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Various proxies and numerical models have been used to constrain O₂ levels over geological time, but considerable uncertainty remains. Previous investigations using 1-D photochemical models have predicted how O₃ concentrations vary with assumed ground-level O₂ concentrations, and indicate how the ozone layer might have developed over Earth history. These classic models have utilised the numerical simplification of fixed mixing ratio boundary conditions. Critically, this modelling assumption requires verification that predicted fluxes of biogenic and volcanic gases are realistic, but also that the resulting steady states are in fact stable equilibrium solutions against trivial changes in flux.

Here, we use a 1-D photochemical model with fixed flux boundary conditions to simulate the effects on O₃ and O₂ concentrations as O₂ (and CH₄) fluxes are systematically varied. Our results suggest that stable equilibrium solutions exist for trace- and high-O₂/O₃ cases, separated by a region of instability. In particular, the model produces few stable solutions with ground O₂ mixing ratios between 6×10−7 and 2×10−3 (3×10−6 and 1% of present atmospheric levels). A fully UV-shielding ozone layer only exists in the high-O₂ states. Our atmospheric modelling supports prior work suggesting a rapid bimodal transition between reducing and oxidising conditions and proposes Proterozoic oxygen levels higher than some recent proxies suggest. We show that the boundary conditions of photochemical models matter, and should be chosen and explained with care.