  The history of molecular oxygen (O$_2$) in Earth's atmosphere is still
debated; however, geological evidence supports at least two major episodes
where O$_2$ increased by an order of magnitude or more: the Great Oxidation
Event (GOE) and the Neoproterozoic Oxidation Event. O$_2$ concentrations have
likely fluctuated (between $10^{-3}$ and $1.5$ times the present atmospheric
level) since the GOE $\sim 2.4$ Gyr ago, resulting in a time-varying ozone
(O$_3$) layer. Using a three-dimensional chemistry-climate model, we simulate
changes in O$_3$ in Earth's atmosphere since the GOE and consider the
implications for surface habitability, and glaciation during the
Mesoproterozoic. We find lower O$_3$ columns (reduced by up to $4.68$ times for
a given O$_2$ level) compared to previous work; hence, higher fluxes of
biologically harmful UV radiation would have reached the surface. Reduced O$_3$
leads to enhanced tropospheric production of the hydroxyl radical (OH) which
then substantially reduces the lifetime of methane (CH$_4$). We show that a
CH$_4$ supported greenhouse effect during the Mesoproterozoic is highly
unlikely. The reduced O$_3$ columns we simulate have important implications for
astrobiological and terrestrial habitability, demonstrating the relevance of
three-dimensional chemistry-climate simulations when assessing paleoclimates
and the habitability of faraway worlds.
