This is a useful systematic discussion of different ways of assessing the climate impacts of hydrogen emissions. I have no objection to it being published following modification and clarification, although overall many of the qualitative results could have been anticipated from discussions of the climate impacts of short-lived forcers, compared to CO2, already in the literature

However, I struggled with the motivation. It is tied closely (in the title) to the Ocko and Hamburg (OH) paper, and the prime reason for doing this appears to be an objection to OH’s use of a GWP assuming constant emissions. This objection (which I have sympathy with, although I find OH to be an otherwise very useful paper) only really comes out in the Discussion and Conclusions. It is only tangentially referred to in the Abstract, and not in a negative sense. I think the direct connection (in the title) to OH could be removed, without affecting the content, making this a more general discussion of how the perception of hydrogen climate impacts varies depending on the adopted framework.

Comments

Lines 19-26: I agree with all written here, but it is presented as if it is new.  I believe these points are clear and well established from the previous extensive literature on comparing climate impacts of emissions of short and long-lived forcers. The wording should be changed to indicate this and more reference to this previous literature would be appropriate in the paper as a whole. This way, the reader can separate out what is new in this paper and what is already known.

Lines 111 and 113: This discussion (coupled with lines 330-342 – see later) is confused and unhelpful for what (line 13) purports to be “a step-by-step tutorial”. Instantaneous radiative forcing (line 111) has a specific definition relating to the absence of any physical adjustment (with stratospheric temperature adjustment or full (ERF) adjustment) and so is inappropriate here. The adjustments referred to on line 113 are long-established chemical adjustments (ozone and stratospheric water vapor – including stratospheric temperature adjustment as I understand it) but for some reason this is not made clear to the reader.

Line 149: Apologies if I miss the obvious, but I cannot derive Equation (12d).  It seems to imply that Equation (7b) with H replaced by t is (H-t) times Equation (6b), which it isn’t.

Lines 161-162: “better reflect the underlying conceptual model”. I cannot make sense of this. As I understand it, this paper adopts a different conceptual model (pulse emission from time zero) compared to Fuglestvedt et al. (2010 10.1016/j.atmosenv.2009.04.044). They adopted a 1-year emission, rather than an instantaneous pulse, with a stated aim of reducing time of year dependence for short-lived species. Of course, that conceptual model is open to question, but their equations (noting the interesting comment at Lines 31-32 in Text S1) reflect their conceptual model. I agree that the differences reflect the different underlying conceptual models, but the “better” seems too far of a reach.

Line 194: You need to state the units of the quantities in these equations. Nowhere prior to this are we told that t is in years.

Lines, 194, 207 etc: I wondered why the asterisks suddenly appear in these equations.

Line 195-201: Since these equations are only used in the SI, I suggest they are moved there so as not to burden the main text.

Lines 206 and 209: “emissions” is used on one line and “leakage” on another. Be consistent. I think “leakage” is better in both. Are the leakage rates assumed independent of time?

Line 235: “very beginning” is not correct for the temperature response

Lines 239-241: I did not understand this. If methane (M=16) is affected, then H2 (M=2) should be more affected. Section 8.SM.11.3 of the Supplementary Material to Myhre et al. (2013) outlines the methodology for ppb to kg conversions. Using this, I couldn’t reconcile the numbers in Figure S2. Again, apologies if I miss the obvious.

Lines 254-257, 293-295, 368-369 and elsewhere: These statements are all consistent with the Allen et al. (2009) cumulative emission framework and I wonder why this prior understanding is never acknowledged.

Lines 330: “More important uncertainties”. There are others not referred to here, including the impact of fossil-fuel co-emissions (such as ozone and aerosol precursors) and possible role of where emissions occur, known to be important for some short-lived forcers. In addition, the possible role of oxidant-related aerosol forcing needs alluding to (e.g., O’Connor et al. https://doi.org/10.1029/2022MS002991)

Lines 330-344: This seems confused. On line 330, the fast adjustments referred to are the fast chemical (ozone, strat water vapor) adjustments. The adjustments on line 332 are the physical adjustments that act beyond (or in concert with) these adjustments and are functionally strongly related to the efficacy implied in lines 340-342.

Lines 369-370: “not captured”? Why is it not captured by the GTP? Figure 1 seems to capture it very well.

Line 379: Several of the points here are not new and have been well represented in the literature discussing the climate impacts of short-lived forcers compared to CO2. e.g., Lines 384-387, 393-396 (e.g., Fuglestvedt et al. 2010; Allen et al. 2016 and references therein). Some change of wording is needed to make this clear.

Figure 2 and 3: The font on the y axes of these is too small. I am not sure all this text is needed as long as it is clear in captions and legend.

Tables S1, S2 and S3: The units of AGWP and AGTP need attending to.

Other comments

1. The references to both Ocko & Hamburg (which only points to ACPD rather than the ACP version) and Warwick et al. are incomplete in both the main text and Supporting Information.
2. The front page of the AR5 Chapter 8 makes it clear that it should be cited as Myhre et al. (2013) not Myhre et al. (2014).
3. This is not meant to be a hostile comment. The authors claim no competing interests, but the second author lists a commercial “net zero” company as a second affiliation. As I understand ACP’s competing interests policy, this should be declared. Or perhaps it is already enough that it is declared in the affiliations? This is for the Editors.
4. I wondered why the authors adopted AR5 rather than AR6 methodologies (e.g., on the indirect chemical forcing for methane). Consistency with OH?

Review of acp-2022-810

This long and somewhat tedious algebraic expansion of ordinary differential equations used to describe atmospheric chemistry and global warming begins on the wrong foot, and fails to produce any enlightening results.  In the Discussion and the Conclusions, the paper reiterates well established facts about greenhouse gas warming and draws mainly policy conclusions.  It does not really belong in a science journal like ACP.

This is written as a commentary on Ocko and Hamburg’s 2022 paper.  At 18 pages of text, this is hardly a Commentary.  The authors propose that this work goes way beyond Ocko and Hamburg because it considers impacts out to 500 years does not make sense to this reviewer because any of the impacts of CH4-H2 emissions disappear after 4-5 decades.  Admittedly fossil carbon counts as CO2 does accumulate, but that is a different accounting and does not need the following of H2 and CH4 as done here. Thus integrating their equations out 500 years depends solely on the scenario for future technology and energy use at year 2600.  This is not a scientific issue. 

Their step-by-step tutorial might be useful somewhere if they had not missed the point entirely about indirect greenhouse gases (CO, H2) and chemical feedbacks (CH4).  The authors demonstrate a basic lack of knowledge of the first principles of atmospheric chemistry.  The concept of steady state and how it relates to the pulsed emissions is well known but seems to be overlooked here (e.g. lines 22-23).  From the start (e.g., equation 1-3) the authors miss the point that their ‘taus’ are not constant but through chemical feedbacks depend on the second-order terms.  Moreover, the budget lifetime used in the continuity equations (‘tau’) is most often NOT the time scale for decay of a perturbation. 

This manuscript is clearly not a tutorial. The concept of perturbation lifetime, budget lifetime and timescales is well known.  As is the decomposition of the decaying perturbation into a sum of exponential decays as is done for CO2.  See for example,

IPCC WGI AR4 7.4.5.2

AR5 8.2.3.3

AR6 7.6.1.1, 7.6.1.5

Holmes, C. D. (2018). Methane feedback on atmospheric chemistry: Methods, models, and mechanisms. Journal of Advances in Modeling EarthSystems,10, 1087–1099. https://doi.org/10.1002/2017MS00119

Fuglestvedt, J. S., Isaksen, I., & Wang, W.-C. (1996). Estimates of indirect global warming potentials for CH4, CO and NOx.Climatic Change,34(3–4), 405–437.

Prather, M. (1994). Lifetimes and eigenstates in atmospheric chemistry.Geophysical Research Letters,21(9), 801–804. http://doi.org/10.1029/94GL00840

Prather, M. J. (2007). Lifetimes and time scales in atmospheric chemistry.Philosophical Transactions of the Royal Society A,365(1856), 1705–1726. http://doi.org/10.1098/rsta.2007.2040

Nguyen, N. H., Turner, A. J.,Yin, Y., et al (2020). Effects of chemical feedbacks on decadal methane emissions estimates. Geophysical Research Letters, 47, e2019GL085706. doi.org/10.1029/2019GL085706.