We have attached our responses to RC1 in the pdf below.

Responses (italics) to Reviewer’s comments (normal text)

General comments:

This study presents a new model-free method to constrain NOx emissions using TROPOMI NO₂ and ERA-5 wind data. The new method is based on mass balance theory and considers the NO_x/NO₂ ratio, NO_x lifetime and NO_x transport. Based on this approach, daily NO_x emissions over Shanxi province are estimated during 2019-2021. Some comments should be addressed before its publication. Additionally, the authors apply EOF to TROPOMI NO₂ and relate the first three PCs to NO_x emissions, UVAI, and NO_x transport. The method and conclusions are important, but some comments should be addressed before its publication.

Specific comments:

1. When TROPOMI NO₂ is not available due to cloud or other reasons, how do you deal with it? My understanding is when TROPOMI NO₂ is not available, Eq. 3 does not work. And how the missing data affect the estimated emission inventory?

This paper introduces a new methodology and makes a first attempt on the combine use of NO₂ column loadings and high spatial and temporal frequency observations of ground emissions, within the confines of a first order approximation to the overall mass balance framework. You are correct in that when and where there is missing data, that the emissions cannot be calculated at that exact place and time. We have examined the PDFs of the output emissions at each location and found that they are relatively smooth. For these reasons, unless the missing NO₂ observation were statistically very high or very low compared with the other values that already exist, they would not make a large difference in the overall emissions. However, including more observations from other existing and new observation platforms, or using other remotely sensed species in tandem will also help to improve the emissions estimate. Thank you for this suggestion, as it provides a path for future work.

1. In Sect 3.1, why a priori emission inventory (CEMS or MEIC) is needed to estimate new emission inventory? According to 3, it does not require a priori emission inventory.

In order to fit the first order terms approximating thermodynamics α₁, chemistry α₂, and transport α₃ in Eq. 3, an initial guess of emissions is required to complete the multiple linear regression. This then allows the distributions of the parameters α₁, α₂, and α₃ to be subsequently used in Eq. 3 to calculate the final emissions. It also allows for error analysis, since the fitted terms themselves have a range of possible solutions. In this work, two different emissions a priori were selected, with the goal being to demonstrate what differences this would have on the computed emissions.

This procedure is similar to how chemical transport models (including GEOS-Chem, WRF-Chem, etc.) have their initial uncertain variables fitted. The major differences being in this work the variables are sufficient simple so as to be flexible and presented in an open way. This allows for a wider range of possible emissions datasets to work within the model environment, which may not be possible with more heavily fitted or constrained modeling approaches. We believe the work herein demonstrates robustness as an entire system.

1. How EOF is applied to the daily TROPOMI NO₂ columns when data are not available in some grids?

When TROPOMI NO₂ columns are not available in some grids, the climatological average value in that grid is assigned in order to compute the EOF. The grid is also tagged and after the EOF is computed, the grid in space and time is reset to NaN, following Cohen (2014).

1. I’m curious why the seasonal variation of NO_x lifetime shown in Fig. 13b is so small. For example, Lamsal et al. (2010) estimated that the lifetime is NO_x is 7.6 h in summer and 17.8 h in winter, while this study showed that lifetime is ~12 h regardless of season.

Lamsal, L. N., Martin, R. V., van Donkelaar, A., Celarier, E. A., Bucsela, E. J., Boersma, K. F., Dirksen, R., Luo, C., & Wang, Y. (2010). Indirect validation of tropospheric nitrogen dioxide retrieved from the OMI satellite instrument: Insight into the seasonal variation of nitrogen oxides at northern midlatitudes. Journal of Geophysical Research: Atmospheres, 115(D5). https://doi.org/10.1029/2009JD013351

The median values of NO_x lifetime do demonstrate a range from 9.0 hours to 14.7 hours in different months. The 10^th and 90^th percentile values match with your reference paper quite well, being 7.1 hours and 18.1 hours respectively. The results in this work are based on the total column values, which includes temperature, UV, climate, and aerosols which are observed in Shanxi. Based on the results herein, the largest values are found in June or July and the smallest values are found in September. This is due to the complex local conditions and forcing factors including the complex boundary layer height, the variable aerosol loading, cloudiness, and other factors.

1. The authors concluded that “Thirdly, the general variability in geography, month of the year, and years before and after COVID-19 are all consistent with what is known.”, while readers cannot find any analysis that is related to COVID-19 in the manuscript.

The results herein show clearly that the emissions before COVID-19 were higher than after COVID-19. In specific, the time series shows that while there is a variation as a function of the time of the year, there is also a disturbance in this variation due to the timing of onset of COVID-19. What is important is that the emissions results match well with what is known by the community in terms of month-to-month changes, and geographic diversity, variability, and consistency across different industrial sources and under different oxidative and transport conditions. We have reorganized here in the following way:

“Thirdly, the variability of emissions in terms of different geographic location, source types, special events which changed the emissions levels (such as the onset of COVID-19), and general oxidative, photochemical, and transport conditions of the atmosphere on a monthly-scale, are all consistent with what is known.”

Technical corrections:

Line 202: the first three PC account for less than 50%

The first point is that the community acknowledges there is an uncertainty in TROPOMI observations of NO₂ which ranges as high as 30% to 50%. In this case, 30% to 50% of the PCs will be representative of this uncertainty, meaning their signal pattern while mathematically correct, is physically meaningless. Therefore, the results herein represent nearly all of the remaining variability. The three spatial modes [EOF1, EOF2, and EOF3] contribute 29.4%, 8.4%, and 4.4% respectively (accounting for 42.2%), while the fourth mode onward all contribute less than 4.0%. Next, the first three modes all have a high degree of correlation with known underlying driving phenomenon, while the fourth mode and onward show no such relationship. There are many other factors that affect the pollutant column loading in the atmosphere, and if we had more data to analyze, a way to bring in more variables, or a way to reduce the uncertainty, we would also like to search for and work more on attribution. Thank you for helping to carefully guide and clarify our thought process.

Line 26: NO₂ columns identifies -> NO₂ columns, which facilitates to identify

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Line 47: However -> Moreover

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Line 49: also impacting -> that impact

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Line 51: Nitrogen Monoxide -> nitric oxide

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Line 60: statistics on -> statistics for

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Line 67: differences -> the differences

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Line 84-85: Kong et al. (Kong et al., 2019) and Beirle et al. 85 (Beirle et al., 2019) -> Kong et al. (2019) and Beirle et al. (2019)

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Line 88: costly -> cost

Thank you, “costly to run” has been modified to “computationally intensive”.

Line 106-109: “The fact that …… variations observed.” This sentence is not easy to understand; it is better to rewrite.

We have reorganized here in the following way.

“This method has been used in different situation such as over different months, over multi-year changes in the environment, under different actinic flux and atmospheric oxidation conditions, under complex meteorological domains, and over sources which are both thermodynamically stable as well as unstable. That permits this study to explore the full range of variations”.

Line 126: Henk Eskes, 2021 -> Henk et al., 2021

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Line 126-128: “Furthermore, …… being discarded.” This sentence is not easy to understand; it is better to rewrite.

We have reorganized here in the following way.

“Furthermore, an additional filter is applied to set all individual gird of NO₂ column which is less than 1.4×10¹⁵ molec cm^-2 to be NaN. This is done to avoid issues where the observed signal may be smaller than the uncertainty of the signal itself (J.H.G.M Van Geffen, 2021; Qin et al, 2022)”.

Line 130: 2021are - > 2021 are

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Line 149: as discharged -> emitted

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Line 151: NOx concentration measuring -> measuring NOx concentrations

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Line 163: 24 is convert -> 24 is used to

Thank you, it has been modified to “24 is used to convert units from hours to days”.

Line 168: highest -> the highest

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Line 179: uniformity -> uniformly

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Line 201: (Björnsson and Venegas, 1997) and (Cohen, 2014) -> Björnsson and Venegas (1997) and Cohen (2014)

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Line 208: transport to -> transport

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Line 222: basis. -> basis

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Line 225: and not -> rather than

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Line 232: 𝛼1 𝛼2 and 𝛼3 -> 𝛼1, 𝛼2, and 𝛼3

Thank you, it has been modified in the whole paper.

Line 259: area. -> area,

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Line 387: Fig. 12(a) -> Fig. 12a

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References

Cohen, J. B.: Quantifying the occurrence and magnitude of the Southeast Asian fire climatology, Environ. Res. Lett., 9, https://doi.org/10.1088/1748-9326/9/11/114018, 2014.

J.H.G.M. van Geffen, H. J. Eskes, K.F. Boersma and J.P. Veefkind: TROPOMI ATBD of the total and tropospheric NO₂ data products, Open File Rep., 2021.

Qin, K., Shi, J., He, Q., Deng, W., Wang, S., Liu, J., and Cohen, J. B.: New Model-Free Daily Inversion of NO_x Emissions using TROPOMI (MCMFE-NO_x): Deducing a See-Saw of Halved Well Regulated Sources and Doubled New Sources, ESS Open Archive [preprint], https://doi.org/10.1002/essoar.10512010.1, July 26, 2022.