the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 07 Feb 2025
Improving the computation efficiency of a source-oriented chemical mechanism for the simultaneous source apportionment of ozone and secondary particulate pollutants
Abstract. Source-oriented chemical mechanisms enable direct source apportionment of air pollutants by explicitly representing precursor emissions and their reaction products in atmospheric models. These mechanisms use source-tagged species to track emissions and their evolution. However, scalability was previously limited by the large number of reactions required for interactions between two tagged species, such as the NOx-NOx or VOC-NOx reactions. This study improves computational efficiency and scalability with a new method tracks the total concentration of tagged species, reducing the n² second-order reactions for n sources into 2n pseudo first-order reactions. The overall production and removal rate of individual species remain unchanged in the new approach. The number of reactions and number of model species increase linearly with the number of source types, thus greatly improved the computation efficiency. In addition, a source-oriented Euler Backward Iterative (EBI) solver was implemented to replace the Gear solver used in previous applications of the source-oriented mechanism. The source-oriented EBI solver has been assessed by comparing predicted results with the Gear solver. Good agreement between those two methods has been achieved, as the results from the EBI scheme are linearly correlated to Gear and average of absolute relative error is below 5 %. In the timing assessment, the proposed EBI scheme can effectively reduce the total chemistry time by 73 % to 90 % for grids with different resolutions, which leads to the reduction of total simulation time by 46 % to 74 %. The proposed source-oriented scheme is efficient enough for practical long-term source apportionment applications on nested domains.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2025-44', Anonymous Referee #1, 03 Apr 2025
Xu et al. develop a source-oriented chemical mechanism that with tags that is computationally efficient. A novel and useful contribution is the ability to retain the source tags through secondary chemistry with complexity that scales linearly with number of sources, rather than quadratically.
An algorithm that reduces the computational complexity from quadratic to linear with number is in itself a useful contribution (analogous complexity-linearized algorithm have been very useful in other subfields of atmospheric chemistry and physics, e.g. the superdroplet method). This approach is also well explained in section 2.1. However, the authors dedicate much of the paper to the Euler Backward Iterative (EBI) solver, where the motivation, methodology, and novelty is still unclear after several readthroughs. In a revision, the authors should make clear why EBI can’t be applied to the fully expanded mechanism in V1, and make clearer what its contribution is and how the EBI relates to the linear reduction method.
I believe this paper could be a good fit for ACP (or perhaps the related journal GMD), but should address a few major issues that can be resolved with clarifying a few sections.
Below are specific questions and suggestions, divided into major and minor comments.
Major comments
Line 22: There are a few sentences here that are copied and pasted verbatim into the conclusions. While these are the key points, I would discourage exact repeating of text in different parts of the manuscript.
Lines 130-137: In this paragraph, it is unclear on how the EBI solver is incompatible with source-oriented mechanisms (without the linear reduction approach introduced in this paper). This is important motivation for the rest of the paper, but is not clear. What is a “non-typed regular mechanism” ? What does “applicability” mean, specifically? By “explicit solutions”, do the authors mean closed-form solutions, e.g. algebraic solutions derived from pseudo steady-state assumptions, or explicit Euler solvers, e.g. forward Euler solvers with many small explicit timesteps? Refining the language in a revision may help with clarity, and clearly explaining the limitations of applying EBI to source-tagged mechanisms is important for motivating this study.
Equations 3a and 3b: This approach only works for bimolecular reaction rates, is that correct? It seems like the separation by source in this way is only compatible with the mass action law because of the bilinearity of k[Atot][Btot]. This would be good to acknowledge, or if compatible with other rate laws or reaction orders, perhaps include a note of how it is compatible.
Lines 253-256: I don’t understand this sentence. Is there a separate solver to predict the total concentrations, and then the ratios between the summed tagged concentrations and independently solved total concentrations used to scale each tagged concentration?
Line 260: The use of “final” here is ambiguous. Would it be more accurate to say “current iteration”? The use of t in the subscript already implies final in terms of time (though the authors refer to this as current timestep, which also seems appropriate). But from what I understood from the results in 3.1, this must be applied at every iteration up to convergence, not just an adjustment applied post convergence to the solution to make the “final” solution ~20% (or 1-alpha) more like the previous timestep? This would be important to make clearer in a revision.
Fig 2 and table 2: This is a very interesting result, and a revision could go in more depth on these results, which would be a major addition to the study. I noticed the dynamic under-relaxation factor is not fully monotonic, is there a reason for that? More generally, how did the authors obtain the values for alpha shown in table 2? Is there any explanation why the solution in later iterations should weight the previous timestep more heavily? Finally, do the authors have any explanation (or intuition) for why a dynamic under-relaxation factor converges faster than a constant alpha?
Minor/technical comments
Line 25 and the copied phrase in the conclusion: improved -> improving
RS1: To distinguish source from stoich, I would suggest using superscripts for tags or operators (NO)_S1 + (NO_3)_S1
RS2: Would a different example with tagged products be better here, to illustrate the relevance? I know this is just an example, but why have different reactions if RO2_R and RCHO products are the same species for every reaction? This approach is more useful than just for estimating different sinks of reactants.
Line 59: Is this “also” as in additionally, or is it specifically for the reason in the previous sentence? If also refers to species quadratic scaling as well as reactions, maybe this point could be made right before the N2O5 example.
Line 94: Jacobin -> Jacobian
Line 121: I would suggest reminding the reader here of ∆C_t^(m+1) here, to avoid ambiguity between changes in C over time versus changes in C over iteration.
Line 127: The use of explicit here is confusing (see the major comment). The authors can disambiguate in many ways, e.g. if explicit solutions mean closed-form algebraic expressions arising from pseudo steady-state assumptions, say that. In the context of iterative solvers, explicit often refers to forward Euler methods versus implicit backward Euler methods.
Line 212: unknows -> unknowns
Line 237: quadradic -> quadratic
Table 1: Maybe some point in the text explain V2-S is V2 with SMVGEAR?
Line 324-325: “For most of the species, a relative tolerance of 1e-3 is used”. What are the exceptions, and why do they differ?
Line 359: “for more than three folds” was confusing at first. Not sure if it refers to the 74% figure comparing total time to V2-S, or some other comparison in Table 1. Maybe this could be a little clearer where this conclusion is coming from. I might also suggest wording such as “by more than threefold” or “by a factor of 3 or more”.
Line 402: “than” could be substituted with “compared to” or something similar
Line 432: This sentence might work better without “zone”
Line 450: “needs only 11 times of the computation time” Is this the first timing comparison to the non-source-oriented mechanism in the manuscript? This result would be good to report before the conclusions, though fine to reiterate it in the conclusion. For a frame of reference, it would be good to compare the other simulations to the untagged mechanism computation time, at least V1, and ideally V2-S as well. If including this result, why not include it in Table 1?
Citation: https://doi.org/10.5194/egusphere-2025-44-RC1 -
RC2: 'Comment on egusphere-2025-44', Anonymous Referee #2, 15 Apr 2025
General comments:
Overall, this is a strong paper which demonstrates a new method that has the potential to be useful in the field of study. In this paper you have two key achievements. The development of a method to reduce the number of reactions needed for source apportionment, and the implementation of an EBI solver for source apportionment. One difficulty with reading through the paper was identifying which method was used. I suggest giving a name to your method of reaction reduction, such as ‘relative rate reaction reduction’ (or something shorter), to be able to specify when you have used this method. Otherwise, it is often unclear that both methods have been used.
In addition, it is my understanding that the reaction reduction method does not actually add any error, yet you only show error when including the EBI. Given that this reaction reduction is a new method, I would suggest including some result showing that there is no error from reducing the number of reactions as you have done when the original SMVGEAR solver is used with the new reactions.
Unless my understanding is incorrect, these two methods do not need to be used in tandem, and it seems that the reaction reduction could be implemented relatively easily without major modification to a run, so I suggest highlighting that these methods can be used separately but are complementary of each other.
In your discussion of method error, you show that EBI has a tolerable level of error on average across the area measured. However, I think that more detail would be helpful. The biggest concern when introducing a new solver is the propagation of error over time. Here, your runs only go for 24 hours. It would be helpful to justify why you chose that run length. Furthermore, it would be helpful to include some discussion of how the error changes over time. Does the error increase as the run goes on, or is it relatively stable?
Line 124: typo, should be fails to converge
Line 131: built-in
Lines 142-145: Need to rewrite this sentence, it is missing some words and there are grammatical issues.
Line 193: Period instead of semicolon
Line 279-282: Rephrase, confusing sentence
Table 1: # of species and # of reactions are rows without values
Section 2.2.2 Successive under-relaxation: Has this phenomenon been observed in prior EBI papers, or is this a new phenomenon. Additionally, did you come up with the relaxation coefficient or was that defined previously as well. How does it effect the time dependent concentration of species that are not at equilibrium?
Table 3: Is there a time-dependent element to the errors? Do they increase over the course of the run. One concern that is not yet addressed is whether or not this method is stable for longer runtimes, and it is not clear from the results whether the error increases over time.
Figure 3: Include a dotted line for the 1:1 matching as you have in Figure 4
Suggestion for Figures 3 and 4: It is unclear from the figures and captions alone which method is new and which method is the baseline. Furthermore, the baseline method is on the y-axis and your new method is on the x-axis makes this more confusing. I suggest clearly stating in the caption which method is new, and consider switching the axis as well.
All CMAQ results figures: please include a brief description of the run in the caption. For example: Results from a one-day CMAQ simulation with XX resolution and meteorological inputs from WRF. I know that these details are given in section 2.3, but from looking at the figures alone, key details are missed.
Figures 6 and 7: Consider showing the difference between gear and ebi in a third column, as it is difficult to quantify the differences visually.
Line 421: SMVEAR typo
Lines 449:451: sentence should be rewritten for clarity.
Line 456: what are “adverse meteorological conditions”? Consider rephrasing.
Citation: https://doi.org/10.5194/egusphere-2025-44-RC2
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