This is an ambitious paper that attempts to follow up on the Goldblatt et al. (2006) analysis of the bistability of atmospheric O2 at times surrounding the GOE. The authors are to be commended for producing a 3-D coupled dynamical-chemical model of the atmosphere that is useful in many ways for testing the predictions of simpler 1-D photochemical models.

            That said, there are fundamental problems with the hypothesis put forward in this paper. The main one is that the authors have an incomplete understanding of the redox balance of the early atmosphere. They focus on the reaction between O2 and CH4 and on hydrogen escape, while largely ignoring such factors as organic carbon burial and the input of reductants (reduced volcanic gases and ferrous iron) to the system. To their credit, they begin the paper by writing out some of the important redox reactions. The two most important are eqs. (1) and (3)

CO2 + H2O + hv −> CH2O   + O2                                                                            (1)

2CH2O −> CH3COOH −> CH4 + CO2                                                                     (3)

The first of these reactions represents oxygenic photosynthesis. The second represents fermentation and acetogenic methanogenesis. What the authors do not do is to combine these together and consider the consequences. If one multiplies eq. (1) by 2 and add it to eq. (3), one gets (after cancelling out two CO2’s):

CO2 + 2H2O --> CH4 + 2 O2

In other words, if the CH4 is all coming from organic matter produced by oxygenic photosynthesis, and if none of the organic matter is buried, then CH4 and O2 are produced in stoichiometric quantities. CH4 can thus not be a net sink for O2, and vice versa. CH4 does indeed contribute to O2 production when it leads to hydrogen escape. But that process cannot cause O2 to accumulate, i.e., it cannot trigger the Great Oxidation Event (GOE), because as soon as O2 starts to accumulate, atmospheric CH4 decreases. To trigger the GOE, one needs for one of two things to occur: 1) Organic carbon burial must increase, producing more net O2, or 2) the abiotic sinks for O2, e.g., reduced volcanic gases and ferrous iron in the oceans, must decrease. These points are discussed in more detail in points 6-8 below. In the latter half of the paper, the authors do begin to consider the O2 sinks, which are represented by the variable ‘r’ in the Goldblatt et al. (2006) paper. But this part of the paper has other problems, as discussed in point (11).

            In revising their paper, the authors should read up on the concepts of atmospheric and global redox balance. One place to do this is in the 2017 book by Catling and Kasting (see point 6). That discussion is taken from Kasting, Chem. Geol. 362: 13-25, 2013, and that discussion, in turn, relies on a parameter, K_oxy, defined by Claire et al. (2006), referenced in the present manuscript. K_oxy represents the ratio of O2 source to O2 sinks, neglecting those that only arise after the atmosphere has become oxygenated, or that disappear at that time. The GOE is triggered when K_oxy becomes > 1. The terms in K_oxy have nothing to do with biogenic methane; indeed, even hydrogen escape does not enter into its definition.

            In summary, there are some good points to this paper. It is interesting to see the comparisons between 1-D and 3-D photochemical results. But it is important to frame the discussion properly and to not get confused about what is causing what. The mechanism discussed here cannot be the cause of the GOE, but it could potentially influence the question of O2 bistability, first pointed out by Goldblatt et al. (2006). Indeed, Fig. 15 makes it look like this phenomenon might largely disappear in 3-D. That is what I would focus on in the revision.

            You may reveal my name to the authors.

Detailed comments:

1. (l. 20) ‘During this event, the amount of oxygen increased from less than 10⁻⁵ present atmospheric level (PAL) to a maximum of 10⁻¹ PAL around 2.2 Gyr ago before stabilising approximately at 10⁻² PAL (Lyons et al., 2014).’

--This misstates the conclusions of Lyons et al. The upper limit on Mid-Proterozoic pO2 is more like 0.4 PAL, as that is when the deep oceans are predicted to become oxic. The pO2 range favored by Lyons et al. is actually well below 0.01 PAL. They consider values as low as 10^-4 PAL.

2. (l. 23) ‘In the Archean anoxic atmosphere, the sulfur photochemistry was responsible for mass-independent fractionation of sulphur isotopes in sedimentary rocks (Kasting et al., 1989).’

--A better reference for this statement is Pavlov and Kasting, Astrobiology 2: 27-41, 2002. This is the paper that explicitly studied mass-independent fractionation of S isotopes using a 1-D photochemical model.

3. (l. 26) ‘~0.01 PAL of oxygen is sufficient to generate enough UV shielding by ozone to block the sulfur photolysis (Zahnle et al., 2006).’

--Read Pavlov and Kasting (2002). 10^-5 PAL of O2 is sufficient to eliminate S-MIF production in the atmosphere. Shielding of SO2 from photolysis has little to do with this. Rather, it’s a question of how many atmospheric exit channels exist for sulfur.

4. (l. 30) ‘Consequently, the GOE likely induced a mass extinction for anoxygenic form of life, including heterotrophic methanogens (i.e. organisms producing methane).’

--Many microbiologists would argue that microbes never go extinct. They simply retreat to different habitats where they can continue their existence. Methanogens are poisoned by O2, yet they are ubiquitous in anaerobic soils (or in anaerobic chambers within animals) on the modern Earth.

5. (l. 34) ‘The decrease of the biological methane productivity and the methane photochemical lifetime could have reduced its abundance and thus its warming contribution, potentially triggering the Huronian glaciations that took place between 2.4 and 2.1 Gyr.’

--You might consider adding a reference to Kasting et al., Precambrian Res. 20: 121-148, 1983. This is not a new idea. Also in this paragraph, a good reference to greenhouse warming by methane is Haqq-Misra et al., Astrobiology 8: 1127-1137, 2008. Earlier calculations by Pavlov et al., JGR 105: 11,981-11990, 2000, turned out to be in error.

6. (l. 38) ‘Before the appearance of oxygenic photosynthesis, the redox state of the atmosphere was ruled by the balance between reductant fluxes from volcanism and metamorphism and the hydrogen atmospheric escape (Catling et al., 2001).’

--Well, these processes are important but other factors enter in, as well. One needs to consider both the atmospheric redox budget and the global (combined atmosphere-ocean) redox budget. See Catling and Kasting, Atmospheric Evolution, Cambridge Univ. Press, 2017, Ch. 8.

7. (l. 59) ‘CO2 + 2H2O −> CH4 + 2O2 −> CO2 + O2 + 4H(↑)’

--This reaction is somewhat misleading. If you leave out the intermediate products and cancel out the remaining CO2’s you are left with

            2 H2O --> O2 + 4 H(↑)

This is something that was going on well before the GOE. Water vapor photolyzes quite rapidly in the absence of UV shielding by O2 and O3. But in the Archean, something (volcanic gases plus other reductants like dissolved Fe+2) was taking up the resultant O2. You have to make organic carbon and bury it before atmospheric O2 can rise.

8. (l. 62) ‘But whatever precipitated the GOE, the rise of oxygen seems to be linked to an atmospheric instability caused by the formation of the ozone layer and its impact on the photochemical methane oxidation. Slowly increasing O2, by oxygenic photosynthesis, would have accumulate enough starting the ozone layer formation. The ozone layer provides a photochemical shield which limits the oxygen photochemical destruction leading to the methane oxidation. Therefore, the oxygen could have accumulated more easily, producing more ozone, shielding more efficiently the oxygen destruction and then rising an instability of growing oxygen until other processes would have limited the oxygen abundance, such as rock oxidation.’

--No references are given in this paragraph, although Goldblatt et al. (2006), referenced in the following paragraph, is responsible for this idea. You should reference them here. Also, keep in mind that the atmospheric instability identified by Goldblatt et al. cannot be the sole cause of the GOE. If it were, then the GOE might have occurred earlier than it did, given the evidence that cyanobacteria were around well before it. You still need either an increases in O2 sources (e.g., organic carbon burial) or a decrease in O2 sinks (e.g., reduced volcanic gases) to trigger the GOE. The methane feedback then amplifies that change and may make the system bistable, as Goldblatt et al. suggested.

9. (l. 91) ‘Halogen, heterogeneous and nitrogen chemistry is not taken into account due to the weak constraints available and considering its negligible effect on the oxygen chemistry studied.’

--I agree with you that halogen and heterogeneous chemistry can be safely neglected. I’m not sure I agree about nitrogen chemistry. Nitrogen photochemistry has been shown to play an important role in eliminating ‘false positives’ for life (i.e., high abiotic O2 levels) by catalyzing the recombination of CO and O to form CO2 (Harman et al., ApJ 866:56, 2018). This paper was concerned with NOx species produced by lightning within the troposphere. The same chemistry could conceivably be important in the development of the GOE on early Earth.

10. (l. 139) ‘We ran the 1D model until steady state for a range of O2 vmr from 10⁻⁷ to 10⁻³ and CH4 vmr from 10⁻⁶ to 10⁻³.’

--What do the vertical profiles of O2 look like in these models? In my own 1-D photochemical models, O2 is never well mixed once its surface mixing ratio goes below about 10^-4 PAL, or roughly 10^-5 by volume. See, e.g., Kasting and Donahue, JGR 85: 3255-3263, 1980, Fig. 3. ..Ah, I got down further in the paper. You show O2 profiles in Fig. 6. It is well mixed at fO2 = 10^-3 but not at fO2 = 10^-7. We are in agreement!

11. (l. 213) ‘Figure 11 shows FCH4 (equivalent to ½ FO2) as a function of surface temperature.’

--This figure shows only the photochemical effect of changing the surface temperature. But at surface temperatures below 273 K, the oceans would be frozen and most of the methanogens would be dead, so there wouldn’t be any biogenic methane.

--The entire second half of the paper suffers from the same problem. The authors are trying to determine the effects of surface temperature on atmospheric oxidation. But they only consider the effect of temperature on the O2-CH4 reaction rate. That neglects the much bigger effect of surface temperature on the methane production rate. This would be a fatal flaw of their hypothesis even if the CH4 sink for O2 was the only one that needed to be considered. But the real problem is more complicated, as discussed elsewhere in this review.

This manuscript concerns the Great Oxidation of Earth’s atmosphere, with one of the first treatments of the chemistry in a GCM, and discusses possible links to the Palaeoproterozoic glaciations. The manuscript uses a mix of 3-D and 1-D photochemical modelling, and additionally uses a simple box model to explore some of the implications of the photochemical modeling results. These two methods are quite different, so I have separated my review into two parts to address them both.

The manuscript is on a very interesting topic, and uses an appropriate set of methods. I recommend that it will be suitable for Climate of the Past after suitable revision.

Photochemical modelling

Summary comments: I’m really happy to see some 3-D work on the oxygen photochemistry, but I think the presentation of the 3-D results is quite lacking, so the (no-doubt) interesting results from the modelling work are not made available to the reader! Also, much of the work presented and used in the manuscript is actually from a 1-D model, and clearer distinction of this needs to be made. Statements about code availability, sufficient explanation of the methods to realistically enable reproduction, and an archive of model output are needed.

There is not sufficient information in the methods to allow the work to be repeated. Via online repositories of code and/or machine-readable supplementary information, it is now possible to make modelling work genuinely reproducible. This should be done. If for some reason this cannot be done, an exceptional justification is necessary. There is no statement about the availability of the codes used in the manuscript, which is necessary (are the codes open source? If not, how can they be acquired?). Complete sets of inputs need to be provided (what are the actual boundary conditions for each model run – e.g. what fluxes of which reductants are used?). A machine readable version of Appendix A should be included. Some details are vague (e.g. line 108 speaks of an eddy diffusion coefficient, whereas typically a vertical profile of these are used) – all details need to be clear.

There no archive of model outputs, which should be important, especially for the GCM runs which are very costly to produce. I would recommend, in the strongest terms, that authors make their data (model output) available following FAIR principles (https://www.go-fair.org/fair-principles/). Providing this to other researchers will add significant value to the manuscript.

The photochemical models use fixed mixing ratio boundary conditions at the surface. An excellent recent paper by Gregory et al. (2021) compares fixed mixing ratio and fixed flux boundary conditions, and concludes that fixed flux boundary conditions are preferable. This should be discussed, and the approach used here justified in that context, including discussion of any bias that fixed mixing ratio boundary conditions might introduce.

You note that the ozone column is large in 1-D (line 150). Is this a genuine difference between 1-D and 3-D approaches, or is your zenith angle simply poorly tuned in the 1-D model, given knowledge of the 3-D results?

The justification for using methane fluxes as a proxy for oxygen fluxes (line 163-4) is not clearly justified. Use of molecular oxygen to oxidize CO (which I suspect you include as a boundary condition) would plainly be an oxygen loss. You need to be clearer about why this is excluded.

Overall, I found the presentation of the results from the 3-D modelling a disappointment. There is only one figure which shows anything other than global means (Fig 5, which shows vertically resolved zonal means). Surely there are actually some interesting results in 3-D?! Conversely, if there really are not, then it would be a great service to the community to robustly make the case that 3-D models are quite unnecessary for this problem, so that no-one else need bother!

To be clear here: I strongly recommend more detailed presentation of the results from the GCM. For example, the questions that I would start with are: What is the model climatology of ozone and water vapour above the tropopause, and how does this compare to climatology? What is the model Brewer-Dobson circulation, and how does this compare to climatology? Note that this may well affect the ozone distribution, and how the rates differ from 1-D. How do these change with model temperature? Is there any feedback between changed ozone levels and the climate?

I am a little surprised by how cold the stratosphere gets. Does your radiation scheme include near-IR absorption by methane, which has been shown to cause significant warming in 1-D models (Byrne & Goldblatt, 2015)? Also, note that at line 205 you refer to 220 and 280K, whereas Figure 12 shows results for 260 and 280K.

In appendix B, dominant photochemical pathways are presented. However, there is no discussion of the methods by which they were found, which is necessary. As with all the methods, this discussion should be sufficient for these to be reproducible, including reference to the codes used. There is no substantial discussion of these in the text of the manuscript, which would be important to contextualize them.

There has been prior work that has used 3-D models to examine atmospheric oxygen photochemistry, which should be referenced (e.g. Cooke, 2022).

Minor comments

Line 103: Orbital period in days is confusing if day length is changed.

Eq 6: Use a symbol in place of ‘dens’

Line 139: define vmr

Line 140: “These results are consistent with the previous study by Zahnle”: if you are making this point, you must show this to the reader. Include results from Zahnle in your graph (scrape from his graphs if necessary).

Figure 4: is too small to read – make bigger, for readers with older eyes! Also, the x-axis is truncated before -10^-16, which appears to mean that much of the structure is lost for low oxygen runs; show these lower magnitudes too.

Line 188: What do you mean to imply with “the tropospheric temperature profile follows a moist/dry adiabat”? That it is prescribed as such?! Presumably the GCM has more physics than that? Or are you talking about the 1-D model here?

Line 213: ‘decade’ means 10 years. Do you mean ‘order of magnitude’?

Line 211-228: This paragraph run-on, and becomes difficult to follow. Suggest improve the  paragraph structure for the benefit of the reader.

Line 233: Suggest alternate phrasing for clarity: “Temperature appears to have a significant impact on atmospheric loss”.

Box model

Summary comments: Use of the simple model is a nice way to contextualize the implications of the photochemical modelling work. However, I have some concerns about the parametrizations chosen, and the conclusions thus drawn.

Re original model by Goldblatt et al (2006). Unfortunately, the polynomial fit constants were truncated in the manuscript, but more decimal places are needed. Use p = { 0.0030084, -0.1655405, 3.2305351, -25.8343054, 71.5397861} to reproduce the result shown (I’m sorry about this!). Note also that the value of hydrogen escape coefficient was calculated incorrectly in the original manuscript; the correct value is s = 3.7e-5, but that doesn’t have a very big effect (see Goldblatt, 2008, if a reference is needed for that; there is also a bonus chapter on the model there which might be interesting to you).

The original model is modified with parameters to make the methane oxidation rate smaller and the primary productivity bigger. I understand the motivation of the former, but not the latter, given that N is a variable in the original model, not a constant or function. Why not simply talk about increasing N? Results for changing N are presented in the original manuscript, so the result that higher productivity gives more atmospheric oxygen is not novel.

Please be clear about what results came from your 3-D GCM, and which came from your 1-D column model (a 1-D model is not a GCM: do not refer to it as such! See lines 272 & 284 and Fig 15). Note also, line 272, 1-D and 3-D results were shown to be similar, not “identical”.

You argue (line 284) that oxidation is faster with interpolated model results, not the parametrization. This does not appear to be strictly true; I think you actually show that steady state oxidation levels (which are essentially what you are showing) are more sensitive to r, where r varies with time over very long timescales. I recall the actual great oxidation in the simple model takes only about 10,000 years.

Please explain why oxygen levels are shown to be constant at low oxygen and high r in Figs 15 & 16. My guess is that this is bogus: that you have used a constant value of your oxidation rate below 10^-7 O2, where you do not have model results, which would be erroneous. Either some extrapolation of results is needed, or do not show your results at such low oxygen levels.

You state (line 299) that a reduced methane flux at higher oxygen levels is not treated in the model. This is functionally incorrect, as the methane flux is a very strong function of oxygen via parameters d and g (while the words used in the paper were about organic carbon available to methanogens, and consumption by methanotrophs, the effect is functionally as you seek!).

The realism of the scenario of altering productivity and methane oxidation rate, and the relative timing of these (e.g. Fig 20) need to be justified. What motivates the very long period of high productivity, starting before the glaciations? Why do you show four glacial periods (see, for example, Gumsley, 2017)? In the glacial periods, you keep productivity the same, whereas most people assume that synglacial productivity is much reduced. This is important, because reduced productivity would more than offset the effect of slower methane oxidation.

Figure 18 should be compared to the geological record. Perhaps plot the carbonate record? This gives an opportunity to test your results.

You assert that methane would produce a substantive greenhouse effect, and reduction of this could lead to glaciation (e.g. lines 33, 324, 341), but these comments are not supported. There has been some historical misunderstanding about the strength of this, owing to erroneous results twenty years ago. Recent papers should be consulted, based on which a quantitative estimate can be made of how strong an impact this is (e.g. Haqq Misra et al, 2008; Byrne and Goldblatt, 2014; Byrne and Goldblatt, 2015). I am rather doubtful that the radiative forcing from methane would exceed that from changes in carbon dioxide (not modelled!). I am extremely doubtful that methane would have cause cycles, and have a stronger effect than known cycles or carbon dioxide (e.g. Mills et al, 2011) – though, of course, if you could make the case, then I would be fascinated!

Minor comments

Fig 13: r and Fw are shown with the same line type! Show with different line types or colour.

Line 318: The Archean-Proterozoic transition is defined (presently) by a GSSA at 2500Ma. The glaciations, and the Great Oxidation, are thus Palaeoproterozoic (Siderian) age.  

General: you use the terms “over-abundance” of methane or oxygen, whereas I think you simply mean “higher”. “Over-abundance” implies some value judgement, which is not transparent.

References:

Byrne, B. and Goldblatt, C.: Radiative forcings for 28 potential Archean greenhouse gases, 10, 1779–1801, https://doi.org/10.5194/cp-10-1779-2014, 2014.

Byrne, B. and Goldblatt, C.: Diminished greenhouse warming from Archean methane due to solar absorption lines, 11, 559–570, https://doi.org/10.5194/cp-11-559-2015, 2015.

Cooke, G. J., Marsh, D. R., Walsh, C., Black, B., and Lamarque, J.-F.: A revised lower estimate of ozone columns during Earth’s oxygenated history, 9, 211165, https://doi.org/10.1098/rsos.211165, 2022.

Goldblatt, C. Bistability of atmospheric oxygen, the Great Oxidation and climate, PhD Thesis, University of East Anglia, 2008. (http://www.colingoldblatt.net/files/goldblatt_thesis_final.pdf)

Goldblatt, C., Lenton, T. M., and Watson, A. J.: Bistability of atmospheric oxygen and the Great Oxidation, 443, 683–686, https://doi.org/10.1038/nature05169, 2006.

Gregory, B. S., Claire, M. W., and Rugheimer, S.: Photochemical modelling of atmospheric oxygen levels confirms two stable states, Earth and Planetary Science Letters, 561, 116818, https://doi.org/10.1016/j.epsl.2021.116818, 2021.

Gumsley, A. P., Chamberlain, K. R., Bleeker, W., Söderlund, U., Kock, M. O. de, Larsson, E. R., and Bekker, A.: Timing and tempo of the Great Oxidation Event, PNAS, 114, 1811–1816, https://doi.org/10.1073/pnas.1608824114, 2017.

Haqq-Misra, J. D., Domagal-Goldman, S. D., Kasting, P. J., and Kasting, J. F.: A Revised, Hazy Methane Greenhouse for the Archean Earth, 8, 1127–1137, https://doi.org/10.1089/ast.2007.0197, 2008.

Mills, B., Watson, A. J., Goldblatt, C., Boyle, R., and Lenton, T. M.: Timing of Neoproterozoic glaciations linked to transport-limited global weathering, Nature Geosci, 4, 861–864, https://doi.org/10.1038/ngeo1305, 2011.

Note: For abundance of clarity, I’d like to let the authors know that my group has also been working on a paper on temperature effects on the Great Oxidation. A student has been working on this since Sept 2020, and had all their results before I saw your manuscript. Our paper will be submitted in March/April 2022. I have not cross referenced the two manuscripts while reviewing.