The Oxygen Valve on Hydrogen Escape Since the Great Oxidation Event

The Great Oxidation Event (GOE) was a $200$ Myr transition circa 2.4 billion years ago that converted the Earth's anoxic atmosphere to one where molecular oxygen (O$_2$) was abundant (volume mixing ratio $>10^{-4}$). This significant rise in O$_2$ is thought to have substantially throttled hydrogen (H) escape and the associated water (H$_2$O) loss. Atmospheric estimations from the GOE onward place O$_2$ concentrations ranging between 0.1% to 150% PAL, where PAL is the present atmospheric level of 21% by volume. In this study we use WACCM6, a three-dimensional Earth System Model to simulate Earth's atmosphere and predict the diffusion-limited escape rate of hydrogen due to varying O$_2$ post-GOE. We find that O$_2$ indirectly acts as a control valve on the amount of hydrogen atoms reaching the homopause in the simulations: less O$_2$ leads to decreased O$_3$ densities that reduce local tropical tropopause temperatures by up to 17 K, which increases H$_2$O freeze-drying and thus reduces the primary source of hydrogen in the considered scenarios. The maximum differences between all simulations in the total H mixing ratio at the homopause and the associated diffusion-limited escape rates are a factor of 3.2 and 4.7, respectively. The prescribed CH$_4$ mixing ratio (0.8 ppmv) sets a minimum diffusion escape rate of $\approx 2 \times 10^{10}$ mol H yr$^{-1}$, effectively a negligible rate when compared to pre-GOE estimates ($\sim10^{12}-10^{13}$ mol H yr$^{-1}$). Because the changes in our predicted escape rates are comparatively minor, our numerical predictions support geological evidence that the majority of Earth's hydrogen escape occurred prior to the GOE. Our work demonstrates that estimations of how the hydrogen escape rate evolved through Earth's history requires 3D chemistry-climate models which include a global treatment of water vapour microphysics.