Review comment for “Anthropogenic CO2 emission estimates in the Tokyo Metropolitan Area from ground-based CO2 column observations”

Overall comments:

The paper is packed with useful information, and it seems the authors have invested tremendous effort. While some details are missing, making certain parts challenging to follow, the prior simulation itself is commendable. I believe this paper is suitable for publication in EGUsphere once the authors address the comments.

I would like to suggest that the authors dedicate some time to refining the sentence structures for a smoother reading experience. Additionally, as mentioned below, I recommend relocating certain paragraphs from the Results section to the Methodology section or the supplementary materials, as the two sections appear to be mixed.

Furthermore, I have a specific request regarding Figure S5: It would be beneficial to include a scatter plot comparison that depicts “local” enhancements by subtracting the background. I am curious about how the background estimation was carried out and affects the scatter plot comparison. Additionally, I am curious to know whether the inversion was performed after the background subtraction.

I hope that the authors will thoroughly address the detailed comments below.

Detailed comments:

L28-29: The following statement is subjective because it depends on the a priori assumption. For example, if the prior is assigned with large uncertainty, the percentage of uncertainty reduction in the posterior will be larger, e.g., even larger than a factor of 3. So, the author needs to clarify this sentence: “In addition, the inverse analysis reduced the uncertainty in total CO2 emissions in the TMA by a factor of ∼2.”

L30 – 31: Instead of the current conclusion, I recommend the authors use a statement, e.g., the posterior emissions are X+/-Y times the prior emissions (at the 95% CI). This way, the readers get more information, e.g., how tightly the measurements constrain the emissions.

L76 – 78: I strongly recommend that the authors add a couple of sentences describing this work’s unique contribution in addition to the previous work for the TMA.

L90: I would recommend that the authors add a map of Japan as an inset to show the relative location of the study area. The elevation map is good, but it is hard for those unfamiliar with the area to make sense of the study area relative to the entire country.

L142: Was the footprint normalized? The unit for footprint should be “ppm/flux” or, specifically, “ppm /(umol/m2/s)”? It seems that clarification is needed.

L258: Are the authors referring to the GVF data from VIIRS? It would be useful to add the exact VIIRS product name.

L263: As written, it is not clear. Was the ratio of the interpolated GVF versus the original GVF applied to the NEE data at 1 km? Or something else?

Section 3.3: Overall, I think the authors did a good job of making the prior fluxes more accurate!

L264 – 265: Suggestion for rewriting to improve clarity: “The downscaling process was conducted in a manner that ensured all original sums of the NEE data from the TMA were preserved following the downscaling.”

L268: “forward” seems wrong. First, WRF-STILT is not a physical “forward” model in this setting, although it can be used for forward simulation. Second, this is a linear or nonlinear model, statistically speaking.

L269: I suggest that the authors present H(x, b) more explicitly, e.g., by writing out the Jacobian matrix and x together. That way, the reader can understand the nonpoint and point source inversion more easily. This is related to Eq. (3), where “K” is introduced. Showing how “K” is associated with “b” should be useful (unless it is presented in the supplemental; I don’t see it).

Also, it is not clear at which temporal resolution the authors solve for “x.” Are you solving for sub-daily emissions for each pixel? Yes, is it also solved for each pixel as well? If so, how the “b” matrix is constructed? I am asking this question because the authors use hourly emissions, at least for NEE and anthropogenic. Then the “b” matrix should be extensive. As it is written, many things are not clear.

L270: I would not recommend using “state” in the fixed quantity as in the sentence “b is the fixed state vector”; “State” is typically suitable for parameters (please change accordingly if “state” was used for “b.” in other places)

L272-273: Based on “the state vector x includes spatially resolved nonpoint source emissions and a scaling factor of the large point source emissions,” the reader may be confused about how the inversion was done. Are you solving for the “flux” directly for the nonpoint source but the “scaling factor” for the point source? If it is the case, it is ok. But it needs clarification. Maybe, the authors did this way, but it is not clear from the writing.

L288: How is “the Levenberg–Marquart parameter” estimated? Or prescribed?

L314-315: I am curious how the authors matched the vertical profiles between CarbonTracker (CT) and EM27 to get the background for EM27. A weighting scheme was used? Ideally, the particle trajectory for each receptor (at different locations and vertical levels) of EM27 should be computed and then averaged using a kernel (or a set of weights, likely based on pressure distributions) compatible with EM27. To sample values from CT (using particle trajectories), the same method should be used to match the vertical profile between the two. I wonder if the authors did that or something else.

L310: By “XCO2 differences”, do the authors mean “enhancement” above the background? The phrase “XCO2 differences (XCO2Diff) from daily background values” needs to be revised for clarification.

L313: How did the author account for the background uncertainty based on this “5 percentile” assumption?

L318: Please add “diurnal” so that it reads “The average diurnal XCO2Diff.” By the way, I think “ΔXCO2” is more informative to represent the local signal (I find both are used). Some people use “XCO2” to describe the local mixing ratio (after subtracting background). I suggest the authors review the notation a bit more to avoid confusion. In fact, what is the difference between “XCO2Diff” and “ΔXCO2” in Line 277? I may have misunderstood, but further clarification would help. Thank you.

L321: I am a bit confused to see that there is a moderate-level effect of biogenic fluxes while the authors said, “the biogenic flux was allocated to the state vector b” in Line 276; it was assumed negligible there. Any clarification?

L323: It is unclear what the authors mean by “the high early morning values at Saitama may reflect an airmass-dependent bias.”

L330-334: The sentence sound awkward. Please revise.

L330-345: I would recommend that the authors move this particular paragraph to the Methodology section or possibly to the supplementary materials. As it stands, the Results section seems a bit extensive, and this adjustment could help with maintaining focus and flow.

L350-355: Here, the authors describe the background again, which I thought was done in Section 4.1. Given that both mention “Tsukuba,” I understood that site measurements were used as the background common to the other sites. What’s surprising to me is that the authors subtract the simulations at “Tsukuba” from the “Tsukuba” measurements to remove the local enhancements for the background site. It is possible, but it adds more uncertainty to the background because the simulated quantity itself is uncertain. Typically, using the particle trajectories from the STILT model, we would sample 4-D background data (over the ocean) simulated from a global model. The method used here is somewhat convenient but adds uncertainty.

Also, I suggest this paragraph be merged this the relevant paragraph in Section 4.1. Otherwise, the manuscript gets longer, and the reader is distracted/confused.

L358-359: I suggest the authors add a scatter plot for predicted versus measured, corresponding to Figure 8, only for the 15-min average. I think the figures are already many, but Figure 2 and Figure 4 (maybe more) can be moved to the supplemental.

L360: By “the sum of the WRF–STILT ΔXCO2 value every 15 min at each site and the background XCO2 value”, I assume “ΔXCO2” is the local enhancement. It needs to clarify between “ΔXCO2” and “XCO2diff.”

L361: “forward”? STILT back trajectories were used.

L363: What kind of point source? Is it identifiable, e.g., a power plant?

L369: I don’t necessarily agree with the statement: “Therefore, we attribute this large model–observation discrepancy to errors in the WRF-STILT model rather than to the emission data.” First, I don’t expect ERA5 to perform better than WRF because it is a much coarse resolution model product (I also see that in this work’s Figure S3). From my experience, it can be much worse than WRF, depending on the region. I would say that the authors only considered a limited set of meteorology, not exploring a broader set of meteorological data. So, it is possible that the limited meteorology didn’t capture the temporal variation. However, as the author said, it is still possible that the short-term local source not included in the prior fluxes is associated with this discrepancy between measurements and predictions. To summarize, although it is likely that the transport source is the primary source of the discrepancy, I don’t see evidence for the strong statement above.

L380: Equation 7 is confusing. What is the purpose of this equation? If this should be included, it should be presented in the section (e.g., 4.1) where the background is described. Based on the earlier description, wasn’t “𝑋𝐶𝑂BG “ derived from 𝑋𝐶𝑂Tsukuba_TCCON? As pointed out, this whole paragraph should be in the Method section, not the Result section.

L387-445: This should be included in the Method section for the abovementioned reason. There is no meaningful result described or discussed. They would agree with me if the authors read similar inverse modeling papers.

L417-418: This work differs from the system in Turner et al., where they have a dense measurement network. I cannot offer any temporal correlation length scale for this work, but I am not quite sure about adopting the 1-hr length scale.

L448: Which period does Figure 12a represent? Is it the average of the hourly posterior fluxes during the study period?

L470-471: Related to Equation 1, how many scaling factors were used/solved? Is this value of “0.856” just the average of many scaling factors? A simple average of many scaling factors would not work, though.

L512-513: Can the author offer further discussion on the difference between this study and Pisso et al.?

L535: With “forward simulation,” as pointed out above, how is footprint-based (backward is assumed unless explicitly stated) inversion possible?

L540: The mismatch between predictions and observations could be due to local sources not included in the prior, not necessarily due to transport error. Do you have evidence that there was a clear transport error? For CH4, EDGAR is generally not as good as regional inventories. I see both CO2 and CH4 measurements are significantly higher later in the afternoon (from Figure S3). It seems that the CO2 and CH4 sources are correlated. It may be the transport model didn’t capture the afternoon winds. Any evidence for that?