Positive semi-definite variants of CBM4 and CBM05 chemistry schemes for atmospheric composition models
Abstract. Carbon bond chemistry models are widely used to describe tropospheric chemistry reactions in atmospheric chemistry transport models. The standard implementation of these carbon bond models includes a species for paraffin carbon bond which is positioned in chemistry reactions such that its concentration can be easily driven to negative unless additional mechanisms have been implemented around the scheme. Here we describe an alternative formulation which is positively semi-definite, while preserving the main structure of the carbon bond mechanism. We apply the formulation to CBM4 and CBM05 schemes. The new formulation substantially improves the numerical robustness of the schemes and relaxes the need for external mechanisms to enforce positive concentrations.
Risto Matias Hänninen et al.
Status: final response (author comments only)
RC1: 'Comment on gmd-2023-3', William Carter, 31 Mar 2023
- AC1: 'Reply on RC1', Risto Hänninen, 16 May 2023
- AC3: 'Final reply on RC1', Risto Hänninen, 31 May 2023
RC2: 'Comment on gmd-2023-3', Anonymous Referee #2, 01 Apr 2023
- AC2: 'Reply on RC2', Risto Hänninen, 16 May 2023
- AC4: 'Final reply on RC2', Risto Hänninen, 31 May 2023
Risto Matias Hänninen et al.
Numerical example on how to convert CBM4 chemistry scheme into positively semi-definite https://doi.org/10.5281/zenodo.7763872
Risto Matias Hänninen et al.
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This paper proposes revised methods to implement two Carbon Bond mechanisms, CBM4 and CBM05, into airshed model software that should remove a potential for numerical instability when used in atmospheric models. Unfortunately, this work has several serious problems that prevent it from being suitable for publication. The serious problems are (1) they did not describe how they came up with the changes for the two mechanisms and gave no guidance on how to do this for future mechanisms of this type, and (2) the one scenario that was simulated to test the transformations was not comprehensive or representative of actual applications where CBM may be used. In addition, the authors have not made a convincing case that it is worth the effort for current CBM4 and CBM05 users to change their mechanism implementation software and their emissions processing assignments.
Although I am not an airshed modeler myself, as a developer of chemical mechanisms who has worked with airshed modelers, I do not remember any of them complaining about numerical instability of the many models that run the widely-used CBM mechanisms. In fact, many working modelers prefer CBM because of how fast simulations using CBM are compared to other mechanisms, despite the greater chemical approximations compared to the larger mechanisms. The paper does not actually make the claim that this is a problem with actual airshed applications using these mechanisms, and cites no references supporting this. They just state that that it might be a problem under certain circumstances, but no specific examples were cited. The apparent problem they noted around line 120 where [PAR]0 ~ [OLE]0 does not look like a realistic atmospheric situation.
The paper is correct in observing that these mechanisms can predict negative concentrations under certain situations, leading to numerical problems. However, these CBM's were designed, adjusted, and optimized for use with ambient mixtures dominated primarily by anthropogenic emissions, in part because their development was funded primarily for emissions impact assessment applications. These anthropogenic mixtures always have much more PAR when represented by CBM than OLE or other VOC model species, both because of the large amounts of alkanes emitted, and because of the use of PAR to represent carbons in other types of larger molecules. Although perhaps not initially designed for biogenic simulations, these mechanisms have a more explicit representation of isoprene, and terpene emissions introduce large amounts of PAR into the system, so numerical problems when simulating biogenic-dominated mixtures is also not expected.
The one test simulation that is presented is a static simulation using approximately equal amounts of PAR and OLE, which is the same thing as simulating a mixture of only propene and NOx (plus a small amount of some alkane). None of the CBMs are designed for simulations involving single organic compounds or even simple mixtures. If a single compound is deemed to be important, as has happened in the past with compounds such as isoprene, ethanol, and MTBE, then an explicit representation is just added to the mechanism.
It is very unlikely that present users of CBM4 and CBM05 would do all the work needed to revise the implementation of these mechanisms in their modeling software and emissions assignments just so the models will be more stable when the mechanism is applied to scenarios for which the use of CBM is not appropriate. Neither of these are the current version of CBM (CBM06 is in CMAQ), so if CBM users wanted to make all these changes, they might as well change to the latest version, such as CBM06. The main reason out-of-date mechanisms such as CBM4 and CBM05 continue to be used in models is the effort and cost involved in changing the mechanisms in the models.
However, this work COULD be a useful contribution to the literature if provided an algorithm of software that could be used to make corrections to any mechanisms that are not positive semi-definite, such as future versions of CBM or even new mechanisms that might use novel reduction approaches. However, the paper just shows the reaction changes (Tables 2 and 3), but does not show how they were derived. Without this information, this paper is relevant only to users of CB4 and CB05, and, as discussed above, it is unlikely they will find it useful. Note that just showing a series of equations is not sufficient -- they need to specify an objective algorithm or software that any user can apply to any applicable mechanisms.
Information on how the transformations were derived is also necessary to assess whether the transformations are in fact mathematically appropriate or at least a good approximation, and to determine the conditions where they are valid. They may still be acceptable for use by CBM4 or CB05 users if the paper shows it gives the same results as the original version for the full range of conditions where the models may be used, but this was not done. Instead they did a single simulation of what amounts to a propene - NOx mixture with a small alkane impurity and showed that the results were the same for all model species (shown) except for PAR. Does this work for simulations of PAR - NOx - air systems as well, such a system dominated by alkane emissions? It seems to me that the proposed changes would change the rate of consumption of PAR if it is in excess, affecting simulations of products formed when PAR reacts. But they also need to include simulations of realistic anthropogenic and biogenic mixtures. Those more realistic simulations using the original mechanisms with higher PAR levels may not have the numerical problems of their propene simulation, but it is necessary to show that the modification does not affect their results.
In Section 3 they state that one of the changes proposed for CB4 included "defining" "ROR4" as ROR + 2.1 PAR. This does not make sense because ROR is a model species representing alkoxy radicals that rapidly formed and reacts, and has a very low concentration compared to model species representing non-radical compounds such as PAR. Apparently what they actually mean is that the ROR is replaced by ROR4 -2.1 PAR in reactions forming it. They need to make this clearer.
The proposed changes for CBM4 would require re-speciating emissions for the many types of emitted VOCs that are represented by OLE. However, what about compounds such as 1,3-butadiene, that are represented by OLE alone, which would be represented by negative amounts of PAR? From Table 3 it is clear that the changes to CBM05 would require changing assignments for compounds represented by NTR, CRES, TOL, IOLE, ETHA, ISOP, and TERP, as well as OLE, but the paper does not indicate exactly how such species should be mapped. Therefore, the paper does not provide information on how emissions should be changed when modifying CBM05 as suggested.
I do not think a complete listing of the CB05 mechanism is necessary to include in this paper. Files implementing the standard and modified CB05 are in the supplement, and a formatted table could also be included in the supplement. The journal space would be better used describing how the CB05 corrections were derived, how emissions assignments need to be modified using it, and showing results of a more comprehensive set of test calculations.