General comments

In this paper Thanwerdas et al. use a 3D inverse modelling with a 3D chemical transport model to investigate reasons for the post 2007 increase in atmospheric methane. The reasons for the post 2007 increase in methane (and corresponding depletion in δ¹³C) have been investigated in several other papers in recent years (e.g. Nisbet et al., 2016;  Lan et al., 2021; Basu et al., 2022), but there remains uncertainty on the partitioning of the sources. The use of δD (δ²H) as another constraint has been used a little in the past (notably in Fujita et al., 2020 and for the Arctic by Warwick et al., 2016) but not in as many studies because the observational network is much sparser and we have less available data on δD signatures of the sources.

The paper investigates the influence of uncertainties in both emissions and source signatures. The work demonstrates that if uncertainties in the source signatures are taken into account there is a difference in whether wetland emissions have increased or decreased. The question of whether wetland methane emissions are increasing and consequential feedback effect is of importance to global climate change (see recent papers by Zhang et al., 2023, https://doi.org/10.1038/s41558-023-01629-0).

The conclusions are supported by the model results. I agree with the authors that the inversion system that has been presented is a helpful step towards improved quantification of sectoral emissions and the global methane budget. The incorporation of δD into the assimilation does not help very much with the constraints in the current work, but could do in future if the uncertainty in δD isotopic signatures is reduced and with more atmospheric measurements.

The paper is well written and an important contribution to the debate about the global methane budget. I recommend publication following some minor revisions.

Specific Comments

The abstract lists percentage changes, but could an estimate in the uncertainties of these changes be included?

Line 42 – it would be useful to indicate the best estimates of the percentage of methane that is removed by each of these sinks.

Line 89 – A range of the source values for δ¹³C is given, but not for δD. It would be useful to give an indication of this. The introduction should also explain how the sink processes affect the isotopic composition of atmospheric methane, noting the strong isotopic fractionation by the sinks in particular for δD.

It should be noted that although the model is run from 1998 to 2019 the δD isotope data are only available for a part of this so the full run cannot be constrained with this isotope.

The explanation of the model is clear and builds on previously published work by the group (e.g. Thanwerdas et al., 2022a) using this chemical transport model and inversion. The new part of this work is assimilating both δ¹³C and δD observations in the same inversion and optimising for both source signatures δ¹³C and δD, and investigating the effect of the uncertainties in source signatures.

Table 1 – how well are these fractionation factors known? I think there needs to be some discussion of this as it could have a significant effect on the results if slightly different values are used. Was this considered in the sensitivity studies?

There is a good explanation of how the isotopic signatures were selected in section 2.4. I agree with the authors that the regional uncertainties in δ¹³C that have been used are probably overestimates, but it is difficult to improve this estimate. How useful would more data on isotopic signatures of δD be, and are there particular sectors for which this is most lacking? 

In section 2.9 it is mentioned that just the period 2002 to 2014 is included in the run. I think it should be mentioned in the abstract what time period is being considered, because if there have been significant changes from a particular source since (e.g. increase in emissions from wetland, such as in Zhang et al., 2023) then that wouldn’t have been seen.

Just a few years of δD data observational data have been used. Is there any evidence of an isotope trend in this, or is the time period too short to see this? Perhaps this should be commented on in section 3.1.

The section comparing with the recent paper by Basu et al., 2022 is useful as the results of the inversions are quite different. The reasons for the differences have been considered.

Technical corrections

Line 36 – capital C for Climate

Lines 81,82 – explain what R₁₃ and R_D represent (ratios of ¹³C/¹²C and ²H/¹H in the sample). Also note that these δ values are multiplied by 1000 to give values in ‰.

Line 84, R_PDB should be 1.12372 x 10^-2

Line256, Arctic (not Artic). You should mention that INSTAAR is part of University of Colorado.

Data availability: Is the δD data from INSTAAR archived anywhere? 

This study presents a new inverse modelling system for estimating emissions using observational constraints from methane and its stable isotopes. The results are compared with previous studies, which arrived at different conclusions about the dominant drivers of the observed methane increase in the past decades. This is easily explained for inversions that do or do not optimize source signatures. However, even when treating the isotopic fractionation in the same way, important differences are found that are not easily explained. Overall, the added value of isotopic measurements seems limited, mainly because of the uncertainty in fractionation factors. In addition, the use of Dd data is found not to make an important difference. This could be a good sign that CH4 and 13C-CH4 already provide sufficient constraints on the emissions. However, as explained in further detail below I suspect that the inversion setup may not have been favorable to effectively utilize the added value of Dd. A few more points are raised in this review report that require careful attention before the manuscript can be accepted for publication.

GENERAL COMMENTS

The time dimension of the isotopic signatures in the control vector is not clear. The results suggest the INV_REF optimizes these signatures per year. The justification for doing this is missing. The discussion section mentions that an intermediate solution (between fixed and full optimization of signatures) may be preferable. To me it would make sense to optimize time domain averaged signatures only, potentially with a trend for processes for which this might be relevant. I wonder how variable to year-to-year signature adjustments are, which is not shown. The risk of the current approach – if I understand it correctly - is that uncertainties of annual signatures strongly covary with the uncertainties of emissions, and therefore emission IAV ends up as IAV in isotopic signatures.

The most promising added value of dD measurements is to facilitate the independent estimation of methane sources and sinks. However, the current setup only supports the optimization of emissions. Sensitivity tests are done to evaluate the use of different OH scenarios, but it is not clear which of them is most consistent with the dD data. Without in depth analysis of the benefit of dD for estimating methane sinks I do not think it is justified to conclude that the usefulness of dD measurements is limited.

Some further discussion is needed of the absence of posterior uncertainties in the current setup. Strictly speaking, without posterior uncertainties the statistical significance of the emission adjustments that are found cannot be judged. I can accept an argument that the current system is not prepared to generate them yet, although I do consider it a major shortcoming. For this reason, some discussion is needed of options and future plans to address this important methodological limitation of the system that is presented.    

SPECIFIC COMMENTS

Line 5: ‘amount fractions’. What is the reason to divert from the common use of mole fractions? ‘amount’ is much less clearly defined as ‘mole’, so I do not see the advantage of using ‘amount’. 

Line 84: ‘PDB’. Confusion should be avoided about isotopic standards. Vienna PDB is used as the standard according to the text, but the value of the old PDB standard is mentioned. Furthermore, the notation in the equations suggests that the old PDB is used instead of VPDB.

Line 230: How are source signatures discretized in time in the control vector?

Line 278: Clarify the meaning of ‘aggregated’ here. Do you mean ‘averaged’?

Line 291: How are initial conditions discretized spatially in the control vector?

Line 330: ‘using a sequence of short periods’ Some discussion of equilibration times in the context of isotopic inversions is presented in Houweling et al, 2017.  To get this issue resolved once and for all, best would be to do an inversion using short and long-time windows to determine of the longer equilibration time of isotopes really makes a difference in inversions that do optimize the initial condition. Note that the equilibration time of CH4 itself is also significantly longer than then spin-up/down-time that is used. If that is not a problem in inversions using only CH4 data, then why would it be a problem in inversion that use isotopic data?

Line 335: 3-4 years is still within the range of transport spin up times (for the largest time scales of atmospheric mixing). Tans et al discuss much longer time scales (see my previous comment)

Line 385: Ostler et al indeed do not find a strong influence when replacing MIPAS, but they show a significant sensitivity to scaling MIPAS to ACE-FTS and conclude that the accuracy of these satellite measurements is probably not good enough yet to answer this question.  

Figure 6: Which simulation is this?

Line 475: What is the justification of wetland flux anomalies persisting for as long as 4 years? 

line 643: For comparison to future studies, it would be useful to provide absolute emission increases in addition to fractional contributions to the total increase.

line 654: ‘enriched’ and ‘depleted’ seem reversed in this sentence.

TECHNICAL CORRECTIONS  

line 188: remove ‘Database’

line 293: 'setup IS detailed'

line 374: section 3.4.

line 447: 'applies' io 'apply'

line 457: 'who suggest' io 'that suggests"