General comments

This study estimates daily NOX emissions at a 3-km resolution in Beijing and its surrounding areas using an emission inversion framework. The framework assimilates TROPOMI NO2 column concentrations with an Ensemble Kalman Filter coupled with CMAQ. The results reveal that proxy-based bottom-up emission datasets tend to overestimate NOX emissions in densely populated areas, providing crucial insights for urban air quality regulations. Robust sensitivity analyses further strengthen the study by evaluating the effects of satellite retrieval parameters (e.g., a priori profiles and averaging kernels) and an observation localization radius parameter on the inversion results. Specific comments on the manuscript are outlined below.

Specific comments

Figure 3 and Figure S4: What ground air quality monitoring station data is used for this comparison? Is it based on a single station or a multi-station average? Additionally, how does this comparison vary across different ground stations, such as those in densely populated areas versus suburban or rural areas?

Page 4, Lines 118-119: “The MEIC emission inventory is spatially and temporally allocated to match the CMAQ model domain using spatial proxies and empirical temporal profiles.” What are the temporal and spatial resolutions of the MEIC inventory? What types of spatial proxies and temporal profiles are used to allocate emissions to the CMAQ model domain? Please elaborate further on these details in the paragraph.

Page 5, Lines 151-152: Does the inversion system presented in this study scale prior emissions on a daily scale? If so, how does the inversion system address hourly variations in NOX emissions? Does the inversion system adjust the hourly profiles of the bottom-up emission inventory? Please provide additional details on the time steps used for assimilating TROPOMI NO2 data to scale prior emission inventories.

 

Page 9, Lines 249-250: I recommend including additional error metrics, such as mean percentage error, to further illustrate the improvement in posterior emissions simulations. This would help address the question, “In which season is the most significant improvement observed after inversion?”

Page 9, Lines 251-252: What spatial proxies are used in MEIC? For example, does it utilize road network shapefiles? Providing specific examples would make this argument more compelling and relevant.

Page 9, Lines 253-254: “However, the NO2 TVCDs from prior simulations indicate substantial overestimations in urban environments across various seasons…” Please specify the seasons or months to provide clarification.

Page 10, Lines 282-286: Why doesn’t the simulated O3 concentration exhibit the “summer bias” that is clearly evident in the comparison between simulated NO2 and observations? Please provide a more detailed discussion of the factors that could explain the differences between the simulations of NO2 and O3.

Page 10, Lines 295-296: “However, the posterior emission maps substantially reduce emissions from city centers and reallocate these emissions to other areas, such as increasing emissions from inter-city transportation, among other changes.” This is an important finding, but it requires more supporting evidence. From Figure 4 alone, it is challenging to identify the locations of inter-city transportation, making it difficult to confirm whether the reduced emissions from city centers are reallocated to road networks. Consider including an additional figure that overlays the locations of major inter-city roadways with the areas of increased emissions in the posterior estimates.

Page 10, Lines 301-302: “The posterior NOx emissions for the year 2020 (657 kt NOx) decreased by 23.7% compared to the prior inventory (861 kt NOx). The largest reductions occurred in winter and autumn, with declines of 44.5% and 36.4%, respectively.” Does the bottom-up emission inventory (prior) account for the impact of COVID-19? If so, please provide an explanation in the paragraph.

Page 11, Lines 319-321: “The seasonal variation of the posterior NOx emission estimate in our research is similar to the results obtained by previous studies (Wang et al., 2007; Qu et al., 2017; Miyazaki et al., 2017). Qu et al. (2017) utilized OMI measurements to infer the NOx emissions in China, and the seasonal pattern of NOx emissions for China and Beijing City is consistent with our study.” How similar are these findings? Consider adding quantitative metrics to describe the seasonality of NOx emissions as observed in this study and in previous studies.

Page 12, Lines 364-365: “To evaluate the impact of different L values on the NOx emission inversions, we perform two additional experiments with L = 3 km (Exp_L3km) and L = 81 km (Exp_L81km), respectively.” What are the reasons for choosing these specific L values, 3 km and 81 km, for the sensitivity analysis? Please provide an explanation.

Figure 5: Consider adding a visual marker to highlight the implementation and relaxation of COVID-19 containment measures, as well as notable events such as the Chinese Lunar New Year holiday.

Figure 5: It appears that the prior emission inventory exhibits a consistent diurnal cycle of hourly NOX emissions. How does this compare to the diurnal cycle in the posterior NOX emissions? Does the inversion system reveal a similar pattern? Please consider adding a figure and/or a paragraph to discuss this comparison.

In their paper, Yawen Kong and co-authors present the results of a NOx emission inversion system applied to the region around Beijing. It is one of the first emission assimilation systems targeting a high model (and emission) resolution of 3 km, matching well the TROPOMI footprint size and resolving the fine-scale information provided by the satellite. This inversion provides strong evidence that the proxies used to distribute the emissions in the MEIC inventory, especially the scaling with population density, has shortcomings. The paper is well written, has a good set of references and the figures provide a good documentation of the results. I am in favour of publishing these interesting results after my (relatively minor) comments have been dealt with and the answers have been incorporated in the text of the paper.

Comments:

l 113: "simulations over the first and second domains were performed before the inversion experiments to provide boundary conditions for the third domain." Because the emissions in D02 are not adjusted, this may lead to inconsistencies inside/near the boundary of D03 and sub-optimal emission estimates. Please comment or refer to a later discussion of this nesting feature. 

l 116: Please provide the spatial resolution of the MEIC inventory. 

l 116: Please elaborate on the temporal profiles in MEIC: does this include sector-dependent seasonal, weekday and diurnal patterns? Are these considered to be realistic? 

l 119: "inventory is spatially and temporally allocated to match the CMAQ model domain" Is the grid of CMAQ adjusted to match MEIC, e.g. 3x3 gridcells of MEIC in one gridcell of CMAQ? 

l 133: The TROPOMI reprocessing with processor version 2.4 is now available for several years. Why did the authors use 2.3.1?

Section 2.2: Please discuss also the satellite retrieval uncertainties. Did you use the uncertainty from the L2 file to compute the covariances? 

l 136: " quality assurance value greater than 0.5" and "cloud fraction exceeding 40%". This is not following the default recommendation, which is a value greater than 0.75 for most applications. Please motivate why you deviate from the standard filtering?

l 135: It would be good to mention here that the averaging kernels are also used in the observation operator. 

l 139: Gridded satellite product on 3x3 km grid? I get the impression that the satellite data is first mapped onto the model grid of 3x3km, and that subsequently these grid observations are assimilated. Is this true? The normal procedure would be to (area) average the model over the footprint of the satellite. Is there a reason why this approach was chosen?

l 151: "optimizing the initial NO2 concentrations by assimilating the satellite observations has minimal impact ". Please refer to Miyazaki, who is adjusting both concentrations and emissions. Would there be an advantage (disadvantage) of using such a mixed concentration and emission state vector?

l 150: x is an emission scaling factor. Please state that x=1 means that the emission is equal to the MEIC emission at a given location and time. This will be helpful for the reader. 

l 154: What is the assimilation time step? Is it one day?  (t - 1 = t - 1 day?)

Eq 1: In line 149, x has an ensemble member subscript. In Equation 1 the subscript refers to time. Please improve. 

Eq. 1: Please explain this choice in more detail. Why is the average over two days (and not e.g. only the last day) Why is the "+1" term added, which relaxes back to the prior emission inventory? Why is persistency (x_t = x_{t-1}) not a better choice?

l 179: "the prior error covariance maintains a fixed uncertainty value to prevent filter divergence, which is similar to our previous study (Kong 2022)" Please provide more details here. 

l 186: Sensitivity experiments: The choices 3 and 81 km are very far apart. For me it would be more logical to test also 10 km and see if this improves the analysis.

l 187: "exclude the days with satellite coverage below 70%". Why is this needed? If part of the domain is cloud-free, the observations in this part could lead to useful constraints for emissions.

l 194: "retrievals are resampled to model 3km grid." (related to my earlier comment) Normally model values are resampled to the satellite footprint in the observation operator to represent individual observations. The procedure is not very clear to me.  Please provide details and motivate why a resampling of observations was done. Are the kernels resampled in the same way? 

Section 2.6: The equipment used to measure NO2 for air quality monitoring purposes is known to be influenced by other nitrogen oxides like PAN or HNO3. In previous studies, like e.g. Lamsal et al., 2008, doi:10.1029/2007JD009235, the comparisons with ground-based observations have been done by including these other species in the comparison, see e.g. eq.1 in this paper. What about the Chinese surface measurements? Are they also based on molybdenum converter instruments and do they have a similar problem? If so, I would propose to mention the issue and possibly correct for it in the comparison with CMAQ.

Fig.2. I assume that the kernels have been used in this comparison (e.g. Exp 1 in Table 1). Please mention this in the caption.

l. 267: "Our inversions at the 3 km scale were limited to optimizing emissions in the innermost domain and did not address emissions outside this area." The high-resolution domain is quite small (350km) and especially the edges of the domain will be influenced by the coarser-resolution middle domain. Transport of NOx from the source can cover 50-100km. As future improvement it may be useful to apply the assimilation also to the D02 domain for a better consistency.

l 276: "during the summer was relatively limited". I was wondering if the results may have been influenced by the free tropospheric column? Did the authors check if free-tropospheric NO2 concentrations and profile shapes in CMAQ are reasonable, especially in Summer? Are there e.g. aircraft profiles available? Alternatively, the profiles (Fig. S5) may be compared by other modelling results, e.g. with the CAMS simulations (as described in the Inness paper). Deep convection and lightning are important sources in Summer. 

Sec 3.2.2. MEIC shows a clear weekly pattern. This is not so clear in the satellite derived emissions. Please add a remark on this. I was wondering if the emission time averaging (Eq 1) is removing most of the weekly cycle. Or is there still a weekly cycle signal available in the posterior emissions?

l 329: "the prior biogenic emissions are significantly underestimated". Fig. 6 is interesting and shows a clear enhancement of the biogenic part in the assimilation. But these results may be partly misleading. The problems with the spatial disaggregation of MEIC anthropogenic emissions (too much following the population density) may be partly compensated by increases in biogenic NOx (which are more pronounced outside the populated areas). Furthermore, the biogenic emissions for this D3 region are much smaller than the anthropogenic emissions, as shown by Fig. 6. So, to my opinion the conclusion that biogenic emissions are underestimated should be formulated carefully.  Are there references which support the statement that biogenic (soil) emissions are underestimated (in China)?

l 350: "it may not be necessary to update the a priori profiles in each assimilation step". These are nice and convincing results, presented in Figs S7 and 8.  Because domain D03 is such a high emission domain, the profile shape is mainly resulting from the emissions from the surface. But perhaps the results may be different  for other regions with lower anthropogenic emissions, where the free-tropospheric relative contribution to the satellite-observed column may be larger, increasing the dependency of the profile shape to changes in surface emissions. 

Sec 4.2: The choice of the localization length is also a trade-off between ensemble size and "emission noise" resulting from the limited number of ensemble members. Are there indications of spurious emission increments in the 81 km experiment? 

Sec 4.2: The step between 3 and 36 km is very large. For me it would have been logical to include also a L=10 km experiment. 

Sec 4.2: I was missing a discussion about covariance inflation, which is normally needed to avoid a collapse and too much trust in the analysis. But I understand (line 179) that the prior error covarance maintains a fixed value to avoid filter divergence. Please provide the details: what is the fixed value used, and how is this implemented?

l 380: "min-afternoon" ?

Sec 4.3. The GEMS geostationary observations are not mentioned. Is it considered to make use of GEMS hourly data in the future?

Section 4.3 / conclusions: 

Some extra discussion on factors influencing the derived emissions would be useful. Emissions are clearly not the only uncertain factor in the model. The lifetime of NO2 in the atmosphere is a key factor to relate satellite-observed concentrations to emissions, and errors in this could introduce a seasonally-dependent bias. The profile shape was discussed well, but was not really validated/verified with independent observations or modelling results. Natural emissions and concentrations in the free troposphere may not be very important for the D03 high emission region, but could be important elsewhere (It is mentioned that lightning is not included). And also the satellite retrievals have systematic uncertainties which could also introduce a seasonality.