Development of a parametrised atmospheric NO<sub>x</sub> chemistry scheme to help quantify fossil fuel CO<sub>2</sub> emission estimates

Schooling, Chlöe Natasha; Palmer, Paul I.; Visser, Auke; Bousserez, Nicolas

doi:https://doi.org/10.5194/egusphere-2024-3949

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https://doi.org/10.5194/egusphere-2024-3949

Preprints

13 Mar 2025

| 13 Mar 2025

Development of a parametrised atmospheric NO_x chemistry scheme to help quantify fossil fuel CO₂ emission estimates

Chlöe Natasha Schooling, Paul I. Palmer, Auke Visser, and Nicolas Bousserez

Abstract. Success of the Paris Agreement relies on rapid reductions in fossil fuel CO₂ (ffCO₂) emissions. Atmospheric data can verify the ffCO₂ reductions pledged by nations in their nationally determined contributions. However, estimating ffCO₂ from atmospheric CO₂ is challenging due to natural fluxes and varying backgrounds. One approach is to combine with nitrogen oxides (NO_x = NO + NO₂), which are co-emitted with CO₂ during combustion. A key challenge in using NO_x to estimate ffCO₂ is the computational cost of modelling atmospheric photochemistry. Additionally, the NO₂:NO column ratio must be well understood to convert model NO_x columns to NO₂ columns for comparison with satellite data. We use random forest regression to parameterise NO_x chemistry, relying only on meteorological parameters and NO_x concentration. The regression is trained on outputs from a nested GEOS (Goddard Earth Observing System)-Chem model simulation for mainland Europe in 2019. We develop a monthly NO_x chemistry parameterisation that performs well when tested on perturbed emission runs (R² > 0.95) and on unseen meteorology for 2021 (R² > 0.79). We also parameterise the NO₂:NO ratio (R² > 0.99 on perturbed outputs, R² > 0.92 on unseen meteorology). Additionally, we present an alternative method to predict NO_x rates by scaling baseline NO_x rates with changes in NO_x concentration (R² = 1.0 on perturbed outputs). Our models reproduce NO₂ columns with minimal deviation from full-chemistry models, with reconstruction error smaller than the TROPOspheric Monitoring Instrument (TROPOMI) precision in over 99.9 % of cases, supporting robust ffCO₂ inversion efforts. These results provide a robust framework for accurately estimating fossil fuel CO₂ emissions from atmospheric data, enabling more reliable monitoring and verification of global emissions reductions.

Received: 02 Jan 2025 – Discussion started: 13 Mar 2025

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Chlöe Natasha Schooling, Paul I. Palmer, Auke Visser, and Nicolas Bousserez

Status: final response (author comments only)

RC1:
'Comment on egusphere-2024-3949', Anonymous Referee #1, 12 May 2025
This paper presents a methodology for parameterizing NOx chemistry to enable the inversion of CO₂, combined with NOx, for constraining fossil fuel CO₂ (ffCO₂) emission estimates at reduced computational cost. The authors employ a machine learning-based random forest regression model to predict the rate of change of NOx, thereby replacing the need for full-chemistry mechanism simulations during inversion. Second model estimates the NO₂:NO ratio to convert satellite-based NO₂ column measurements into total NOx column density. It is trained using GEOS-Chem outputs from a 2019 model run and validated against simulations with randomly perturbed anthropogenic NOx emissions, as well as a 2021 model run. Conceptually, this work on parameterizing NOx chemistry is useful to constrain ffCO2 emissions, but requires more robust model design and validation to be published.

General Comments:
Please provide a more detailed explanation of your machine learning model configuration process to ensure that readers who are not familiar with machine learning can follow. For example, include a description of the hyperparameter tuning and the forward feature selection procedures.

I believe the current design of the model training and testing has a significant limitation. Validating the model on a simulation with perturbed emissions but under the same atmospheric conditions as the training data may lead to overly optimistic validation results, as it does not sufficiently test the model's generalizability to independent atmospheric states. The authors do evaluate the model on a 2021 simulation; however, I recommend adopting a more rigorous validation approach. Specifically, consider randomly selecting 75% of the full dataset across both grid cells and time steps for training, and using the remaining 25% for evaluation. This would provide a more robust assessment of the model's generalizability across spatial and temporal domains.

For model configuration, the authors tested the nine selected features along with pressure, air density, planetary boundary layer height, and the relative mixing ratio of ozone to carbon monoxide. Among these, please explain why the relative mixing ratio of ozone to carbon monoxide is expected to help predict the rate of change of NOx.

I would also suggest exploring additional input parameters based on our understanding of NOx chemistry. For example, incorporating time of day could help distinguish between daytime and nighttime chemical processes. Including satellite-derived variables such as O₃ column density and HCHO column density could provide insight into VOC levels, allowing the model to better account for variations in NOx chemistry under different VOC conditions. Variables such as J(O¹D) and H₂O concentrations could help to better represent hydroxyl radical (OH) levels, which play a key role in NOx chemistry.

I also recommend providing a more detailed description of the parameter selection criteria, starting with an analysis of the impact of individual parameters on model performance. It would be helpful to show how the inclusion of each parameter incrementally improves the model's accuracy.

Minor Comments:
- Line 35: correct to methodology
- Line 107-108: please use NO2+O2NO+O3
Citation: https://doi.org/10.5194/egusphere-2024-3949-RC1
- AC1:
  'Reply on RC1', Chlöe Schooling, 26 Jun 2025
  We thank the reviewer for their interesting and insightful comments. See below for our responses to their main points:
  1. A more detailed explanation of this will be added.
  2. Thank you for the valuable suggestion. We agree that validating a model only under similar atmospheric conditions as the training data could lead to optimistic results. However, in our current setup, we aim to assess the model's performance under emission perturbations while keeping the meteorological conditions fixed, to isolate the response of NOx chemistry to emissions alone. This design choice reflects our target application: the machine learning models are intended for use in inversion studies, where emission perturbations will be applied under consistent meteorological inputs. Therefore, assessing model performance under this constrained setup provides a more relevant test of its predictive capability in the intended use case.
  That said, we would like to emphasize that our validation approach already incorporates several elements of rigorous generalisability testing:
  We draw from a very large GEOS-Chem dataset: 117 × 114 = 13,338 horizontal grid cells, across 15 vertical levels and 24 hourly time steps for every day in a given month. This amounts to approximately 2.2 × 10⁸ data points per month.
  
  For model training, we randomly sample 10% of the unperturbed dataset across all spatial locations and time steps, which ensures a representative but compact training set.
  
  For testing, we sample 0.25% of the perturbed dataset (∼570,000 points) across the same spatial and temporal domain. These test points are drawn from a model run with different emission inputs, meaning the model is evaluated on physically different conditions it was not trained on.
  
  Due to the random selection of both training and testing points across time and space, the overlap in specific spatiotemporal conditions between the training and testing sets is minimal. An expected~10% of the test data may overlap with the training distribution in space and time.
  
  Importantly, the emission conditions in the test set are entirely unseen by the model, adding an orthogonal source of variability that the model must generalise across.
  
  Thus, while we do not fully separate the training and test sets by atmospheric state (e.g., by using different months or years), the validation set still covers a broad range of meteorological variability due to its random sampling and includes unseen combinations of space, time, and emissions. We will revise the manuscript to clearly explain this validation strategy and better communicate the robustness of our approach. We hope this convinces the reviewer that the validation approach is robust.
  3. Apologies we realise that the wording of this description was misleading, we will adjust the wording of this to make it more clear. To clarify, we tested two separate parameters – ozone column mixing ratio, and CO column mixing ratio (not the relative ratio between the two).
  Ozone concentration affects NOx concentrations by reaction with NO to form NO₂, shifting the NO/NO₂ balance through rapid photochemical cycling. Additionally, higher ozone increases the production of hydroxyl radicals (OH), which accelerates the irreversible removal of NOx via the formation of nitric acid (HNO₃). Additionally, CO affects NOx concentrations by reacting with OH radicals, reducing the OH available to oxidise NO₂ into nitric acid (HNO₃), thereby slowing NOx loss. As a result, higher CO can increase NOx lifetime by competing for the atmosphere’s oxidative capacity.
  We decided to examine these input parameters because satellite retrievals for both metrics are available, making it possible to use this data to inform our model runs. However, we found that while each of these parameters had some predictive power on its own, they were not essential for the models. Including or excluding them did not provide any additional valuable information or improve the predictive performance when combined with other parameters, which is why they were not included in the final models. We can include the detailed analysis of these parameters showing why they were excluded as final model inputs.
  4. Thank you for the suggestions. We agree that the proposed variables are highly relevant to NOx chemistry rates and could serve as informative predictors. In our current setup, we included water vapor (H2O) as a volume mixing ratio and solar zenith angle (SZA), which served as proxies for photochemical activity and time of day. These were selected to help capture aspects of OH variability in the absence of explicit radical chemistry.
  As noted in response to Comment 3, we tested the O3 column mixing ratio was tested but found that it did not improve model performance during feature selection and was thus excluded for parsimony. While HCHO column density is often a useful proxy for VOC reactivity, our initial tests found it to be weakly correlated with NOx chemistry rates in this setup (for example, much lower correlation compared to O₃ and CO columns). Regarding J(O¹D), we agree it is an important driver of OH production. However, because our models are designed to operate on simulations with chemistry mechanisms disabled—including OH and related photolysis reactions—J(O¹D) is not available. Our overarching goal is to develop a machine learning parameterisation for NOx chemistry that relies only on variables accessible in offline model configurations, primarily meteorological and spatiotemporal features.
  We hope the reviewer agrees that the selected input parameters strike a balance between physical relevance and practical availability and that the resulting model performance demonstrates the viability of this approach for approximating full-chemistry outputs in a computationally efficient way. We can add a few lines into the discussion to include some of these details.
  5. A more detailed description of the parameter selection criteria will be added.
  
  Citation: https://doi.org/10.5194/egusphere-2024-3949-AC1
RC2:
'Comment on egusphere-2024-3949', Anonymous Referee #2, 13 Jun 2025

The authors report on a method to derive NOx concentrations and NO2:NO ratios, from a machine-learning method which uses as input variables apart from NOx concentrations the meteorological factors and location, as well as a reaction rate scaling method.
They describe their approach, and validate this against simulations done with the parent CTM (GEOS-Chem), both for the same year but perturbed emissions, and for an alternative year (with alternative meteorology).
Overall, both methods were shown to sucessfully capture the simulated NOx, as well as simulated NO2 columns when compared to the full-chemistry solution. The errors in NO2 columns were reported typically an order of magnitude smaller than the differences between GEOS-Chem and TROPOMI, and the TROPOMI column precision.

I recommend publication in ACP after addressing the comments given below.

The Introduction could be strengthened, by checking and adding a few more references, as it appears that the authors make quite a few statements that are not well backed up with the given references, and in cases the formulation is a bit sloppy.

In my view a further discussion on the selection of input parameters (Table 1) is welcome. e.g. What happens if the longitude/latitude is excluded from the parameter list? the thing is that by including this you make implicit assumptions on local conditions in the model, including local emissions, which is actually exactly what you want to derive from the model. This location dependence makes the model implicitly to account for local conditions, but also suggests that the method cannot directly be adopted for other places in the world, as I understand?
Also can you provide a metric that actually describes the importance of each of the physical input quantities. You briefly describe also other parameters (line 131-133) for the training, but exclude them. I’d be interested in a more detailed description / quantitative assessment to underline the arguments why the current selection of training parameters was made.

In figure 3 the authors present the skill of the trained model against the actual rates, i.e. from quick reading it appeared that the same data that was used for the training, while in Figure A5 in the Appendix they present the same results, but on more independent data (i.e. data for another year). I would argue to swap the figures, i.e. to show Figure A5 in the main body (which is the more important independent evaluation) while moving the intermediate result, which shows the minimal validity of the regression model to be functional) towards the appendix. Then this allows to report on the correlation performance using the more independent evaluation with a bit more emphasis. This then also allows to trace back the number reported in the Abstract (R2>0.79) in the main body of the text..
Re-reading, I Realize that Figure 3 was created with the perturbed emissions experiments, so there is some modification compared to the training dataset, if I understand well. Please update the figure legend to point this out, for the reader.

Line 171: ” so, if the concentration doubles then we assume a doubling in the net chemical rate of change”. . Here the authors discuss the characteristics of the lifetime / reaction rate scaling method. I’m a bit puzzled by the use of negative lifetimes. Especially small negative lifetimes, which likely happen to occur now and again in the results, sounds like a recippee of blowing up the model, in case the rate of change is positive (i.e. a net increase in NOx). Could you please elaborate?

Smaller comments:

Lines 21 - 29: Many statements made by the authors, but I miss proper referencing here, e.g. wrt the availability of bottom-up inventories.

line 21 “reaching net zero” : net zero what? please use more explicit description.
line 23 “ how does a country know” this is also a bit sloppy formulation of the question, to my taste. please reformulate
line 25 uncertainty -> “uncertain”
line 29: “subject to uncertainties”: can you add references here of key uncertainties?
line 33: you jump directly to your method, without proper introduction of the link between NOx and CO2. I would expect such a more expicit introduction, + references to past studies who have made attempts in this direction.
line 35 ”methodlogy”
line 41 , please check sentence.
line 45 “to facilitate the production of NO (..)”, suggest to add the phrase something like “.. which is therefore co-emitted with the CO2 emissions”.

line 47 “parent emissions” please change to “parent NOx emissions”. the linking to CO2 is yet another step that deserves its own discussion, to my taste
line 50 “becomes a widely used approach”, but please also give an overview of the main issues, apart from the computational costs. This is missing so far.

Figure 1 - this figure is introduced at the end of the introduction - but the steps are difficult to follow. Please expand the description of this figure on line 64, or refer more specifically to the various steps in this figure in the consecutive subsections.

line 75 “or a scaling-based method” is this method described further down the text? If not, remove reference to this..

line 78 “for data assimilation” : add “on a high horizontal resolution” ?
line 81: add a reference to a default description of GEOS-Chem (paper? Website? other?)
line 84: “30 models below tropopause” given the importance of near-surface processes, can you specify the depth of the first model layer? I think this is larger than the one used operationally in IFS in its default vertical resolution (10 m, see, .e.g. https://confluence.ecmwf.int/display/UDOC/L137+model+level+definitions) - would that have implications on the accuracy of simulating NOx chemistry, surface fluxes, and dynamics?

line 110: can you discuss, and explain the shape of the diurnal cycle in the NOx tendency over the season? e.g. what explains the large sink in NOx during night-time?

Figure A3: please check the x-axis for the temperature plot.

Line 156 “the atmospheric lifetime becomes negative”: it is unclear to me what is the physical meaning of a negative lifetime, as well as any possible implications on the model results. Could you please elaborate, especially in the case of small negative lifetimes?

Figure 2b: as many the points are plotted on top of one another, it might be better to present this information in terms of a scatter density plot. Also, the judgement when delta-NOx changes are considered irrelevant appears a bit ‘ad hoc’

line 182 “below” => Above ?

Citation: https://doi.org/10.5194/egusphere-2024-3949-RC2
- AC2:
  'Reply on RC2', Chlöe Schooling, 26 Jun 2025
  We thank the reviewer for their useful comments. See below responses to their main comments.
  We agree that the Introduction would benefit from additional references to better support key statements and to place our work more clearly within the context of previous studies. We will carefully review the Introduction to identify and address any unsupported claims, improve the clarity of the language, and add relevant citations where appropriate. These revisions will help ensure that the motivation for our study is clearly and rigorously presented.
  
  As in response to reviewer 1 we plan to include a more detailed description of the parameter selection criteria, including the procedure of why parameters O3 and CO were excluded. Alongside this we will include a detailed analysis of parameter importance and how performance changes when different parameters are excluded. The inclusion of the location coordinates is worth discussing and we certainly acknowledge the potential drawbacks of this highlighted by the reviewer, which we will discuss further in the revised manuscript.
  
  We will make sure to update the caption in figure 3 to make it clear that the data used for testing is independent (Unseen perturbed emission input).
  
  In our framework, a negative chemical lifetime simply reflects an instantaneous net production of NOx rather than a loss, meaning that at the given grid point in space and time, the chemical production of NOx exceeded its chemical loss. This results in a positive net rate of change and a correspondingly negative lifetime when calculated as lifetime = -[NOx]/(d[NOx]/dt). Using these negative lifetime values in the scaling method does not destabilize the model or cause it to “blow up.” It simply leads to a scaled net chemical increase in NOx when the new concentration is higher than the original, consistent with what the local chemical tendency already indicates. Furthermore, these cases are typically rare and associated with specific chemical or meteorological conditions, and the magnitude and frequency of these negative lifetimes are generally small enough that they do not dominate the overall behaviour. We will revise the manuscript to clarify this interpretation and explicitly note that the scaling method can accommodate both net loss and net production regimes without numerical instability.
  
  Citation: https://doi.org/10.5194/egusphere-2024-3949-AC2

Chlöe Natasha Schooling, Paul I. Palmer, Auke Visser, and Nicolas Bousserez

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Short summary

This study presents a new method to estimate fossil fuel CO₂ (ffCO₂) emissions by modelling NO_x chemistry. Our regression models predict NO_x chemical rates and NO₂:NO ratios with R² values above 0.95 using meteorological inputs. Incorporating these regressions reduces computational time compared to traditional methods and enables integration into model inversion frameworks. This scalable approach supports global emissions monitoring and climate change mitigation efforts.


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Development of a parametrised atmospheric NOx chemistry scheme to help quantify fossil fuel CO2 emission estimates

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Development of a parametrised atmospheric NO_x chemistry scheme to help quantify fossil fuel CO₂ emission estimates