the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 27 Aug 2025
Kalman filter inversions on NOx and VOCs emissions in China using TROPOMI satellite observations
Abstract. Kalman filter inversions with multipollutant may improve the accuracy of inversion results and model performance. A joint inversion of VOCs and NOx emissions was conducted using the HCHO and NO2 column data from the TROPOspheric Monitoring Instrument and the simulated sensitivities of VOCs and NOx from an air quality model from June to September 2019. The results showed that joint inversion results typically outperformed that of separate inversion in reducing model bias and error and regional variations of emission estimates under satellite data constraints. The inversed NOx emissions over China decreased from a priori by approximately 30 %, and the inversed VOCs emissions over China increased from a priori by around 50 %. Joint inversion results aligned more closely with satellite-observed NO2 and HCHO columns, capturing the unique belt-like distribution of HCHO and stabilizing maximum NO2 column at approximately 15 molec/cm². The accuracy of simulated ground-level ozone concentrations was enhanced by the joint inversion, with the mean bias decreased by 11.6 μg/m³ overall. Meanwhile, ozone sensitivities prevalently shifted towards NOx-limited conditions during summer after the joint inversion.
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CC1: 'Comment on egusphere-2025-2687', Amir Souri, 29 Aug 2025
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AC1: 'Reply on CC1', Xiaohui Du, 08 Sep 2025
Dear Dr. Souri,
We would like to sincerely thank you for taking the valuable time to give feedbacks for this paper. We have studied many of your publications, and your insights into the application of joint inversion for multiple species have provided us with key perspectives for understanding the integration of atmospheric modeling and inversion methods. The work conducted by your team in the field of joint inversion using multiple satellite data has long been a crucial reference for our research.
The questions you raised regarding the statements that reference your research (Souri et al., 2020) may have led to unnecessary misunderstandings, and we sincerely apologize for this matter. We must make it clear that this paper has no intention of denying the efforts of your research in accounting for nonlinear chemical processes within inversion methods. In fact, the approach adopted by your team that uses a nonlinear Gauss-Newton optimizer to iteratively update the Jacobian matrix and avoid overcorrection of the state vector is a wonderful solution to address nonlinearity in the inverse modeling.
The primary cause of this misunderstanding lies in the ambiguity of the conceptual boundaries of "nonlinear chemical processes" and "cross interactions between species". What this paper truly aims to emphasize is that, building upon the existing inversion methods, it is important to include interspecies interactions from chemical transport models to deal with the nonlinear relationships in the iterative inversions. As stated in your earlier paper (Souri et al., 2020) in AE, which we will reference in our study as well, the impact of NOx on HCHO formation is indeed of great significance. Hence, we further incorporate cross-sensitivities between different species (i.e., the cross sensitivities of HCHO to NOx and NO2 to VOCs) from chemical transport models to supplement information at the level of species interactions.
To correct this phrasing, we will revise the sentence of “However, the Jacobian matrix settings in previous studies incorporated only the sensitivities of multiple pollutant concentrations to self-emissions during inversion process, without considering the cross-sensitivities of species interactions. It is important to include interspecies interactions from chemical transport models to deal with the nonlinear relationships in the iterative inversions." to: "It is important to include inter-species interactions from chemical transport models to complement on the species-specific sensitivities in the iterative inversions." This revision clearly focuses the innovation of this study on "supplementing information on cross-sensitivities between species," thereby avoiding any potential misunderstandings.
Once again, thank you for your careful feedback and corrections!
Du Xiaohui
Citation: https://doi.org/10.5194/egusphere-2025-2687-AC1
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AC1: 'Reply on CC1', Xiaohui Du, 08 Sep 2025
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RC1: 'Comment on egusphere-2025-2687', Anonymous Referee #1, 15 Sep 2025
This manuscript applies a discrete Kalman filter inversion using TROPOMI NO2 and HCHO data to jointly constrain NOx and VOC emissions over China, and evaluates impacts on ozone simulations. While the topic is relevant and the methodology is presented in detail, the study suffers from fundamental limitations in data representativeness, methodological assumptions, and validation strategy. These flaws seriously undermine the robustness and reliability of the results and conclusions. For this reason, I recommend rejection.
- The study is restricted to June–September 2019, a single summer season. O3 precursor emissions and chemical regimes exhibit strong seasonality, and summer alone cannot represent annual or multi-year behavior.
- More critically, the actual effective TROPOMI sampling at the grid scale is extremely sparse. For many grid cells, only 1 valid day per month is available; even the best cases show only 7–8 days. It is questionable whether such limited sampling can be considered statistically representative. The monthly “averages” used in the inversion may be dominated by noise and random sampling artifacts rather than true emission signals.
- In some cases, the posterior simulations perform worse than the prior when compared against neutral independent observations (e.g., ground-based O3). This is deeply concerning: if the inversion were truly improving emissions, performance against independent data should consistently improve.
- Such deterioration suggests one or more unresolved structural problems: (i) temporal representativeness of the satellite data; (ii) spatial representativeness, given TROPOMI coverage gaps; or (iii) vertical representativeness, as column retrievals may not align with near-surface concentrations. The manuscript does not analyze or even acknowledge these critical issues.
- VOCs are treated as a single aggregated species. However, O3 formation in China is highly sensitive to differences among VOC classes (aromatics, alkenes, aldehydes, etc.). A bulk VOC inversion lacks chemical meaning and risks producing misleading results, particularly when the posterior shows a +50% increase in VOC emissions.
- Without species-level constraints or validation, the VOC conclusions cannot be considered credible.
- The assumption of diagonal observational error covariance is unrealistic for TROPOMI products, where retrieval errors are spatially correlated, especially over polluted regions. This simplification likely underestimates uncertainties and biases the inversion.
- The manuscript presents posterior estimates without confidence intervals or quantified uncertainties, making it impossible to judge robustness.
- The study lacks cross-comparison with other emission inventories (e.g., MEIC, EDGAR), independent ground or aircraft observations, or alternative satellite products (OMI, IASI).
- In particular, the VOC inversion results are not validated against any independent dataset, leaving their reliability entirely unsubstantiated.
- The claim that ozone sensitivities nationwide shift predominantly to NOx-limited conditions after inversion relies solely on model output. No independent evidence (e.g., HCHO/NO2 ratios, MAX-DOAS, or mobile observations) is provided.
- Without observational support, these sensitivity changes may simply reflect model self-consistency rather than the real atmosphere.
Citation: https://doi.org/10.5194/egusphere-2025-2687-RC1 -
RC2: 'Comment on egusphere-2025-2687', Anonymous Referee #2, 18 Sep 2025
Comments to “Kalman filter inversions on NOx and VOCs emissions in China usingTROPOMI satellite observations” by Du Xiaohui et al.
This study employs a discrete Kalman filter approach to invert NOx and VOCs emissions over China and evaluates its impact on simulation results. The topic is novel and addresses the challenging nonlinear inversion problem related to O3-NOx-VOCs chemistry, which requires careful consideration when inverting NOx emissions. However, the manuscript has limitations in its methodology. The description of the method is not sufficiently clear, and the inversion results require more rigorous examination. I recommend a major revision before further consideration.
Specific Comments:
- Equation 2 is an incomplete and potentially misleading expression. The subscript ”i”is conventionally used to denote a specific time step, which is particularly relevant in emission inversion problems where a time window links concentrations to emissions. The authors' use of Ei+1 to represent the "analysed state of Ei" is unconventional. I suggest using superscripts ”Ea” (analysed) and ”Eb” (background) for clarity. The formula for generating the ensemble perturbations should also be explicitly provided.
- Based on the Methods section (Lines 155-157), the authors appear to treat VOCs as a single species. This assumption could significantly impact the inversion results, as VOCs are highly complex and different species exhibit vastly different reaction rates with NOx. The manuscript needs to provide stronger evidence to support the reliability of the inverted VOC emissions.
- The observation error should encompass both instrument error and representativeness error. The current overly simplistic configuration may affect the results and needs to be revisited.
- How does the method account for spurious correlations, a common issue in ensemble-based inversion systems?
- Please clarify how the nonlinear relationships between O3, NOx, and VOCs are constructed and represented within the inversion framework.
- Please clarify how was the observation system simulation experiment designed? Were the background NOx and VOC emissions perturbed? Specifically for VOCs, were all species perturbed randomly? Were the "observations" used to constrain the background emissions column concentrations, identical to the satellite product? Please clarify.
Additionally, should the y-axes of Figures 2a and 2c read "HCHO column from background emissions" and "NO₂ column from background emissions", respectively? Tables S2 and S3 are missing units. - Please specify the initial chemical conditions and boundary conditions used in the model.
- What is the proposed explanation for the underestimation of emissions observed in Figures 3 and 4 when inverting only NOx or HCHO emissions? Please discuss.
- Figure 7: Are the O₃ data used for evaluation instantaneous values or 8-hour maximum values?
- Table 2: In some regions (e.g., CC, NWC, SWC), the joint inversion does not yield the best performance. What are the potential reasons for this?
Minor Comments:
- Line 42: The statement that "differences exceed a factor of 2" regarding bottom-up NOx emissions should be nuanced. The literature often suggests total inventory uncertainties are within ±35%, so this claim should be carefully revised and supported.
- Many figures and tables lack units for emission rates and concentrations.
- Table 2: The "Obs" data column only needs to be listed once per region, not repeated for each row within a region.
Citation: https://doi.org/10.5194/egusphere-2025-2687-RC2 -
RC3: 'Comment on egusphere-2025-2687', Anonymous Referee #3, 14 Oct 2025
Du et al. constrains NOx and total VOC emissions in a bottom-up emission inventory using Kalman Filter and TROPOMI column observations. The authors compare results between individual and joint inversions, and show implications for surface ozone simulations and formation regimes. The topic is relevant for ACP, and the results can be useful for the emission and modeling community. However, substantial improvements are needed before the manuscript can be accepted.
Major comments:
- The methodology is not very clear to me. Line 231 states that the adjustment factors are uniform across a region, but from Lines 154-155 it seems that the inversion is conducted at the model grid level. Please clarify.
- It is also unclear whether and how the averaging kernels in TROPOMI retrievals are considered in the inversion.
- Uncertainties in biogenic VOC emissions and how that may impact anthropogenic VOC inversion should be acknowledged and discussed. Although mean bias in HCHO simulations reduces after inversion, a 20-30% underestimation still exists (Table S7) which may be due to uncertainties in biogenic emissions. Similarly, how are NOx emissions from other sources considered (such as from soil)?
- The NOx inversion results seem to be worse for joint inversion than for individual inversion (Figure 5), and sometimes worse than a-priori (Table S7) when compared with TROPOMI tropospheric NO2. Visual inspection at Figure 5 seems to show an overall NO2 overestimation after joint inversion, but Table S7 shows underestimations in every region. More diagnoses and explanations are needed here. Is averging kernel considered when comparing simulations with TROPOMI observations?
- It may be helpful to compare with other widely used inventories (EDGAR, MEIC) to better put the results in context.
Minor comments:
- Lines 35-38: Time frame and citations are needed.
- Line 41: I am not sure how NOx’s lifetime is relevant for the overestimation for bottom-up emissions.
- Lines 59-61: This statement is not true. The GEOS-Chem adjoint used in Wang et al. (2020) inherently considers cross-species sensitivy.
Wang, Y., Wang, J., Xu, X., Henze, D. K., Qu, Z., and Yang, K.: Inverse modeling of SO2 and NOx emissions over China using multisensor satellite data – Part 1: Formulation and sensitivity analysis, Atmos. Chem. Phys., 20, 6631–6650, https://doi.org/10.5194/acp-20-6631-2020, 2020.
- Lines 72-74: Perhaps mention the time period of the study here?
- Figures 2(a) and (c): Should the label of y-axis “a-priori”?
- Table 1: Is the unit “tons during the study period”? Perhaps include the relative change in the table to facilitate comparisons?
- Line 100: More descriptions about the a priori emissions are needed. For example, what are the spatial and temporal resolutions?
- Line 103: What VOC species are considered?
- Lines 204-205: “The inversed NOx emissions over China decreased from a priori by 39% and 17% via individual and joint inversions” seems to be in disagreement with the claim in the abstract “The inversed NOx emissions over China decreased from a priori by approximately 30%”. Perhaps add a row in Table 1 for the entire China?
- Figures 3-6: Units are missing. Perhaps consider plotting the relative between posterior and a priori to make comparisons easier.
- Line 282: What is the NO2/HCHO threshold used to define ozone formation regimes? This should be clearly stated in the methods.
- Lines 321-323: What is the metric being discussed here? Is it MDA8 ozone?
- There are grammatical errors throughout the manuscript. A few examples are:
Line 43: remove “occurred”
Line 53: “since nonlinearity” -> “since there is nonlinearity”
Line 59: “as one of interacted pollutant undergo changes” -> “as one of the interacting pollutants undergoes changes”
Citation: https://doi.org/10.5194/egusphere-2025-2687-RC3 -
RC4: 'Comment on egusphere-2025-2687', Anonymous Referee #4, 20 Oct 2025
The authors present a joint inversion of NOₓ and VOC emissions in China using TROPOMI HCHO and NO₂ data. The topic is relevant and timely, especially given China's ongoing challenges with surface ozone pollution. The application of a Kalman filter for multi-precursor inversion is a valid approach. However, several fundamental aspects require substantial improvement to meet the high standards of ACP. The core issues are a lack of clear novelty and insufficient treatment of uncertainties. Therefore, I recommend major revision for the reasons detailed below.
Major concerns:
1. The study applies an established methodology (Discrete Kalman Filter with CAMx-DDM) to a known problem (NOₓ/VOC emissions in China). To strengthen its contribution, the authors may need more explicitly differentiate their work from previous studies (e.g., Jung et al., 2022; Souri et al., 2020). The introduction mentions that prior work did not fully consider cross-sensitivities, but it remains vague. The authors may want to revise the Introduction and Discussion to clearly state what specific, novel scientific insight or methodological advancement this work provides. For instance, does their implementation of the joint inversion offer a significantly different outcome or provide new, groundbreaking insights compared to the cited studies? A dedicated paragraph in the Introduction should frame this research question and explicitly state how this study advances beyond the current state-of-the-art as defined by these references. Merely combining existing methods and applying them to China may not constitute sufficient novelty for ACP.
2. The manuscript lacks a thorough analysis of how uncertainties in key inputs and assumptions impact the final emission estimates. This is particularly critical when using satellite data and complex model sensitivities. I find the choice of prior error estimates (50% for NOₓ, 150% for VOCs) appears arbitrary without justification or sensitivity tests. And the description of TROPOMI data uncertainties is general and not integrated into the interpretation of the inversion results.
3. The manuscript does not sufficiently benchmark its results against prior top-down emission estimates for China. How do the derived 30% decrease in NOₓ and 50% increase in VOCs compared to other published inversion results? Are the spatial patterns truly new? In the Results and Discussion, the authors may want to add a direct comparison with key previous studies. A table summarizing different inversion results (method, period, key findings) for China would be highly effective.
Minor comments:
1. Line 23, what does “15molec/cm²” mean? Do you mean 10E15 molec./cm²?
2. Line 43, NO2, subscripted. Same in Line 122 for CFCl3
3. Line 57, “. Müller en Stavrakou, (2005)”, inconsistent reference style. Same in Line 287, “Wang et al. 2023.”
4. Line 107, Figure 1, the caption is minimal. Please describe what the different colors represent (e.g., major regions or provinces). The figure itself would benefit from clear borders and labels for key areas (e.g., Beijing-Tianjin-Hebei, Yangtze River Delta), particularly if they are discussed in the text. Also it seems there is too much blank space in the right and upper area.
5. Line 129, missing “:” after “as”
6. Line 213, Figure 3, there is no unit associated with the color bar. Same issue for Figure 4, 5, and 6.
7. Line 230, “15molec./cm2”, I don’t understand. Same puzzle in Line 241 as it comes to “12molec./cm2” and “15molec./cm²” in Line 325.
8. Line 285, “OMI satellite-based”, should be “TROPOMI satellite-based”?
9. Line 344, “This work was supported by” is in blue.
Citation: https://doi.org/10.5194/egusphere-2025-2687-RC4
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Our work (Souri et al., 2020) is, to our best knowledge, the first joint inversion of NOx and VOCs using multiple satellites, performed to constrain net ozone production rates using an analytical Gauss-Newton method. Here, the authors mentioned in their introduction that our work did not consider the non-linear chemistry because we omitted the cross-relationships between NOx-HCHO and VOC-NO2. They specifically claimed: "Jung et al. (2022), Souri et al. (2020), and Wang et al. (2020) conducted several studies on joint inversion of multiple species such as NOx and VOCs, SO2 and NOx, and CO and NOx emissions. However, the Jacobian matrix settings in previous studies incorporated only the sensitivities of multiple pollutant concentrations to self-emissions during inversion process, without considering the cross-sensitivities of species interactions. It is important to include interspecies interactions from chemical transport models to deal with the nonlinear relationships in the iterative inversions."
While I appreciate the inclusion of the cross-relationships to provide one new piece of information (the amount of information gained from HCHO on NOx and NO2 on VOCs), I'd like to clarify that we did implicitly consider the non-linear chemistry impacts through the use of a non-linear Gauss-Newton optimizer. That was the entire selling point of applying the optimizer to update Jacobians iteratively, so we do not overcorrect the state vectors. For each iteration, the non-linear feedback gets embedded into the first-order derivatives. Therefore, the authors should reconsider the claim that we do not consider non-linear chemistry. In fact, an earlier paper (https://www.sciencedirect.com/science/article/pii/S1352231020300820) discussing the impact of NOx on HCHO formation was the driving force behind this type of joint inversion. Nonetheless, it is essential to highlight the benefits of considering cross-relationships to gauge the information gained from each cross-species comparison.