CoMIAR v1.0: a hybrid system for multi-species adjoint inversion of atmospheric emissions with online adaptive regularization

Mai, Zelin; Shen, Huizhong; Liu, Qiming; Zhang, Ruixin; Guo, Peng; Shen, Han; Luan, Tiancheng; Xu, Junpeng; He, Jinling; Zheng, Zhiyu; Chen, Yilin; Zhao, Shunliu; Hakami, Amir

doi:10.5194/egusphere-2026-3583

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https://doi.org/10.5194/egusphere-2026-3583

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27 Jul 2026

| 27 Jul 2026

Status: this preprint is open for discussion and under review for Geoscientific Model Development (GMD).

CoMIAR v1.0: a hybrid system for multi-species adjoint inversion of atmospheric emissions with online adaptive regularization

Zelin Mai, Huizhong Shen, Qiming Liu, Ruixin Zhang, Peng Guo, Han Shen, Tiancheng Luan, Junpeng Xu, Jinling He, Zhiyu Zheng, Yilin Chen, Shunliu Zhao, and Amir Hakami

Abstract. Accurate estimates of anthropogenic emissions are fundamental to air quality and climate assessment. Satellite-based top-down inversion offers an independent constraint on bottom-up emission inventories, but two key limitations remain. First, dynamically constrained 4D-Var optimization often relies on fixed regularization parameters, which can destabilize convergence during iteration. Second, most inversions treat chemical species separately, even though atmospheric species are chemically coupled. Here, we develop CoMIAR v1.0 (Coupled Multi- species Inversion with Adaptive Regularization), a hybrid system implemented with CMAQ- Adjoint to address these limitations. CoMIAR combines mass-balance initialization with 4D- Var optimization, extends the adjoint formulation to a fully coupled multi-species control system, and incorporates an online Iterative-Adaptive Regularization (IAR) strategy that updates the species-specific regularization factor at each iteration using the L-curve criterion, thereby avoiding fixed empirical tuning. In observing system simulation experiments over China, IAR suppressed the convergence oscillations observed under fixed-parameter schemes. In the single-species SO₂ regularization experiment, IAR reduced emission NRMSE by 50.5 % from the 4D-Var starting point and achieved the lowest final error among the tested schemes. Joint multi-species inversion further exploited sulfate-nitrate-ammonium thermodynamic coupling to separate emission biases that single-species inversions could not resolve. CoMIAR remained robust under spatially heterogeneous prior errors. Together, CoMIAR provides a stable and chemically consistent approach for emission inversion in complex atmospheric systems.

Received: 21 Jun 2026 – Discussion started: 27 Jul 2026

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Zelin Mai, Huizhong Shen, Qiming Liu, Ruixin Zhang, Peng Guo, Han Shen, Tiancheng Luan, Junpeng Xu, Jinling He, Zhiyu Zheng, Yilin Chen, Shunliu Zhao, and Amir Hakami

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RC1:
'Comment on egusphere-2026-3583', Anonymous Referee #1, 11 Aug 2026 reply
This study developed a joint emission inversion technique (CoMIAR v1.0) that combines mass-balance initialization with CMAQ-Adjoint 4D-Var and online, species-specific regularization. The problem is well chosen. Multi-species inversions are difficult to tune, and the SO₂-NH₃ experiments give a example of how chemical coupling can shift emission corrections between species. The sequence of OSSEs is sensible, moving from a single-species regularization test to a two-species coupling case and then to six constraints. The code and figure data are archived, and the reported change in SO₂ emission NRMSE from 6.5 to 3.2, a 50.5% decrease during the 4D-Var stage, is supported by the source data. These are useful strengths.
The main issues concern methodological clarity rather than the overall design of the study. The numerical error assumptions, species weighting, and update bounds need to be stated explicitly, and the scope of the idealized OSSEs and the trade-offs in the multi-species results need a more measured interpretation. I recommend major revision.
Major comments
Lines 161-184: The standard variational formulation in Eq. (2) is suitable as an overview, but the numerical assumptions used in the experiments are not yet sufficiently clear. Please state the values and units assigned to the prior and observation errors, the diagonal or identity weighting actually used. The definition of alpha also appears to be reversed relative to its stated purpose; please check the expression and list the six values used. Finally, the archived optimizer constrains each 4D-Var emission update to 0.8-1.25, but this bound is not reported in the manuscript. Please state that it is a per-iteration update limit and distinguish it from the clipping used during mass-balance initialization.

Lines 199-220: The first and third experiment groups use spatially heterogeneous prior perturbations, but their construction is not described. Please give the perturbation formula, amplitude or distribution, spatial structure, random seed if applicable, and whether the same or independent patterns were used for different species.

Lines 318-334 and 359-365: The joint inversion performs better in the aggregate, but not for every species, metric, or region. For example, the domain-wide SO₂ concentration improvement is smaller than in the single-species inversion, and some regional AOD emission results deteriorate. These cases should be discussed directly. Please define the reported system-level result as an aggregate across the six constraints and avoid wording that implies uniform improvement of all control variables. The conclusion would be more accurate if it stated that the joint inversion maintains comparable aggregate performance while allowing species- and region-specific trade-offs.

Specific comments
Lines 218-220: The 50-iteration horizon is useful for examining late-stage behaviour, but it is not a convergence criterion. State that the experiments were evaluated over a common fixed horizon and avoid "nominal convergence" unless a quantitative test is given.

Lines 169-174 and Sect. S1: Please clarify how gamma was selected at each iteration. Give the number, range, and spacing of the candidates for each experiment group, since the same candidate set was not used throughout.

3. Lines 138-146 and 226-230: Give the stopping rule and the realized number of mass-balance iterations for each experiment group. Also state the clipping limits and the treatment of small or zero simulated columns.

4. Eq. (3), lines 189-198: Eq. (3) contains sigma_sp twice. The second term should be sigma_ap, as in Eq. (S2).

5. Lines 185-198 and Sect. S2: The Supplement denotes the wavelength only as lambda. Please state the wavelength explicitly and provide the sources of the coefficients in Eq. (S3)–(S4).

6. Sect. 2.3 and Figs. 2-4: Define NRMSE mathematically.

7. Fig. S7: CO is part of the six-constraint experiment but is missing from this figure. Add it or explain the omission.

8. Fig. S2 caption: Replace "significantly" unless statistical significance was tested. "Substantially" or "numerically" would be more accurate.

9. Lines 213-215 and Table S1: Define "uniform 200% perturbation" as an explicit multiplier and state the direction applied to SO₂ and NH₃.

10. Lines 153-159 and 199-207: Describe how pseudo-observations were sampled in space and time, how columns were formed, and what masks were applied. It should be clear whether this is full-grid model sampling or a satellite-like sampling pattern.

11. Lines 318-328 and Fig. 4: Explain how mean NRMSE across the six constraints was calculated and weighted. Species-level values should be available in the text, a table, or the Supplement.

12. Lines 309-312 and 361-365: Recast the factor-of-six statement as a reduction in the number of CMAQ forward-adjoint integrations at matched iteration counts, rather than a measured sixfold speedup.

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Citation: https://doi.org/10.5194/egusphere-2026-3583-RC1
RC2: 'Comment on egusphere-2026-3583', Anonymous Referee #2, 25 Aug 2026 reply

The authors present a system for multi-species 4D-Var chemical data assimilation, with dynamic regularization factor optimization and mass-balance initialization, within the CMAQ ecosystem. The OSSE results are promising and suggest that the model itself performs well, but more work is required on the text of the manuscript to best present the model and its evaluation (especially the assumptions used in the OSSE). I support publication upon the satisfactory response to the following comments:
Major comments:
The methods section is not sufficiently detailed for a GMD paper. My biggest concern is section 2.3, as I cannot fully evaluate the results of the OSSE without details about the error covariance matrices used (background, observational), the way observations are simulated (what errors are imputed?), details about boundary condition treatment, and so on. For example, satellite constraints on SO2 are typically very noisy and sensitive to boundary layer dynamics (I think of it as harder to constrain than NH3), so readers cannot fully understand section 3.2 unless observational errors (for example) are discussed. I would also like to see more discussion of CoMIAR as a model. How do users interact with CoMIAR if they already have CMAQ-Adjoint running (if this model is aimed at a broader audience)? What additional information, e.g. background error, do they need to provide? What diagnostic plots or outputs are generated by the model? Of course, the authors should not write a manual, but I would like a sense of this aspect of CoMIAR if I am to support publication in a model development journal.
In my experience, L-curve regularization factor optimization can be unstable, and indeed the oscillating regularization factor in Figure 2b is potentially concerning. Would the authors be able to comment on the issue? Is the regularization factor just absorbing noise that would otherwise appear in an oscillating cost function? Adaptative background error covariance matrices are also often discussed in the literature, and it would be valuable to have a more detailed discussion of (1) the construction of the background error matrix and (2) why the authors opt for adaptive regularization factors instead of an adaptive error structure. I was very intrigued by the authors’ separation of regularization into the alpha term weighting concentration magnitudes. Does alpha implicitly capture observation densities (it will depend on how the standard deviation is constructed)? Different observation densities across species are often a problem in these multi-species systems.
Minor comments:
Line 61: Miyazaki’s work is pioneering in EnKF chemical data assimilation, but he is not the only one working on the topic. Consider adding some recent work on SO2 (10.5194/acp21-4357-2021), CH4 (10.5194/acp-25-14353-2025), CO (10.5194/acp-25-15527-2025), and/or NH3 (10.5194/acp-22-951-2022).
Line 66: I don’t think we know that 4D-Var is best for resolving non-linear chemical feedbacks. The meteorological community is split on variational and ensemble methods, and there are various arguments about equivalence under certain conditions.
Paragraph at line 95: Lots of work has been done on these multi-species issues, but people seem mostly concerned about background error covariance matrix constructions. Consider framing your adaptative regularization approach in this context. It would also be worth citing some work that is more recent than Hansen2001, since this is an active area of research.
Eqn 2: Be sure to define all the terms here.

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Citation: https://doi.org/10.5194/egusphere-2026-3583-RC2
RC3: 'Comment on egusphere-2026-3583', Anonymous Referee #3, 10 Sep 2026 reply

This paper presents CoMIAR v1.0. It joins a mass balance step with CMAQ Adjoint 4D-Var and adds an adaptive regularization method (IAR) that updates the regularization factor for each species using the L-curve. The system is tested with 2-day OSSEs over China.

Building an adaptive regularization method inside an adjoint system is a reasonable technical effort, and the point that a fixed regularization factor can be hard to tune is fair.

However, I have serious concerns about how the study is framed and how it is tested. In its current form, the paper (i) points at the wrong issue as the main difficulty of multi-species adjoint inversion, (ii) supports its motivation with an introduction that is uneven and in some places wrong, (iii) gives a motivation whose logic does not match the method that is actually used, and (iv) uses an OSSE design that cannot support the claims made in the title and abstract. These problems cannot be fixed by editing the text. They are about the position of the work and the design of the experiments. For this reason I do not think the paper can go forward in this form. It needs a large change in framing and a new set of experiments. I explain each point below.

Major comments

1. The problem is not defined correctly. The paper points at the wrong bottleneck.

The paper says that regularization is the main problem for multi-species 4DVar. I do not agree. Once you have an adjoint, passing chemical sensitivity between species is mostly a matter of computational cost. The forward and adjoint model already do this. The real hard problem is the error covariance. That means whether and how the emission errors of different species are correlated in the prior. The paper skips this. It says the background and observation covariances are diagonal for computational efficiency and moves on. Adaptive regularization only changes the weight of the prior term for each species. It does not deal with the correlation between species. So the introduction should define the real bottleneck, which is the covariance. It should review how earlier work handled this, even with simple methods, such as Qu et al. (2022). And it should say clearly whether CoMIAR deals with cross species error correlation or only with per species regularization weight. The phrase "fully coupled multi species control system" should be changed to match what is really done.

2. The introduction needs a large revision.

The general order (mass balance, then EnKF, then 4DVar, then single and multi species) is fine. But the papers that are cited are not always the right ones, some are biased, and some are described in the wrong way.

(a) Mass balance. The name "mass balance and scaling factor approaches" is not clear. "scaling factor approaches" is not a separate group. Also the paper drops mass balance after saying it has steady state and linearity limits. But mass balance has been developed further. There are iterative methods that reduce transport error, and there are multi species versions, for example Choi et al. (2026).

(b) EnKF. The only EnKF examples are Miyazaki et al. This is too narrow. EnKF chemical data assimilation has been built in several systems, for example WRF-Chem DART, and it covers single and multi species. Please add more references.

(c) Hybrid and unified systems are missing. The paper treats mass balance, EnKF, and 4DVar as three separate options. It does not mention that many recent studies combine variational and ensemble methods, or build unified frameworks such as JEDI. Since CoMIAR calls itself a modern coupled system, it should be placed next to this work.

(d) 4DVar. The paragraph that introduces 4DVar does not cite the basic adjoint development paper, Henze et al. (2007). At the same time, Qu et al. (2017) and Chen et al. (2021) are used here as general method papers, but they are single species application studies (NOx and NH3).

(e) The claim that adjoint 4DVar best resolves nonlinear chemical feedbacks is not supported. Together with the claim that EnKF can struggle with strong nonlinearities, this is one sided. Neither one is always better, and which one is better depends on the problem. Please change the 4DVar claim to talk about optimization over a high dimensional control vector and use of observations across the whole time window, with references, and reconsider the EnKF description.

(f) The single species examples are only NOx and NH3. This is not a fair sample, and it does not match the paper itself, because the main single species experiment here is SO2. Please add more species that are relevant here, for example SO2, CO, CH4, and VOC or HCHO.

(g) The logic. The text goes from the NOx and NH3 examples straight into the sulfate nitrate ammonium discussion. A clearer order would be: single species inversion and its limit, then why multi species is needed, then multi species examples for mass balance, EnKF, and 4DVar, then the sulfate nitrate ammonium case as one clear example.

(h) Qu et al. (2019). The sentence "Qu et al. (2019) extended the hybrid framework" is not correct and has no clear reference. "The hybrid framework" was never introduced before this point. The method that was extended is the hybrid mass balance and 4DVar method of Qu et al. (2017) for a single species. Also, the hybrid MB/4DVar was not developed for multi species problems neither.

3. The motivation does not connect to the method.

There are two linked problems. First, the sentence about cross species error structures evolving during iteration is not clear, and it looks like it mixes 4DVar with EnKF. In standard 4D-Var the background error covariance is fixed during the iterations. Error covariances that change with the flow belong to ensemble methods. Please say clearly what cross species error structure means, and say by what mechanism a fixed regularization factor causes the inversion to stall or oscillate, because this is not a normal result of fixed regularization. Second, the idea that adaptive regularization is needed because of multi species is not right. Choosing a regularization parameter is a general problem for any ill-posed inversion. It happens for single species too, and for both EnKF and 4DVar. In fact the paper's own single species SO2 experiment shows IAR working with no multi species coupling at all, which goes against the stated motivation. So the contrast between single species (fixed factor is fine) and multi species (adaptive is needed) does not hold. Also Hansen (2001) is a review of the L-curve as a way to pick one regularization parameter for a problem. It does not propose updating the factor at every iteration. So it should not be used to support the claim that a fixed factor breaks the iteration, and it should not be the only support for the IAR method. The idea of updating the factor at each step is the authors' own idea and should be presented that way, with support from newer work on adaptive regularization.

4. The OSSE is not designed to a standard that can support the claims.

This is a major problem, at the same level as the framing problems above.

(a) An identical twin. Introduce model error. In CoMIAR the nature run and the assimilation model are the same CMAQ v5.0, so there is no model error, and the paper does not discuss this or try to reduce it. Hsu et al. (2024) has the same starting problem but names it clearly as a concern, reduces it by running the ensemble with different physics settings so the forecast differs from the nature run, shows this creates a real spread that acts as a surrogate for model error, and states in the conclusion that future OSSEs should use two different models. That last point does not depend on the method. In 4D-Var the natural way to do this is a fraternal twin, meaning the nature run uses a different model, configuration, or resolution than the run used in the inversion, or an explicit representativeness error is added. CoMIAR does none of this.

(b) State and justify the observation error, and test how sensitive the result is to it. CoMIAR does not state what observation error was put on the pseudo observations. Without a stated observation error it is not possible to know if CoMIAR's recovery of the prior is a real result of the method or just a result of a clean setup.

(c) Test sensitivity to the main design choices, in particular the assimilation window and the period. CoMIAR uses one window of two days and does not test the effect of this choice. The width of the assimilation window alone changes the emission result significantly.

(d) Represent the error structure that carries the coupling. In 4DVar the spatial and cross species error structure lives in the background error covariance. CoMIAR sets this covariance to diagonal, which removes both the spatial correlation and the cross species correlation. This is the exact structure that represents the multi species coupling the paper claims to solve. So the diagonal choice is not a small simplification. It removes the thing the paper says it is solving. The authors should either build a non diagonal covariance with cross species terms or state clearly that the coupling is only carried through the forward and adjoint chemistry and not through the prior.

5. The study is done in the wrong order, and the scope is too large for the test.

If the main new thing is IAR, the first step should be to show that it is really needed and useful for a single species, using real observations, over a period long enough to mean something. A single species inversion does not need to stay in an OSSE. Real data can be used. Multi species coupling is a later step, and it needs a well designed OSSE of the kind described in comment 4. This paper does neither. IAR is not tested carefully, and the multi species case is not designed well, but the two are put together into a claim that IAR solves a multi species bottleneck. Running a six species joint inversion, where SO2, NOx, NH3, CO, lumped VOC, and aerosol controls all need to be checked, inside a two day identical twin OSSE, is not a good design. I suggest using fewer species, using a much longer window, and designing experiments that test one question at a time.

6. The title, abstract, and overall position claim more than the paper shows.

The abstract does not say clearly what the study does. It does not say if the study is OSSE only. It does not clearly state the region, the period, the species, and the data used. It does not say which observations are assimilated and which emissions are optimized. More important, the title promises a multi species adjoint inversion system with online adaptive regularization. But the multi species coupling is handled by diagonal covariances, so the real coupling problem is not solved. The system is only shown with a two day identical twin OSSE. And the adaptive regularization part is placed as a multi species solution, which it is not. So the position of the paper does not match what is inside it. Changing only the title is not enough. The framing and the evidence have to match. Either the claims are made much smaller, for example a first test of adaptive regularization in an OSSE, or the redesigned experiments described above are done.

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Citation: https://doi.org/10.5194/egusphere-2026-3583-RC3

Zelin Mai, Huizhong Shen, Qiming Liu, Ruixin Zhang, Peng Guo, Han Shen, Tiancheng Luan, Junpeng Xu, Jinling He, Zhiyu Zheng, Yilin Chen, Shunliu Zhao, and Amir Hakami

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https://doi.org/10.5194/egusphere-2026-3583-supplement

Zelin Mai, Huizhong Shen, Qiming Liu, Ruixin Zhang, Peng Guo, Han Shen, Tiancheng Luan, Junpeng Xu, Jinling He, Zhiyu Zheng, Yilin Chen, Shunliu Zhao, and Amir Hakami

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Short summary

Emission inventories underpin air-quality policy yet can diverge from reality. We developed an adjoint-based inversion framework that assimilates multi-source observations to simultaneously optimize multi-species emissions. Observing system simulation experiments over China show that the method recovers emissions with errors below 30 %, while avoiding spurious trade-offs between SO₂ and NH₃, enabling more reliable emission constraints.


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