This article presents an new, improved method for estimating NOx emissions over urban areas based on TROPOMI or other high-resolution spaceborne NO2 data. The method builds on a previous method (Lorente et al. 2019) but introduces a well-thought Bayesian framework for the optimization of NOx emissions and lifetimes. In this way, the various uncertainties are taken into consideration, and overfitting is avoided. The advantages of the method are shown by tests (OSSE) using synthetic observations generated by a high-resolution model. Next, the method is applied to the estimation of NOx emissions over Paris using TROPOMI data. The results lead to several interesting insights on the emissions, including their trends, seasonal and weekly cycles, and variability due to covid-19 lockdowns. Overall, the manuscript is well-written, the methodology is clearly presented, with a few minor reservations (see below), and the results appear robust and useful to the top-down emission community. I see no reason why this method could be applied to many other cities and industrial centers worldwide. I recommend publication in this journal, provided that the authors address the following minor comments listed below.



Minor comments



l. 11-12 and l. 321: The decrease is -27% based on the 2018 and 2023 totals, not 17.5 or 18%. Please clarify.



Abstract and Conclusions: Can this method be applied to other large cities or industrial centers? A bit of discussion would be welcome.



l. 23 NO2+OH is not the only major sink, also formation of PAN  (for example) might be important in VOC-rich areas. PAN and other compounds may play the role of NOx reservoirs, which might partly invalidate the assumptions of the superposition model. I think that this issue should be mentioned and possibly discussed.



l. 24  Dry and wet deposition of HNO3 are about equally important sinks (see e.g. https://doi.org/10.1029/2018JD029133)



l. 90  Why not adopt a temperature-dependent rate for NO2+OH? The rate is higher in cold conditions (~10% higher at 283K compared to 298K)



l. 206-208  Based on Fig. 4, the prior is very close to the truth. Why is that? This might contribute to explain why the Bayesian inversion results are closer to the truth, due to the constraint from the first term of the cost function (Eq. 3).  What would happen if the prior was more different from the truth?



l. 247 Some more explanation (or maybe a reference) might be needed regarding the rotation and re-scaling step.



l. 264 CAMS NOx data are used for the domain average NOx/NO2 ratio. At what altitude above ground?



l. 275 "The NO2 concentrations (...) never completely decreased to the original levels": I do not follow here. Do you mean "increased"?



l. 288 What altitude for CAMS OH? Or is it an average weighted by the NO2 profile?



l. 319-320 The higher variability of posterior emissions is expected due to uncertainties in their derivation.



l. 345 and elsewhere in this paragraph: are the weekdend reduction calculated relative to the weekly (7-day) average, or relative to Mon-Fri average?



l. 350-351 I don't see how the higher cold start emissions in winter would reduce the weekend effect. It would be the other way around since traffic emissions are (expected to be) more strongly reduced during weekends. Therefore, only residential heating would have to explain the much weaker weekly cycle in winter compared to summer. Is this reasonable? What are the relative shares of the different sectors in the Paris area?





Technical / language comments



l. 6  MicroHH: what does the name stands for?



l. 49 "to estimate the NOx and predict CO2 emissions...": not clear why one is estimated and the other predicted. You could replace by "estimate NOx and CO2 emissions".



Legend of Fig. 1: why "grey arrow"? There are several (apparently) black arrows.



l. 95 Delete second "on"



Fig. 3 Use same distance units (preferably km) for all panels



l. 139 "the observed NO2 columns"



l. 152 Make a new sentence "It amounts to..."



l. 210 Figure 4b,d (not 4c,d)



l. 243 "Computation of..."



l. 244 Remove the first sentence since this step is elaborated in the following paragraph.



l. 275 "in between"



l. 317 Missing dot after parenthesis.



l. 340 Did you really filter data for weekdays? Isn't it for weekends?

Title: An improved Bayesian inversion to estimate daily NO_x emissions of Paris from TROPOMI NO₂ observations between 2018-2023

Author(s): Alba Mols et al.

MS No.: egusphere-2025-49

General Comments

            Mols et al. introduce a Bayesian inversion method which determines urban NO_x emissions at daily scale from along-wind line densities. These line densities are produced by integrating TROPOMI NO₂ vertical column densities in the cross-wind direction. The study first shows that a simple forward model can represent the relationship between emissions at each cell and the retrieved line densities. Then, a Bayesian approach is introduced where the inversion of this forward model with measured line densities is used to find emissions. Generally, the spatial distribution of NO₂ depends on both lifetime and emissions. A significant advantage of this study’s approach is the incorporation of prior information on lifetime and emissions into the cost function of the inversion. These priors avoid the overestimation of emissions due to unrealistic representations of the lifetime. The above method is shown to prevent the overfitting of a simpler least-squares inversion, which overpredicted emissions compared to simulated data. The determination of NO_x emissions over Paris between 2018-2023 illustrates interesting effects due to the COVID-19 lockdowns, the low-emission zone, and temperature. The differences between the findings of Lorente et al. and this study are discussed well. The idea is interesting. I recommend publication after attention to the items below.

Major comments

• The assumption that the TROPOMI retrieval is accurate enough to support the authors’ analysis should be further explored. The role of a number of resolution dependent aspects of the a priori used in retrievals that would result in systematic biases between city centers and their surroundings have been reported in the literature. It is important to note that these biases always reduce gradients between peaks in urban plumes and their surroundings. They are not simple random uncertainties. Examples are listed in the references below.
• There are many variations of the fitting approach described by Lorente et al in the literature that also aim to reduce the same biases in lifetime and emissions this paper aims to reduce. The paper should include a more complete summary of these approaches and their strengths and weaknesses relative to the stated goals. Recent papers from De Foy, et al. Liu et al, and Zhu et al. are examples, but there are many others.
• The paper rightly identifies correlation between NO2 concentration (and emissions) and lifetime as key. It should report on trends in the lifetime with reductions in NO2. These are likely of the same magnitude as the emission reductions but are nonlinear as shown by Zhu et al. (and others). Also, the paper indicates increases in O3 as an important effect on lifetime. The authors should compare the effect of increased ozone to the effect of differences in NO2 and VOC at the two comparison points. It is likely that an increased source of OH from O3 photolysis is the smallest contributor of these effects, that VOC changes are also small and that NO2 changes dominate.
• The reported improved performance is based on using the domain average lifetime of the simulation as the prior for the inversion. When applying to measured TROPOMI data, the prior lifetime is estimated from the average OH concentration in CAMS. However, a domain average lifetime is a poor approximation to a lifetime that is an explicit non-linear function of NO2.
• Since the prior is shown to have a significant impact on the inversion, the changing controls on lifetime should be discussed in the context of conclusions on NO_x emissions during different seasons and across long-term trends.

Specific Comments

Line 43: Other methods of simultaneous lifetime/emission derivation have been demonstrated and evaluated with satellite measured NO₂ columns. A more comprehensive summary of the literature and prior analysis is needed here.

Line 115: The ability of the superposition forward model to accurately represent the emissions/column relationship is tested in section 2.2. Photolysis representative for Riyadh is used in the MicroHH simulation, but the application city is Paris. This is confusing. Why was this choice made? Are there any city or latitude specific aspects of the model that are not directly transferrable and affect the interpretation?

Figure 1: Add description of black arrows; are these wind vectors at different locations over Paris?

Line 124: This implies that the symcity line densities are spaced by 5 km. In figure 3 c and f, The line densities are shown at a closer spacing of ~3 km.

Line 186: “We use a prior lifetime uncertainty s_A,k of 30%”. This uncertainty is used for the inversion of the forward model described by equations 1 and 2, where k is the chemical loss rate constant in units of inverse time. With this wording and notation, it is unclear whether s_A,kis referring to the uncertainty in the lifetime or in k. Since lifetime is the inverse of k, a 30% uncertainty in one value corresponds to a 233% uncertainty in the other. Further, the covariance in concentration and lifetime uncertainties is an element of the atmospheric chemistry. What are the downsides of not explicitly addressing this issue?

Line 198: Comment on how appropriate it is to treat the systematic uncertainty in the AMF error as random uncertainty used to draw from a normal distribution. At pixels with high emissions, the AMF error generally leads to VCDs that are biased low. This could lead to improper fitting of forward model parameters at those pixels.

Line 235: Recommended to be reworded. To some readers, this may imply that the TROPOMI V2.4.0 product uses CAMS NO₂ profiles even though it uses profiles from TM5-MP at 1° x 1. Emphasize that the product used is the European product described in Douros et al. with 0.1° x 0.1° resolution profiles.

Line 238: More context could be provided for the correction of TROPOMI bias. What was the existing TROPOMI bias at emission hotspots, and how much of this is corrected for with the 30% increase?

Line 288: See general comments; this is an area where more discussion of using CAMS OH for this purpose is warranted.

Line 293: Expand on the justification of using a 30% uncertainty for the prior lifetime when the common value is 50%. The current explanation is that 30% encompasses most of the expected 50% uncertainty, but is the 50% uncertainty not also a type of standard deviation? If not, then clarify this.

Table 4 caption: The standard deviation of the posterior is estimated using a specific date in the summer. Were other dates tested? The prescribed uncertainties may be expected to change throughout the year, such as during winter when the NO_x lifetime is longer and its absolute uncertainty increases.

Technical Corrections

Line 95: Remove repeated “on”

Line 115: Change “Riaydh” to “Riyadh”

Figure 3 caption: Should be “symcity” instead of “simcity” for consistency?

Table 1: Add units to column “Total E_NOx”

Line 275: Should this be “never completely increased to their original levels”?

References

Beirle and T. Wagner, “A new method for estimating megacity NO_x emissions and lifetimes from satellite observations,” Atmospheric Meas. Tech., vol. 17, no. 11, pp. 3439–3453, Jun. 2024, doi: 10.5194/amt-17-3439-2024.

Benjamin de Foy, Joseph L. Wilkins, Zifeng Lu, David G. Streets, Bryan N. Duncan, Model evaluation of methods for estimating surface emissions and chemical lifetimes from satellite data, Atmospheric Environment, Volume 98, 2014,Pages 66-77, https://doi.org/10.1016/j.atmosenv.2014.08.051.

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,” no. 2.4.0, Jul. 2022, [Online]. Available: https://sentinel.esa.int/documents/247904/2476257/Sentinel-5P-TROPOMI-ATBD-NO2-data-products.pdf

J.L. Laughner, Zhu, Q., and Cohen, R. C., Evaluation of version 3.0B of the BEHR OMI NO₂ product, Atmos. Meas. Tech., 12, 129-146, https://doi.org/10.5194/amt-12-129-2019, 2019

J.L. Laughner, A.H. Zare and R.C. Cohen, Effects of daily meteorology on the interpretation of space-based remote sensing of NO₂ Atmos. Chem. Phys. 16, 15247-15264, doi:10.5194/acp-16-15247-2016, 2016.

J.L. Laughner and R. C. Cohen, “Direct observation of changing NOx lifetime in North American cities,” Science, vol. 366, no. 6466, pp. 723–727, Nov. 2019, doi: 10.1126/science.aax6832.

Liu, F., Tao, Z., Beirle, S., Joiner, J., Yoshida, Y., Smith, S. J., Knowland, K. E., and Wagner, T.: A new method for inferring city emissions and lifetimes of nitrogen oxides from high-resolution nitrogen dioxide observations: a model study, Atmos. Chem. Phys., 22, 1333–1349, https://doi.org/10.5194/acp-22-1333-2022, 2022.

Jin, Q. Zhu, and R. C. Cohen, “Direct estimates of biomass burning NO_x emissions and lifetimes using daily observations from TROPOMI,” Atmospheric Chem. Phys., vol. 21, no. 20, pp. 15569–15587, Oct. 2021, doi: 10.5194/acp-21-15569-2021.

Zhu, J.L. Laughner, and R.C. Cohen, Estimate of OH Trends over One Decade in North American Cities, Proc. Nat. Acad. Sci. 10.1073/pnas.2117399119, 2022.