric O$_2$ concentrations are fixed to values inferred by geological evidence. Applying a unique tool, ours is the first quantitative analysis of catalytic cycles that governed O$_2$ in early Earths atmosphere near the GOE. Complicated oxidation pathways play a key role in destroying O$_2$, whereas in the upper atmosphere, most O$_2$ is formed abiotically via CO$_2$ photolysis. The O$_2$ bistability found by Goldblatt et al. (2006) is not observed in our calculations likely due to our detailed CH$_4$ oxidation scheme. We calculate increased CH$_4$ with increasing O$_2$ during the GOE. For a given atmospheric surface flux, different atmospheric states are possible; however, the net primary productivity (NPP) of the biosphere that produces O$_2$ is unique. Mixing, CH$_4$ fluxes, ocean solubility, and mantle/crust properties strongly affect NPP and surface O$_2$ fluxes. Regarding exoplanets, different states of O$_2$ could exist for similar biomass output. Strong geological activity could lead to false negatives for life.
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