This manuscript presents an inverse modelling system for estimating global methane emissions. It is used to study the causes of the accelerated methane increase during 2020-2022. Compared with previous studies, a larger set of surface and aircraft measurements is used, extending the data coverage in south and east Asia, in addition to the use of alternative GOSAT retrieval datasets. The results highlight the role of increasing Asian emissions in the global growth rate enhancement during this period, attributed mostly to increases in agricultural emissions. The sensitivity of inversion-estimated emissions to the observational datasets is an important – although not unexpected – finding. This study points to a trade-off between African and Asian emission increases depending on the data that are used, which makes an important contribution the scientific understanding of the causes of the global emission increase.      

The manuscript is well written. Provided that the few points raised below are sufficiently well addressed I see no reason to uphold publication.

GENERAL COMMENTS

The method section describes how posterior uncertainties are quantified. However, besides posterior flux covariances and uncertainty reduction very little use is made of posterior uncertainties. How do posterior uncertainties compare with the differences that are found between the different inversions? How about the significance of the most important flux deviations from the prior that are used to explain the 2020-2022 growth rate anomaly? Some of the plots miss error bars. 

Increases in emissions over Africa and southeast Asia are discussed, which have been attributed increases in natural wetlands and agriculture. However, it is not clear to which extend these increases are in the a priori fluxes already. A priori emission estimates in zonal bands are presented that give some indication, but it is unclear whether those differences are representative for what is found for the regions that are used in the sectorial bar graphs.  

The sensitivity to observational datasets and their spatial coverage raises the question whether the size of regional observational constraints could drive the differences in the outcomes of different inversions. If Asian data are added, the importance of Asian emissions increases, if data over Tropical Africa are added (i.e. proxy-method GOSAT retrievals) the importance of African emissions increases. It could be coincidence but might also be a symptom of sampling bias. It would be useful to add a data thinning experiment to distinguish between the extra information on methane emissions that new measurements bring versus the impact of their added observational constraint. 

SPECIFIC COMMENTS

line 30: “increase” compared to what? It misses a notion of the extent to which this is expected or not given the a priori fluxes.

line 35: Agreement was found between what?

line 119: How do you mean 'derived'? From what?

Equation 1: Parentheses are missing indicating the limits of the sum over i processes (that is only for a part of the equation, but it is unclear which part). Why are some processes corrected using delta-alpha and others using delta-f? This treatment makes an important but unexplained difference. Does delta-f cover grid boxes for which the corresponding f has zero emissions?   

Sect. 2.2: What spatial and temporal error covariances are assumed of the 1x1 degree a priori monthly and annual fluxes?

line 163: How large are the wetlands, rice, soil uncertainties derived from VISIT?

line 172: How about the temporal coverage of data that have been used? Is the sampling network changing over time?

line 187: 'deemed to be comparable' within what accuracy?

Equation 2: How does balancing of data constraints work out for the observational weights of surface, aircraft and GOSAT data? How do the corresponding terms in the cost function compare?

Line 307: How does the inversions performance evaluation in Figure 2 distinguish between data that are or are not used in the inversion?

Figure 6: uncertainty reductions are a % reduction?

Appendix A: Using the method that is presented reduces the likelihood of negative emissions but does not prevent that negative emissions might happen. To which extent is this still the case?

Appendix B: line 644: It is mentioned that GOSAT retrievals are biased, but this need not be the case. There could also be an inconsistency between modelled surface and total column mixing ratios due to a transport model problem. I doubt that comparisons between GOSAT and TCCON show this bias. Past studies that used GOSAT struggled with this too, but concluded that the problem was probably more a model problem than a retrieval problem. 

Appendix C: The description of the method is clear, but it would be helpful add a map of what the resulting OH reduction looks like?

TECHNICAL CORRECTIONS

line 599: “for several reasons” instead of “through several reasons”

The manuscript entitled "Multi-observational estimation of regional and sectoral emission contributions to the persistent high growth rate of atmospheric CH4 for 2020–2022" by Yosuke Niwa and coworkers presents a detailed description of global CH4 fluxes estimated from atmospheric observations and an inverse modelling framework. Special attention is given to the recent rise in atmospheric methane growth rates. By employing an emission optimisation (inversion) by region and source sector Niwa et al. present the most likely drivers of the recent increase in CH4 emissions. The applied inversion tool and the analysis are sound and state of the art, the study appropriately addresses the limitations and uncertainties of the approach. Presentation of results is clear and concise. At this point I only have minor suggestions for modifications and additional clarifications.

General comment

Although the study carefully scrutinises the main results by presenting several sensitivity inversions (different observational constraint, OH impact) and analysing posterior covariance between regions and sectors, more attention should be given to the posterior uncertainties themselves. None of the plots contains uncertainty estimates on any of the emission time series, nor are any uncertainty statements given in the text when emissions for a given region, sector or global total are discussed. The estimated posterior uncertainties could easily be employed to analyse the statistical significance of the observed, step-wise, increase in CH4 emissions after 2020 and support statements made about the equivalence of results obtained from different inversions. A discussion of uncertainty reduction was used to showcase which regions/sectors were well constraint by the observations, but the additional use of the absolute posterior uncertainties could largely enhance the discussion.

Specific comments

Abstract: Consider an alternative start that gives a bit more room for setting the stage. Something like: "Atmospheric methane (CH4) growth rates reached unprecedented values in the years 2020-2022. In order to identify the main drivers of this increase, we present results from an inverse modelling study estimating regional and sectoral emission contributions for the period 2016 to 2022. Three inverse estimates based on different sets of atmospheric CH4 observations (surface observations only, surface and aircraft observations, GOSAT satellite observations) consistently suggest notable emission increases from 2016-2019 to 2020-2022: ... "

Abstract, following line 37: I am missing a discussion of the fossil emission trends here. Fig 10 shows a considerable (though smaller increase) as well for different Asian regions. I think this is worth mentioning in the abstract as well.

L37f: What is this quantification of constraint based on? The uncertainty reductions? Instead of only discussing the difference in constraint, I suggest to mention the general differences in GOSAT vs SURF inversions in terms of spatial and sectorial allocation.

L39f: The statement on OH impact is not well formulated. Nor is the analysis in section 4.1 very detailed. I suggest updating after a revision of section 4.1 (see comment below).

L54f: Sentence somewhat convoluted. Consider rephrasing. My suggestion: "In particular, CH4 has recently attracted global attention because due to its short lifetime, the mitigation effect on global warming when reducing its emissions occurs sooner than when reducing CO2 emissions. Hence, ambitious reduction targets were envisaged in the Global Methane Pledge for the coming years." Furthermore, a reference for the Global Methane Pledge and a more quantitative statement of its targets would underline the statement.

L65f: Li et al. (2023) report reductions for Jan – Apr for 2022. Main northern hemispheric sink will be in summer. Considering short NOx lifetimes I wonder how much impact can then be expected if emissions returned to previous levels for the rest of the year. Was this considered in the OH sensitivity run?

L67: Sentence unclear: emissions of what? Contribution to what? Global NOx emissions to global OH levels?

L90f: What does 'multidirectional analysis' refer to here? The sensitivity inversions carried out in the present manuscript or something else?

L97ff, last paragraph of Introduction: Please include cross-references to the following sections where details on the mentioned models/analysis can be found.

L113: Instead of 'conventional' I would rather call this a 'traditionally employed rectangular' grid.

L115: Both the horizontal and the vertical grid spacing of the model are rather coarse. How much may this affect the results? My main concerns would be strat/trop exchange and representation of vertical gradients in the boundary layer. Was this model setup (independently of the present inversion) tested against profile observations?

L143: Why not use a monthly factor for the anthropogenic emissions as well? A number of studies have shown strong seasonality in these as well. For example for emissions from natural gas use, which tend to be increased in the cold season when demand is higher.

L163: Could the derived prior uncertainties for rice, wetland and soil be given as well. Would be interesting to compare them to the fixed values for anthropogenic sectors.

Table 1: Last column, last two rows. Instead of N/A consider to repeat the original names (natural, soil).

L191: Most inversions that use continuous observations from tall towers also apply a temporal filter, assimilating only afternoon observations to avoid known model misrepresentation of boundary layer mixing at other times. Similarly, mountain top observations are often filtered to avoid day-time updrafts. Was such a filter applied here as well?

Eq. 2, L218f: Please elaborate on this a bit more. I understand that the standard deviations of observations in a certain spatiotemporal area can be used to quantify the model's representative error. But why the expansion with the number of observations? Intuitively, it does not seem to make sense to assign large uncertainties for observations in areas covered by a dense network.  However, the choice of model-data mismatch is very critical for any inversion study. Which is especially true when mixing different kinds of observations as done here.

L293: Were the continuous in-situ observations not used in the performance analysis or the inversion? It would be useful to see the model performance for these as well. I suppose the performance is much worse than for the flask data, which is expected since the latter will be mostly taken under background conditions and the former are often impacted by recent emission events. Nevertheless, I would urge to show at least prior to posterior improvements to learn if the results are at all comparable to high-resolution regional scale inversions available for Europe and North America. To keep them separate an additional panel for continuous in-situ could be added to Fig 2.

L306ff, Fig. 2: Consider being more specific: Pearson correlation coefficient. How are these stats calculated for the in-situ sites? Pooled for all observations or first by site and then averaged? I would also suggest to include the plot of biases (Fig B1) in Fig 2 as well, since RMSD contains a contribution from the bias and only by showing both one can tell if a large RMSD is due to bias or variability.

In these performance statistics, it is interesting to note, that in the case not discussed in the text (surface observations assimilated) performance against GOSAT observations still largely improves (Fig. 2 c, f), almost similarly well as for GOSAT-based inversions. I think this strongly suggests that GOSAT-based inversions are not fully able to attribute emissions appropriately in the northern extra-tropics, where the surface observations provide the better constraint. With the GOSAT footprint being much wider these emissions are hence allocated elsewhere. Please comment and add to discussion.

Finally, could these performance statistics be compared with previous global inversions?

L332: The opposite could be said about the high latitude emissions in Siberia. They are prominent in SURF and SURF+AIR but little changed in GOSAT. For both changes the differences in observational constraint were already mentioned above, but this could be repeated here as well.

L371f: Unclear what is meant: the observations are independent in the sense of how they were obtained, but not in the sense of which air masses were sampled. Is the latter, what should be expressed?

L390: 'significantly'. In order to judge significance it would be helpful to report posterior uncertainties. See general comment above.

Section 3.2: The discussion does not cover all regions shown in the Fig 6. I wonder if the last statement about no significant trends should not be extended to include other regions without clear trends (like Oceania, North and Central America).

Fig. 6: Does the gray ribbon actually reflect the prior uncertainty or is it just a thick line? Adding uncertainty ribbons or bars to these time series plots may actually be helpful to judge the significance of the results.

L444f: How much could this be a consequence of transport model resolution, prior covariance and/or assigned data-mismatch uncertainty?

L459: 'generally consistent'. One very prominent difference between GOSAS and in-situ obs is the shift from wetland to fossil fuel, which for the total was a shift from tropics to high latitudes. Worth mentioning here.

L480, Fig. 10: Also the large increase estimated for Southeast Asia (S) seems worth mentioning here, which seems to be compensated by the decrease in biomass burning for the same region and the GOSAT estimates.

L489: 'between two'. Actually, correlation pairs for all three sectors are shown. It would be good to show or mention correlation with biomass burning in Souteast Asia as well. See previous comment. There is mentioning of negligible anti-correlations in L506, but is this true everywhere and for correlation with fossil fuel in Southeast Asia (S) in the GOSAT inversion?

Section 4.1: The discussion by region could be more quantitative. How much is the increase in Asian emissions actually reduced if OH is increased? From Fig. C1 is seems clear that the main impact of changed OH is on Tropical African and South American emissions but this is not well reflected and corroborated by numbers in the text. In addition, the role of continued high emissions in 2021 and 2022 could be mentioned in this context again.

L538: Is there a brief explanation why there are more data in the UoL product? Are there any published results concerning spatial or other biases between the two GOSAT products that would help with the interpretation?

L581: How is the seasonal cycle of posterior high-latitude wetland emissions in the three inversions? We would expect these to peak in summer, when GOSAT observations should be available in the area and pick up a signal of increased column densities. However, we also have large fossil emissions in the same area, which may actually peak in winter (larger demand). GOSAT would have trouble to notice these emissions (no sunlight). Fig. 11 suggests that fossil and wetland emissions are not well separated by the inversion for Northern Eurasia (W). How much could seasonal misattribution and seasonal lack of observations contribute to the discrepancies between SURF and GOSAT inversions?

L 594f: How would one explain a sharp increase in emissions from the agricultural & waste sector from one year to the next? Usually changes in these sectors are slow. It seems more likely that wetlands were the sole driver and the inverse method is not capable of separating them fully, as indicated by the negative posterior correlations.

L601: 'agree with each other'. To me this statement is too abbreviated as they do not fully agree in the spatial and sectorial attribution.

L604: 'newly introduced'. Were these data not used in any other global inverse modelling study before? Maybe reword to emphasize this fact.

L606ff: Another conclusion from the study is the need for unbiased satellite products and inversions combining surface in-situ, aircraft and satellite observations.

Appendix B: I suggest to integrate Fig. B1 and the discussion of bias in the main text. See comment above.

Technical comments

L82f: Consider 'spatial coverage is limited' instead.

L83: No 'the' in front of 'low latitudes'. No hyphen in the latter either. 'remain poorly covered by' instead of 'remained poor in'.

L85: Consider 'conditions' instead of 'areas'.

L110: Repeated use of 'transport model'. Would '… adjoint tracer transport model of NICAM-TM (Niwa et al., 2011, 2017b).' work as well?