Diagenesis is an open-system process driven by consumption of Gibbs energy through lowering the extent of chemical disequilibrium between the sedimentary phases and surrounding environments, whether biologically mediated or not. Magnetite forms in the presence of dissimilatory iron-reducing bacteria when the pore water is supersaturated in magnetite according to standard thermodynamic principles6,7 and its formation is not microbially controlled8,9. Isotopic data for the Kuruman BIF requires extensive transport of Fe and C between the sediment and the supernatant water by infiltration of sea water and molecular diffusion through interconnected pore space10. In modern sapropels ocean CO2 concentration penetrates to a depth of about 15 cm in the sediment, from which point it increases more than tenfold downwards11. We conclude that the CO2 concentration in the sediment pore water would have been greater than or equal to the supernatant water. The suggestion by Dauphas and Kasting2 and Reinhard and Planavsky1 that diagenetic siderite formation was a closed-system process is not supported by the studies they quote, which call upon extensive communication with the supernatant water10,12.

Formation of BIFs depends not only on mechanisms for precipitation of solid Fe compounds but also on the transport efficiency of dissolved iron. The saturation constraints on and imposed by siderite and magnetite not only pertain to the BIF, but also to the water body supplying dissolved Fe to sedimentary basins, and thus couple directly to the atmosphere. We note that for our estimated range of the solubility of Fe in sea water is 1–3 μM, which is well within the range necessary for BIF formation13, while at the increased favoured by Reinhard and Planavsky1 and Dauphas and Kasting2 the maximum Fe concentrations are between two and four orders of magnitude lower and within the range of modern ocean water concentrations that preclude BIF formation. (We note that the 1–3 μM range covers the bare Fe2+ ion corrected for activity in sea water at siderite saturation with equilibrium constant for the reaction Fe2+ + CO2, g + H2O = FeCO3 + 2H+ calculated in SUPCRT (see ref. 5) and total Fe calculated using EQ3-6 (ref. 14) for siderite saturation in modern sea water, corrected to anoxic conditions and assuming pH = 8.25 buffered by basalt in accordance with ref. 15. See ref. 5 for thermodynamic conventions and data sources.)

Reinhard and Planavsky1 suggest that siderite and haematite can coexist at 0.1 nM H2 and in the range 30–100 PAL at 25 °C–35 °C, in accord with minimum H2(aq) metabolic constraints of dissimilatory iron-reducing bacteria and phase relations in Fig. 1 of ref. 5. This logic precludes the presence of magnetite in BIFs. Neglecting observed magnetite parageneses in BIFs and selecting a value of H2(aq) far below the stability field of magnetite does not provide a viable geochemical constraint. Dissimilatory iron-reducing bacteria metabolism may have occurred in BIF sediments during the Archean, but we are not aware of geochemical evidence suggesting that the metabolic activity of dissimilatory iron-reducing bacteria in BIF sediments controlled the composition of the Earth's fluid envelopes. On the contrary, the presence of magnetite and the mere formation of BIFs indicate that ambient ocean water had a molarity of H2 considerably greater than 10−10 M, conditions under which haematite is the only stable Fe oxide and Fe would be practically insoluble in ocean water, precluding aqueous iron transport sufficient to sustain BIF sedimentation.

It has never been controversial that there is a large uncertainty about Archean cloud forcing. Our hypothesis reiterates this specifically for an Earth with no continents, no continental dust, no land-plant-generated secondary organic aerosols and only a few other biogenic aerosols from a low-productivity ocean (0.1 to 0.25 times the present value16,17). The cloud physics are affected by an aerosol optical depth that probably showed much lower global values than today and should be evaluated using proper general circulation models. Goldblatt and Zahnle3 miss the point when focusing on dimethyl sulphide from a sulphur-poor Archean ocean and sea-salt aerosols, which seem to contribute only a few per cent of the free troposphere cloud condensation nuclei18.

The net cloud radiative effect of our model was (−18 W m−2) relative to −20 W m−2 from satellite estimates. Our calculations used19 an effective radius of cloud droplets of re = 17 μm (green solid line in Fig. 2d of ref. 5) (we note that although the legend mentions 20 μm, this was erroneous, and should have stated 17 μm; also, we showed the line for 30 μm to show no added effect at larger droplet sizes). Goldblatt and Zahnle’s later published calculations20 use more realistic clouds, which are not very different from ours. Our model values versus theirs19 were: re increase to 16.5 μm, 7 W m−2 versus 7 W m−2; enhanced rain-out, 15 W m−2 versus 4–15 W m−2; aqua planet, 6 W m−2 versus 5 W m−2; 1,000 p.p.m.v. CO2, 5 W m−2 versus 6 W m−2. Our methane contribution was a bit high (9 W m−2; ref. 17’s was 7 W m−2) and should probably be adjusted down to 0.3 × . Rain-out of low clouds (we made no change to high clouds) was calibrated to general circulation model results21, and an estimated forcing three times the re forcing18. Our calculations showed5, as subsequently stated by Goldblatt and Zahnle20, that “…precipitation feedback is of first order importance and must be treated carefully in any model addressing the climatic effect of changed particle size.”

We maintain that formation and preservation of magnetite-rich BIF could not take place under a high- atmosphere. Surface albedo and cloud changes would have significantly decreased the Earth’s albedo and reduced the greenhouse gas concentrations needed for clement conditions on the Earth. We do not claim to have provided a final and unique solution to the ‘faint young Sun paradox’, but rather demonstrate that the presence of liquid water on the young Earth can be explained within uncertainty by constrainable parameters and is thus not so paradoxical.