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
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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
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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
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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
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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.