This paper deals with the global hydrogen budget. An important subject acknowledging potential leakages in large scale deployment of hydrogen in the energy transition. First, the paper presents an evaluation of a multi-model ensemble that simulated the global hydrogen budget. Second, a box model is tuned on the global models, and the global budget is constrained by the observed hydrogen isotopic composition. The authors claim to have tightened the atmospheric hydrogen production, potential geological sources, and the soil sink.

Although the subject and the employed methods are interesting, I find the paper rather messy (e.g. typos, overall structure) in its current state. Moreover, the overall claim that the geological sources are constrained to < 9 Tg H2/yr is not very well substantiated. Below and in the attached annotated pdf file I provide more detailed comments.

Global model evaluation

The different parts in the manuscript are not very well connected. The paper starts with an evaluation of the global models, showing comparisons to CHCO, NO2 and CO satellite data. The paper remains rather vague here. I read that the model is forced to H2 (and CH4) surface observations, and that the soil sink is tuned to reproduce reasonable hydrogen concentrations. This seems a double constraint, and it remains unclear how that impacted the H2 budget. Moreover, no detailed H2 budget terms are presented here (used in the box model?), and the model evaluation is limited, showing figures with many panels that are not very informative. Moreover, in comparing to NO2 (and CHCO) satellite products, Averaging Kernels (AK are important, as well as co-sampling. The authors acknowledge this (and use 3 hr output still without AK). According to me, this evaluation does not add much current knowledge (and the results presented in Sand et al. (2024)). If anything, the model results could be used to estimate the uncertainty in the OH sink and other uncertainties in the H2 budget.

Box model

The box modelling is an interesting way to constrain the H2 budget. But the way the box model is presented and used needs improvement. First, it seems that the starting condition in the box model is not consistent, specifically for the “lifetime 3” case (which should be lifetime 2, but there are many of these mistakes). Second, it is unclear how the H2 budgets differ in the models (needs to be part of the global model evaluation). More detailed information is needed why the isotopic composition differs in the ACM-based box models. Some reasons are given, but this is actually a good way to give the ACM results a decent place in the manuscript. Third, large geological sources are considered unlikely, but I think this is an overstatement of the ability of the box model. Figure 9 is rather misleading, because this show the geological result of the -1000 ‰ signature (at least if I trust Figure A5). Furthermore, Figure 10 suggest that the impact of geological emissions on the isotopic composition is opposite to the effect of OH oxidation. This would imply that a stronger OH sink could compensate for the geological emissions. However, the OH sink is not included in the re-tuning of the model. The soil sink is included, but the soil sink does not enrich the atmosphere.  I would suggest allowing the OH-sink to vary at least over the ACM results (you write: There is a larger diversity in OH indicating more uncertainty and a bigger spread for atmospheric losses).

Other issues

The box model should account for the enrichment of H2 due to inflow of stratospheric air. The authors mention that this can account for a 29-37‰ offset in δD. This is not particularly large but introduces a bias. Overall, I earlier pointed to the work of Pieterse et al., to which the paper refers to now. However, I would expect some further discussion, e.g. about the used isotopic values (Figure A4 looks quite different).

Krishnan et al report on a combined analysis of box and global model simulations with the overall aim of quantifying and reducing uncertainty in the tropospheric budget terms of hydrogen. This is an important topic and their use of isotopes is nice. However, the paper as it currently stands does little in i) critically evaluating the models that we are using to define the budget terms ii) systematically exploring uncertainty in these terms. As a result the authors are unable to significantly constrain any of the budget terms -- albeit that they report that the geological source of H2 must be much lower than 20 Tg/yr (which I don't doubt). 



I would be happy to review a revised paper but I would suggest that the authors focus on the following two major areas in a re-submission: 

1) more critical analysis of the models against observations. Presently the model-obs comparison is rather qualitative. From my understanding of the data, the models and observations are all simulating (observing) different time periods. How can this alias the interpretation? What can be done to minimise this? 

2) we have large uncertainties in a number of terms within the hydrogen budget and there are more elegant ways to explore this joint uncertainty than a series of case studies focusing on high and low end member combinations. It would be interesting to see your box model results if you were to span the range of uncertainties. You could even weight some of these sources of uncertainty by using the results shown in Figure 11, for example. 

Minor points to address:

Line 19: I disagree that the lack of global-scale knowledge of the abundance of OH is the key point here. 

Line 20: Caps for Atmos. Chem. Models but no definition of the ACM acronym. 

Line 21: Hyphens used when it should be em dashes. 

Line 24: Caps used for VOC but VOC not actually defined. 

Line 25: Isotopic composition of what?

Line 33: Define today. 

Line 37: Define VOC and NMVOC.

Line 49: Typo --> release(s)

Line 55: Is this O(1D) + H2O -> H2 + O2 source in any models? My reading of Zellner et al. (1980) suggests that the reaction involved is H + OH -> H2 + O, which I think would only happen in the stratosphere. 

Line 60: typo 2->20? 

Line 71: Please explain a bit more for the general reader what the positive value of delD means (enriched, depleted etc). 

Line 74: "produced H2" sounds odd to me. I suggest a change. 

Line 75: "(Piet.." -> "Piet.. (see marked up pdf). 

Line 78: Define ACM

Around Line 90: I suggest to add in something about H2 yields here also being uncertain. 

Line 99: Suggest adding in "Here". 

Line 148: Delete "which varies between models"

Line 150: How are these calculated? And are they used? Later it is implied that this split is not available. 

Line 162: Is there a reference for this? 

Line 182: What about uncertainty in J(HCHO->H2+CO)? 

Figure 1: Please plot % difference model-obs and the obs using different colour scales to help readers make clear distinctions of areas of difference. For the caption make clear the difference between the observation time period and the model data time period. 

Figure 2: Would it not make more sense to integrate/sum the data? After all the budget terms are totals so why not do the same here? If not, what are the error bars on these averages? 

Line 205-208: Re-word. 

Line 209: Unclear what Figure A3 is showing. See later comment. 

Line 213: Change supplementary to Appendix

Figure 3: Too many plots all together. I suggest splitting this up and again focusing on the obs data and deviations from it (%?) using different colour scales. If the multi model mean is important please show that too and also the % standard deviation in the multi model mean so that spatial features of uncertainty can be highlighted. 

Figure 4a: How useful is the NO2 comparison given the huge impacts of the 3hr vs monthly mean sampling difference shown for OsloCTM3. The difference from sampling is larger than the multi-model range. 

Figure 4b: The difference between MOPITT and TROPOMI is maybe 30% (by eye) of the standard deviation of the multi model mean. In other words observational error means we can only constrain a fraction of the model variance, right? This point is not made very clearly. 

Line 251 and 253: Make clearer what the control and test cases are by adding the details to a table (maybe Table 2?). 

Figure 6: Make clearer what the fraction (ratio) is/means. 

Line 267: How did you implement the TAR formula? It shows a delta OH so what is the reference [OH] at t0?

Section 3.4: My understanding here for the isotope work is that you are modelling 2010 conditions? Make clear. 

Figure 8: Could a ternary plot help visualise the impact on delDatmos to [H2] and [CH4] which seem to vary in all the studies? Or is there a way to normalise the y-axis ([CH4]/[H2])? With so much scatter it's hard for the reader to draw anything useful from this. Would marginal PDFs help the reader? It seems like the brown circles median is around 100permil and the blue triangle mode is around 150permil (closer to the black cross). So does that mean the newer models are better? 

Figure 8 caption: delete "possibly" and the end of the caption: "suggests..."

Line 309: Add in "the"? 

Table 2: Make clear the base year. 

Figure 9: I think in b you can drop "iso" in the labels. In panel d I take it you can't plot a violin plot because you only have four points per bar? The text in the caption for panel d is unclear. Change. 

Line 326: By design this should be the case no?

Line 332: Expand on this please. See my major concern and consider a more formal uncertainty assessment. 

Figure 10: Caption. Change dry dep -> soil sink. Should the y-axis label be "dH2 (ppb)" 

Aside: please replace ppbv with ppb and on first using make clear you mean the mole fraction (nmol/mol of dry air). 

Line 355: Unclear what you mean. 

Line 367: Change "observed" -> "documented". Add "the" 

Figure 11: Make clear what "model values" refers to. I would also encourage a table being added (SI?) with the sources of data used in generating this plot. 

Line 382-383: See the marked up typos. 

Line 393-394: See the marked up typos. 

General comment: When discussing the conclusions and your new constraints it would help to remind the reader of where we started from before this work so we can understand how well constrained we are now. 

Figure A1: Limit the min of the y-axis to 10 ppt

Figure A1 and A2: See comment on pdf. I feel like more should be drawn to the models than the observations so suggest grey symbols for the observations and the models overlaid on top of them. Or, do more detailed analysis of the models and obs. 

Figure A3: I think the key plots are columns a and b, no? What's the point of the other columns? 

Figure A4: Pretty pointless without helping the reader see how the dD values have changed. 



References: 

Zellner, R.; Wagner, G.; Himme, B. H₂ Formation in the Reaction of O(¹D) with H₂O.  J. Phys. Chem., 84, 1980.