the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 14 Jan 2026
Spatiotemporal optimization of NOx and VOC emissions using a hybrid inversion framework and its implication for ozone sensitivity diagnosis
Abstract. Ozone (O3) over South Korea has risen in recent years, underscoring the need to accurately quantify emissions of nitrogen oxides (NOx) and volatile organic compounds (VOC). We develop a hybrid inverse modeling framework that couples the Finite Difference Mass Balance (FDMB) method with four-dimensional variational (4D-Var) assimilation using the Community Multiscale Air Quality (CMAQ) model to jointly constrain spatiotemporal NOx and VOC emissions. The inversion is constrained by Tropospheric Monitoring Instrument (TROPOMI) NO2 and HCHO columns and by surface NO2 and O3 from the air quality monitoring station network. The analysis covers 1–14 May 2022, a period of climatologically high O3. Optimized NOx emissions exhibit strong diurnal adjustments relative to the prior (nighttime reductions up to 51 % and daytime increases up to 14 %). The joint inversion of NOx and VOC delivers the largest improvement in O3 simulations, achieving the best agreement with observations (IOA > 0.8). Constrained emissions shift O3 sensitivity from VOC-sensitive to NOx-sensitive across much of the domain, improving spatial consistency with TROPOMI-derived formaldehyde-to-NO2 ratio (FNR) diagnostics. Adjoint-based hourly ΔO3 responses reveal regime- and hour-dependent behavior: VOC controls are most effective under VOC-sensitive conditions, whereas NOx controls are more direct under NOx-sensitive conditions. Importantly, because O3 titration is immediate while photochemical production requires finite reaction time, emissions released approximately 1–2 hours earlier have the greatest influence on current O3, motivating hour-specific, regime-specific controls. Overall, the hybrid framework improves O3 simulations and sensitivity-regime diagnosis, enabling spatiotemporally resolved precursor emission reduction guidance for effective O3 mitigation.
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- RC1: 'Comment on egusphere-2025-5837', Anonymous Referee #1, 02 Apr 2026 reply
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- 1
The manuscript, „Spatiotemporal optimization of NOx and VOC emissions using a hybrid inversion framework and its implication for ozone sensitivity diagnosis”, presents a methodology for optimizing emission inventory data for regional air quality model simulations in South Korea. This is achieved using hybrid data assimilation approach, which first adjusts the emissions of NOx and VOC using TROPOMI observations with the finite difference mass balance, and then refines the emission optimization with 4D-var data assimilation of ground-based air quality monitoring stations (NO2 and O3) and Pandora spectrometers (HCHO). The conducted study covers a two-week period in May 2022, for which the emission adjustment as well as the simulation analysis improvement are evaluated. Additionally, spatially resolved ozone sensitivity regimes are derived for South Korea, showing a shift towards larger regions becoming NOx sensitive with the newly derived emissions. Finally, the change in O3 response to NOx and VOC emissions is evaluated over time, showing the different precursors’ individual behaviour and their daytime dependences.
Overall, the manuscript’s scientific topic is very important for the air quality community. Since uncertainties in emission inventories remain the primary source of uncertainty in model predictions, the proposed approach offers a sophisticated methods to address the existing challenges in accurately representing ozone concentrations and its primary precursors, NOx and VOC. Furthermore, the presented hybrid inverse modelling method provides an advanced top-down approach that jointly optimizes NOx and biogenic and anthropogenic VOC emission inventories. The current aim of reducing NOx emissions in East Asia results in a shift in the ozone sensitivity regime, as demonstrated here. In terms of guidance for O3 policy management, the manuscript proposes a time and ozone regime dependent analysis of adjoint sensitivities for O3 responses to the precursor emissions. With these comprehensive methods and analysis, the manuscript complies well with the scope of ACP.
Although, I consider the methods and analysis presented in the manuscript to be of high scientific significance and rate the presentation quality as high, I have major concerns about parts of the applied methods, which I will discuss in more detail in the following section. In conclusion, I recommend accepting the manuscript for publication in ACP once my major and minor concerns have been addressed.
Major comments:
Minor comments:
The abstract misses information about the emission being optimized and that the study focuses on South Korea.
In general, the manuscript uses many abbreviations that are partly not very common. If introduced paragraphs ago, the reader gets distracted with going back and searching the abbreviation. Thus, I recommend reducing those, as much as possible. Examples are: in line 29, “IOA” is not even defined in the abstract; in line 82 “ΔO3 responses” are used without introduction; in line 235, FNR is introduced – I suggest, just using HCHO-to-NO2 ratio instead of FNR.
Line 23: insert “data” before assimilation.
Line 26: In the abstract, you refer to “a period of climatologically high O3” (line 26). This is unclear. How can a period of two weeks be climatological? Please improve the wording to better relate the O3 burden of the selected episode to climatological O3 values.
Line 29: I recommend writing “Optimized emissions” instead of “Constrained emissions”.
Lines 31 and 32: The terms “VOC controls” and “NOx controls” are not clear at this stage of the manuscript. Please rephrase.
Line 49: Should the first word not be increase instead of decrease? Please double check.
Line 52: Please delete the word “paradoxically”.
Line 63: Insert “data” before assimilation.
Line 71: Please replace “combining the mass balance and the 4D-Var have been recently proposed” by “combining mass balance and 4D-Var has recently been proposed”.
Line 84: “a unit perturbation” is unclear. Please explain.
Line 89: I would like to suggest using the wording “spatiotemporal corrections” here instead of “spatiotemporal changes” in emissions and concentrations.
Line 98: Please provide the horizontal resolution of the modelling domains, at least for D2 in the text.
Figure 1: The blue triangle ASOS stations are hard to see on the map. Try to remove the province boundaries.
Lines 112 and 113: Please introduce all chemical variables not just by their chemical abbreviation but also by name. Please consider replacing the “or” by an “and”.
Line 119: Please provide information about the initial (for D1 and D2) and boundary (for D1) conditions used for the CMAQ simulations. Do you start from a climatology or from some spin-up simulations?
Line 126: You refer to 619 AQMS sites. Are these divided into data used for the assimilation/inversion and data used for the validation of the posterior analysis? See also major comment (2).
Line 129: Please explain the “(0,10)” and “(1,11)”. At the moment, these values are not clear.
Line 151: Please define AMFapriori in the text.
Line 159: How do you define changes in concentrations and emissions? Is it the correction due to the inversion or is it a change between integration time steps? How do the 10% perturbation of line 164 relate to this? Is this defining ∆E?
Line 178: It is unclear what “employed it as the constraint” means here.
Figure 2: It remains unclear what the input to the FDMB really is (connection between green and blue dashed boxes). Furthermore, it is not explained what “i” is in the equation E(i), because there is no dependence on i here. How does the equation E(i) refer to equation (3) in the text? Why is Ωa−Ωo used here?
Line 187: Please clarify to what the “two-week-averaged column density” refers? Observations or model or both?
Line 195: Please check if “(n)” should not be “i=0, n”?
Line 196 and equation (8): The definition of the observation operator is unclear. The observations are concentrations or column densities, not emissions. Why do you subtract 𝑦𝑖 − 𝐻𝑖−1(𝑒𝑖−1)? Why do the indices differ? Please explain i and t.
Line 198: Please explain the uncertainty of 100%. What does this represent as error considered here?
Line 223: Please specify the observations used here.
Figure 4: Do not separate “Δ” and “O3” in a line break (line 265).
Line 281: The Hybrid_NOx experiment did not change any VOC emissions. Does this mean that there is no adjoint chemistry taken into account in the optimization procedure? Is the optimized emission vector restricted to NOx emissions only in the cost function? Wouldn’t it be possible to also derive corrections for VOC emissions when just assimilating NOx observations, due to the chemical coupling in the ozone chemistry in the model? In contrary in line 337 you refer to little improvements for the VOC in the Hybrid_NOx experiment. How is this corrections induced and why is there no correction in Figure 5?
Figure 5: I would like to suggest difference plots for the analysis increments, because it is not possible to identify if there are only emission increases or also decreases in the posteriors.
Table 1: Please clarify if the values presented are mean values averaged over the all stations and over the analysis period.
Figure 7: The caption misses the “comparison to the observations”. Also, is the data really averaged over South Korea or over all station locations?
Line 339: Please add a short explanation of the index of agreement, as this is not a very common and widely used statistical value.
Line 361: Do you mean the Prior experiment of the Hybrid_NOx approach?
Line 368: Please add a reference to Figure S3 here. Otherwise, the reader is wondering why you compare the posterior to TROPOMI and not the Prior.
Line 394: Is it the mean of 1-14 May 2022?
Lines 394-395: “Panels (a) and (c) show, for each local hour, the ΔO3 at that hour resulting from emissions integrated over all emission times (Eq. (12)).” Please explain, what this means. What is the local hour?
Figure 9: Why is there missing data in the model analysis? Additionally, is there no data over the ocean?
Line 411: Please double check if the first sentence of this paragraph can be expressed clearer after addressing my concerns described in the major comment (1).
Line 433: Please explain how this approach reduces data and why the computational demands decrease?
Line 444: Are their any ideas to what could be expected from a Hybrid_VOC experiment?
Lines 453 and 454: Please add “emissions” after “NOx” and “AVOC and BVOC”.
Line 470: Please revise “NOx contributes” with “NOx emissions contribute”.