  The early Earth's environment is controversial. Climatic estimates range from
hot to glacial, and inferred marine pH spans strongly alkaline to acidic.
Better understanding of early climate and ocean chemistry would improve our
knowledge of the origin of life and its coevolution with the environment. Here,
we use a geological carbon cycle model with ocean chemistry to calculate
self-consistent histories of climate and ocean pH. Our carbon cycle model
includes an empirically justified temperature and pH dependence of seafloor
weathering, allowing the relative importance of continental and seafloor
weathering to be evaluated. We find that the Archean climate was likely
temperate (0-50 {\deg}C) due to the combined negative feedbacks of continental
and seafloor weathering. Ocean pH evolves monotonically from 6.6 (+0.6,-0.4)
(2{\sigma}) at 4.0 Ga to 7.0 (+0.7,-0.5) (2{\sigma}) at the Archean-Proterozoic
boundary, and to 7.9 (+0.1,-0.2) (2{\sigma}) at the Proterozoic-Phanerozoic
boundary. This evolution is driven by the secular decline of pCO2, which in
turn is a consequence of increasing solar luminosity, but is moderated by
carbonate alkalinity delivered from continental and seafloor weathering.
Archean seafloor weathering may have been a comparable carbon sink to
continental weathering, but is less dominant than previously assumed, and would
not have induced global glaciation. We show how these conclusions are robust to
a wide range of scenarios for continental growth, internal heat flow evolution
and outgassing history, greenhouse gas abundances, and changes in the biotic
enhancement of weathering.
