Ishizawa et al. conduct inverse modeling simulations for Canada to estimate wetland fluxes across the country. I think this manuscript addresses several very important topics and makes an important contribution to the literature on methane fluxes from high latitudes. I do worry about some aspects of the methodology, and I think there are more state-of-the-art approaches to inverse modeling that would mitigate some of the unrealistic or unphysical results that the authors highlight at several points in the manuscript.

Specific comments and suggestions:

• Line 15: What kind of gradients are you referring to here? Spatial gradients, vertical gradients, or some other kind of gradient?
• Line 28: What commitment are you referring to here? Does this line refer to thee Global Methane Pledge or to some other commitment?
• Line 52: I'd recommend adding a transition at the beginning of this paragraph. Otherwise, the pivot from wetlands to natural gas feels really sudden and abrupt.
• Line 62: This line mentions that reliable anthropogenic emissions estimates are important for regulation. Are there relevant regulations on methane emissions in Canada? 
• Line 112: The phrase "minimize the impact of local sources" sounds a bit ambiguous or confusing here. For example, it wasn't totally clear to me what "local sources" means in this context or why those sources are bad. Instead of this motivation, I think a stronger motivation is that nighttime and morning mixed layer dynamics are really tricky to simulate, and atmospheric transport models don't always do well at this task. This difficulty can lead to large errors in the atmospheric transport model, which can potentially interfere with the inverse model.
• Line 115: What percentage of data are removed as outliers? What do you think causes these outliers (i.e., what are the possible "unknown sources" cited in line 114)? I can see the rationale for removing outlier data, but I also think it's important to ensure this step doesn't eliminate the atmospheric signal from important emissions sources.
• Line 136: What is the temporal frequency or resolution of these scaling factors? I.e., do you estimate a single scaling factor in each region and apply it to the entire study period (years 2007 - 2017), or do these scaling factors vary by month/season/year? The way that lambda is defined in line 136 seems to imply that there is only a single scaling factor in each region for the duration of the inverse model.
• Line 144 and 145: What are the units on these sigma values, and why were these particular values chosen?
• Line 167: Is 5 days sufficient for the back trajectories? I think John Lin and Christoph Gerbig used 10-day back trajectories in their original studies of CO₂ fluxes from North America, and many regional inverse modeling studies for North America use 10-day back trajectories (e.g., existing studies using CarbonTracker-Lagrange footprints, including those from Sharon Gourdji and Yoichi Shiga). Is 5 days sufficient time for the modeled particles to reach the edge of the modeling domain?
• Line 189: What do you mean by "stronger emissions"? Is that the same as "larger emissions"?
• Figure 5: Both the two and four-region inverse modeling setups seem relatively coarse. The ECCC network has 13 sites (i.e., Table 1). Personally, I think that using only two regions in a scaling factor inversion is really under-utilizing the ECCC network. By contrast, existing regional-scale atmospheric inverse modeling studies often estimate emissions at the model grid scale (e.g., see inverse modeling studies by Sharon Gourdji, Yoichi Shiga, Lei Hu, and Nina Randazzo). Furthermore, I'm worried that the relatively coarse regions used here might mean that the inverse model can't differentiate anthropogenic emissions in Alberta from wetland emissions in other parts of western Canada. As the authors point out, existing inventories tend to greatly underestimate emissions from oil and gas operations in Alberta, while some of the wetland models overestimate wetland methane emissions. The regions in the inverse model might be so coarse, that the resulting scaling factors won't differentiate these contrasting discrepancies between anthropogenic and wetland bottom-up emissions estimates in western Canada.
• Line 267: "in the North" instead of "in North"?
• Line 298: There are ways of constraining the fluxes to be non-negative. For example, you could use a data transformation or a bounded optimization algorithm (Matlab and Python, for example, have several functions that do bounded optimization. These algorithms include active set minimization algorithms and LBFGS-B, among others.). I think there are also other possibilities for why the fluxes are negative here, including errors/uncertainty in background methane levels.
• Line 300: This statement sounds like it belongs better in the methods section than the results.
• Line 321: You definitely wouldn't want a reader to misinterpret these statements in the manuscript and think the inverse model is faulty or untrustworthy (and that your results are therefore untrustworthy). Another possibility here is to look at the posterior uncertainties. Presumably, the posterior uncertainties are large in years when there are few observations. The posterior best estimate might be unrealistic, but the uncertainty bounds could very well encompass realistic values. Overall, I think the "Does it make sense?" litmus test is one way to evaluate the uncertainties in the posterior flux estimate, but the posterior uncertainties are another way to do that. And again, enforcing non-negativity within the inverse model (see above) would be another way to eliminate these unrealistic, negative flux estimates.
• Line 330: What kind of variability are you referring to in this line? Also, see the comments above about how to add a non-negativity bound to the inverse model. Again, you wouldn't want a reader to think that the inverse model is untrustworthy.
• Lines 330 - 340: I don't think that the use of fewer subregions is the solution here. Lots of people in the inverse modeling community have estimated CO₂ and CH₄ fluxes across North America and have estimated those fluxes at the model grid scale (i.e., see the list of authors in an earlier comment). Rather, I think that enforcing non-negativity in the inverse model is a much better path forward. In addition, the purpose of the prior covariance matrix is to regularize problems that are under-constrained by the data. For example, you can include off-diagonal elements in the prior covariance matrix, and these terms will push the inverse model to estimate scaling factors that a correlated from region-to-region (i.e., correlated spatially) or correlated in time. In summary, an advantage of using a Bayesian approach to inverse modeling is that it can accommodate problems that are under-constrained, and I recommend taking advantage of those aspects of the Bayesian approach.
• Lines 355-357: Presumably, one could answer this question by looking at the posterior uncertainties. 
• Line 378: Maybe "estimate" should be "estimates"?
• Line 393: What do you mean by "assimilated well"? Can you use a different phrase here to clarify the meaning?
• Line 465: If not solely temperature, what other drivers do you think are key?
• Line 489: I think this statement represents the challenge of using such large regions in the inverse model. There are some cities in the Eastern region. If one used smaller regions or did a grid-scale inversion, then it would be easier to zoom in on wetland regions like the Hudson Bay Lowlands or the wetlands near Chapais, Quebec.
• Line 491: What do you define as large here?
• Sections 3.5.1 and 3.5.2 seem to focus more on flux totals than on the spatial distribution of fluxes (which is the title of Sect. 3.5). I would consider renaming Sect. 3.5 accordingly.
• Lines 646 - 662: These lines seem like they might fit better in Sect. 3.6 than in Sect. 3.5.
• Section 3.6: What do you think is the overall take-away message or main scientific result of this section? I think it could be helpful to emphasize the main takeaway messages here. The text at the end of the section states that the diurnal cycle is consistent with the inverse modeling results, but I'm not sure if there are other key take-aways in this section. I'm also not sure to what extent the results in this section really validate the inverse model; they're certainly not inconsistent with the inverse model, but I don't know that they specifically validate or provide evaluation of the inverse model.
• Conclusions: Several topic sentences in the conclusions sentences start out with relatively technical references to case "Inv_4R12S." Instead, I would try to focus on the high-level take-away messages and avoid very technical abbreviations in this section. 

The paper deals with the estimation of Canadian methane emissions for the period 2007-2017.  It is a valuable contribution to the topic, performing an ensemble regional inversion constrained with the Environment and Climate Change Canada (ECCC) surface measurement network and provides a new perspective on the important region of Canada, where large uncertainties in the methane budget have previously been recognised. The modelling methodology is well established and the ECCC data are widely used and of high quality.  A couple of questions remain to be clarified:

l 15: what are the gradients mentioned here?

l 50: could maybe mention that some studies indicate a decreasing methane emission trend in the future due to increased evapotranspiration and drying of the soil (Kwon et al, 2022, https://onlinelibrary.wiley.com/doi/10.1111/gcb.16394)

105: LacLaBiche, Egbert and Downsview still have high variability after data selection. I wonder how you ensure that this is not very local influence, as, if I am not wrong,  Egbert and Downsview appear to be within an urban area. Did you use any additional selection methods for these sites, e.g. wind speed?

167: Five days is quite short time for calculating backward trajectories. See e.g. Wittig et al.: The 10-d transport backwards in time in FLEXPART is much smaller than the average residence time of air masses (typically few weeks) in the Arctic. Therefore, part of the influence of Arctic fluxes on observations can be diluted in the background. On the other hand, backward simulations over several weeks would require a very large number of particles to be accurate, at the expense of very high computational costs. Thus, I would suggest doing a test with at least 10-d trajectories.

205: It would be helpful to see the time series or all priors, to ensure that there are no inconsistencies during the time period studied (as there might be in EDGAR time series) that might affect the trend calculation.

217: How do you re-grid the coarser resolution data on e.g wetland extent for use in higher resolution inversions?

273: More recent EDGAR releases include an annual cycle for the anthropogenic emissions. How would this affect your results?

291: In reality, cold months can vary from year to another and the shoulder seasons may have a significant impact on methane emissions. How would this affect your results?

Figure6: What could be the midwinter peak in methane emissions  (especially 2011 and 2013 in East)? Anthropogenic or natural emissions?

Table S2: Can you give a statistical estimate of the significance of the trend, in addition to SD among the ensembles?

396: Could you use trajectories to select those time periods when air masses were transported directly from one site to the other?

465: How about the increase in the depth of the permafrost thaw layer, which progresses through the summer and increases the temperature of the subsurface layers? Could it, in part, explain the later emission maximum?

694: Could it be possible that the diurnal cycle may also be influenced by anthropogenic sources, as the LLC was described as having oil industry in the south of the site.