General comments

The authors present a comprehensive analysis of the flux divergence method (FDA) using model fields created with the LOTOS-EUROS model for the Netherlands. The paper provides new insights in the accuracy of the FDA model. The paper is written well and the structure is clear. The methods are outlined well and clear with a few open questions:

• The conclusions on the accuracy of the FDA model depend on the LOTOS-EUROS simulations. The authors should provide additional information on accuracy of the simulations, LOTOS-EUROS settings (e.g. spatial smoothing) and the impact on the conclusions.
• It is unclear how emissions are released in the model. If NOx emissions are released at the surface, it is likely that NOx will remain within the PBL and thus the approach of considering only the PBL column is feasible. However, as real NOx emissions often occur at stacks, vertical emission profiles should be used, which may result in emissions occurring in the free troposphere. In this case, using only the PBL column may not be a valid approach, especially in the case study for the morning overpass times where the PBL height is low.
• The section on the NOx partitioning factor (Section 3.1.5) is quite short and ignores recent studies that have used values different from 1.32 (see specific comments).

Specific comments

L65ff: The differentiation between "plume dispersion models" and "mass conservation" is oversimplified here. The assumption of mass conservation is also used for methods that are applied to single sources (e.g. cross-sectional flux, Gaussian plume inversion and integrated mass enhancement). The statement "no need to run a computationally expensive CTM" contradicts the main conclusion of the study that CTM simulations are needed (last sentence in the abstract).

L75f: There have been some studies that have analyzed the FDA accuracy using model data: e.g. Goldberg at. 2022 and Hakkarainen et al. 2022.

L109f: You could mention here, why updating the a priori profile only partially corrects the bias.

L137: Please clarify if emissions were released at the surface or vertical profiles were used. If emissions were released at the surface, it is likely that all NOx remains in the PBL. However, vertical profiles can release NOx into the free troposphere (in particular for low PBL), which has implications on the performance of using PBL columns only.

L161ff: Koene et al. 2024 show that divergence should be computed over the smallest region possible to avoid noise negatively affecting the divergence calculation (recommendation 5). A forth-order difference is therefore likely less ideal. You probably do not see the impact here, as you do not include noise in your NO2 fields. However, I think it would be good to note that for application to noisy satellite images, a lower-order operator might be better.

L173ff: While NOX concentrations are stable around TROPOMI overpass, increasing turbulent mixing can still badly break the steady-state assumption inside plumes resulting in biased divergence fields.  

L180ff: Since the NO₂ enhancement will always have a vertical extent, the effective wind speed should be computed using the concentration profile of the NO₂ enhancement. Half the PBL height is a good approximation of the mean wind speed inside the PBL assuming well-mixed NO2 concentrations, which isn't a bad assumption for cities or a few kilometers downstream of stack source (e.g. Krol et al. 2024).

L187f: The wind divergence will remain zero for a total column (assuming incompressible air), but not for partial column (e.g., PBL column), because air can leave or enter at the top of the partial column. In theory, it is possible to compute a two-dimensional wind, but this would require that you know both the NO2 and wind profile (Koene et al. 2024). Thus, errors in the wind are caused by using (a) only a partial NO2 column and (b) the wind field at a single (spatial varying) altitude.

L222f: The paragraph should acknowledge recent studies that have used different NOx partitioning factors: "Often a constant NOx:NO2 ratio is assumed to infer the NO emissions from space-based NO observations. Many studies (e.g., Beirle et al., 2011, Beirle et al., 2019, de Foy and Schauer, 2022, Merlaud et al., 2020, Shaiganfar et al., 2017, Ionov et al., 2022, Potts et al., 2022, Hakkarainen et al., 2021) use the steady-state noontime molar concentration ratio under typical urban conditions of 1.32 based on Seinfeld and Pandis (2006). Recently, model-based concentration ratios have also been calculated using simulations from Copernicus Atmospheric Monitoring Service (CAMS, Lorente et al., 2019, Rey-Pommier et al., 2022) and Comprehensive Air Quality Model with Extensions (CAMx, Goldberg et al., 2022). Beirle et al. (2021) calculated NOx:NO2 ratios according to the photo-stationary steady state. In general, these studies show small deviations from the value 1.32 (e.g., 1.16–1.83), but acknowledge that values near the point sources are likely to be higher. CHIMERE model simulations (Shaiganfar et al., 2017) further indicate that in large circles around Paris, the partitioning ratios are smaller during summer (1.32) than in winter (1.51), due to the higher ozone mixing ratios in summer. In contrast to model-based analyses, the Dutch aircraft measurements of in-plume NOx/NO2 ratios from power stations (e.g., Janssen, 1988, Vilà-Guerau de Arellano et al., 1990, Bange et al., 1991, Hanrahan, 1999) often showed values higher than 10 near the source and values between 2 and 10 up to 15 km from the source." (Hakkarainen et al. 2024).

L245: I am also not aware of any studies that subtracted the background from NO2 observations. The background has also been subtracted from CO2 columns by Hakkarainen et al. (2022). Koene et al. (2024) show that removing the background eliminates the steady-state assumption for the background component.

L304ff: You earlier state that using a second-order difference instead of fourth-order difference had only a minor impact on your results. This contradicts your statement here that the fourth-order difference cause (strong) spatial smearing.

Therefore, the smearing likely has a different explanation: I would expect some smoothing from LOTOS-EUROS depending on the model dispersion settings, as the effective model resolution is typically coarser than grid resolution of 2 km. It is also possible that LOTUS-EUROS is not mass conserving at strong point sources.

L335ff: Is using the PBL column still feasible, if strong point sources release in the free troposphere in particular for low PBLs? Was this include in the model simulations?

L384f: As noted above, many recent studies used values other than 1.32.

L401f: The impact of the divergence-free winds is likely small, because you subtract the background from the NO2 column. Koene et al (2024) show that omitting the wind divergence term is useful if the background is not removed from the column.

L416f/L440ff: Do you use only PBL columns in this case study? I would expect that in the morning the PBL is very low, which would "leak" some NO2 in the free troposphere and thus result in an underestimation of the emissions.

L486: An underestimation of the emissions by 18% is still larger than 11% from the synthetic data. Can you provide a brief a discussion for the reasons? Is the bias due to overestimated emissions in simulation or caused by the FDA method?

L530f: Most studies use ERA-5 wind fields instead high-resolution simulations. Do you expect an impact on estimated emissions using ERA-5 fields?

L553: What are the implications for Sentinel-5 with an overpass time of 9:30 LT?

Technical corrections

L6: Summer -> summer

L98: DOAS -> Differential Optical Absorption Spectroscopy (DOAS)

Figure 3: Mention that the figure is for ID06.

Table 3: Please add units.

Figure A6: Colorscale is not ideal.

References

Goldberg et al., https://doi.org/10.5194/acp-22-10875-2022, 2022.

Hakkarainen  et al., https://doi.org/10.3389/frsen.2022.878731, 2022.

Koene et al., https://doi.org/10.1029/2023JD039904, 2024.

Krol et al., https://doi.org/10.5194/acp-24-8243-2024, 2024.

Hakkarainen et al., https://doi.org/10.1016/j.apr.2024.102171, 2024.

Title: Accurate space-based NOx emission estimates with the flux divergence approach require fine-scale model information on local oxidation chemistry and profile shapes

Author(s): Felipe Cifuentes et al.

MS No.: egusphere-2024-2225

MS type: Model evaluation paper

General Comments

This paper discusses NOx emissions using the flux-divergence approach (FDA) on measurements from space-based instruments, primarily TROPOMI. Specifically, the sensitivity of the derived emissions to the NO₂ lifetime, NO_x-NO₂ ratio, column integration height, wind altitude, and wind divergence were tested. The researchers used the LOTOS-EUROS chemistry transport model at 2x2 km to produce high-resolution values for these various parameters, then compared to fixed values. For example, the varying NO₂ lifetimes produced from LOTOS-EUROS were used in one test while a fixed 4-hour lifetime was used in another.

The study offers valuable contributions for understanding the FDA and its limitations in this application. The various types of comparisons—first with synthetic observations on the model grid, then on the TROPOMI on grid, and finally with TROPOMI observations—helped distinguish which factors affected the error between the model-ingested emissions and the derived emissions. More discussion is advised for the section on real TROPOMI data, where the a priori TM5 profiles are replaced with profiles from LOTOS-EUROS. Since most research will focus on real observations impacted by the retrieval process, the implications of this a priori replacement were underdiscussed. Last, the paper often lacks citation to other related work (especially research on the role of high space and time resolution a priori profiles) which would provide context to the researchers’ experiment design and findings.

Specific Comments

Line 78: As discussed in Douros et al. (2023), a major contribution to this bias is also the a priori NO₂ profile used in the retrieval. This is related to, but different from, the issue of reduced sensitivity near the surface.

Line 130: It would be helpful to clarify how the top vertical layer compares to the typical location of the tropopause, since the synthetic observations are compared with tropospheric columns.

Line 210: Running a CTM at fine resolution has also been shown to reduce NO₂ lifetimes in NO_x-limited regimes (e.g. Li et al., 2023).

Line 215: Notably, the study domain of Rey-Pommier et al. (2022), is Egypt, which has comparatively little forestation. Delaria et al. (2020), indicates that the lifetime to stomatal deposition can be as short as 10 hours in forested regions. The expected lifetime to deposition in the study domain (Netherlands) should be explored.

Line 255: The definition of a “hotspot” is set at 10% percentile of the original emission inventory. This definition is later used to draw key findings: for example, when comparing the use of TM5 vs. LOTOS a priori profiles, TM5 has a smaller positive bias overall but much greater negative bias among hotspots (Table 3). To strengthen conclusions based on the “hotspot” division, the choice of 10% could be further discussed. How sensitive are the study’s conclusions to the choice of percentile? Is there another reason to emphasize the accuracy at these hotspots at the expense of the domain more broadly?

Line 324:  See note on Line 210

Line 337: Were there any spatial trends in the proportion of free tropospheric NO₂?

Line 349: The researchers find limited sensitivity to the altitude selected for wind fields. Table 1 suggests that this was a key question, since 4 of the 7 tests focus on the variation of winds altitude. The discussion centers on how this may be unique to the terrain of the studied domain, but it is not clear if the researchers were limited to this domain or chose not to further explore the effect of a different terrain on this aspect of the FDA.

Line 382: The need to accurately represent lifetime is not unique to the FDA method, especially for larger scale emission retrievals like those discussed above. Plume-based methods (e.g. in Beirle et al. (2011), Valin et al. (2013) and many, many other more recent references  from an array of research groups) rely on simultaneous retrieval of both the lifetime and emissions from satellite observations, with the implications for the estimated emissions explored in-depth. The researchers should show how their findings about the lifetime’s importance builds on previous approaches to deriving NO_x emissions.

Line 433: “Furthermore, the planetary boundary layer (PBL) reaches its peak during this time, aiding in the dispersion and dilution of pollutants.” This is one two reasons provided for the decreased in vertical column densities (VCDs) from 11:00 to 16:00 local time. While vertical mixing will increase at the peak of the PBL, this would not impact the integrated vertical column densities. There could be other reasons that the increased dispersion/dilution at this time would lead to decreased VCDs, but this should be clarified.

Line 445: While this is true for a single instrument, work has been done to estimate changes in vertical column using multiple polar orbiting satellites (Penn and Holloway, 2020)

Line 448: What reactions are expected to start competing at these times? Generally, how are the assumptions about loss to OH complicated by the growing importance of RONO₂ chemistry (Romer Present et al., 2020)

Line 466: What are the temperature-dependent emissions in the model and what direction does this direct the resulting bias? (E.g. are these diesel related as in Grange et al. 2019?)

Line 488: When discussing agreement between FDA-derived emissions and model-ingested emissions, there should be more exploration on the effects of using a priori profiles from LOTOS-EUROS. For example, the model wind fields will impact the retrieved VCDs and not just the divergence term. The importance of using a priori inputs with accurate meteorology are discussed in Laughner et al. (2016) and would impact the gradients that are analyzed through the divergence term.

Line 511: It is claimed that good agreement exists between model-ingested emissions and FDA-derived emissions when LOTOS-EUROS is used for the a priori profiles. The authors claim that “top-down satellite and bottom-up inventory emissions are derived in a independent way, except for the a-priori replacement.” The change in a priori profiles will certainly have an effect on the retrieved VCDs, and therefore the emissions from the FDA. It would be more appropriate to say that the FDA produces values in agreement with known emissions that informed the retrieval. However, if the true emissions were not the same as model-ingested emissions, it is not clear how much agreement would be observed. While this is not necessarily the focus of the study, further elaboration on this point would be advised. This could also build on existing studies investigating the relationship between model-ingested emissions, model resolution, and top-down emissions estimates (e.g. Goldberg et al., 2019). This is important for readers interested in the value of replacing the a priori profiles, but for the purpose of obtaining new emissions estimates rather than verifying an existing one.

Technical Corrections

• Line 97: correct “NO2” to “NO₂” for consistency with rest of paper
• Line 245: correct “FDA approach” to “FDA”
• Line 515: correct “a independent” to “an independent”

References

Beirle, S., Boersma, K. F., Ulrich, P., Lawrence, M. G., and Wagner, T.: Megacity Emissions and Lifetimes of Nitrogen Oxides Probed from Space, Science, 333, 1737-1739, https://doi.org/10.1126/science.1207824, 2011.

Delaria, E. R., Place, B. K., Liu, A. X., and Cohen, R. C.: Laboratory measurements of stomatal NO₂ deposition to native California trees and the role of forests in the NO_x cycle, Atmos. Chem. Phys., 20, 14023–14041, https://doi.org/10.5194/acp-20-14023-2020, 2020.

Douros, J., Eskes, H., van Geffen, J., Boersma, K. F., Compernolle, S., Pinardi, G., Blechschmidt, A.-M., Peuch, V.-H., Colette, A., and Veefkind, P.: Comparing Sentinel-5P TROPOMI NO2 column observations with the CAMS regional air quality ensemble, Geoscientific Model Development, 16, 509–534, https://doi.org/10.5194/gmd-16-509-2023, 2023.

Goldberg, D. L., Saide, P. E., Lamsal, L. N., de Foy, B., Lu, Z., Woo, J.-H., Kim, Y., Kim, J., Gao, M., Carmichael, G., and Streets, D. G.: A top-down assessment using OMI NO₂ suggests an underestimate in the NO_x emissions inventory in Seoul, South Korea, during KORUS-AQ, Atmos. Chem. Phys., 19, 1801–1818, https://doi.org/10.5194/acp-19-1801-2019, 2019.

Grange, S. K., Naomi, J. F., Vaughan, A. R., Rose, A. R., and Carslaw, D. C.: Strong Temperature Dependence for Light-Duty Diesel Vehicle NO_X Emissions, Environ. Sci. Technol., 53, 6587-6596, http://doi.org/10.1021/acs.est.9b01024, 2019.

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

Li, C., Martin, R. V., Cohen, R. C., Bindle, L., Zhang, D., Chatterjee, D., Weng, H., and Lin, J.: Variable effects of spatial resolution on modeling of nitrogen oxides, Atmos. Chem. Phys., 23, 3031–3049, https://doi.org/10.5194/acp-23-3031-2023, 2023.

Penn, E., and Holloway, T.: Evaluating current satellite capability to observe diurnal change in nitrogen oxides in preparation for geostationary satellite missions, Environ. Res. Lett., 15, 034038, https://doi.org/10.1088/1748-9326/ab6b36, 2020.

Rey-Pommier, A., Chevallier, F., Ciais, P., Broquet, G., Christoudias, T., Kushta, J., Hauglustaine, D., and Sciare, J.: Quantifying NO_x emissions in Egypt using TROPOMI observations, Atmos. Chem. Phys., 22, 11505–11527, https://doi.org/10.5194/acp-22-11505-2022, 2022.

Romer Present, P. S., Zare, A., and Cohen, R. C.: The changing role of organic nitrates in the removal and transport of NO_x, Atmos. Chem. Phys., 20, 267–279, https://doi.org/10.5194/acp-20-267-2020, 2020.

Valin, L. C., Russell, A. R., and Cohen, R. C.: Variations of OH radical in an urban plume inferred from NO2 column measurements, Geophys. Res. Lett., 40, 1856-1860, https://doi.org/10.1002/grl.50267, 2013.