the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 05 May 2026
Expanding spatial and temporal coverage of climate change functions: Assessment and comparison with aCCFs
Abstract. Aviation contributes significantly to climate change through CO2 emissions and non-CO2 effects such as contrail cirrus and ozone formation. As the latter effects depend strongly on location and time of emission, non-CO2 impacts could bemitigated through optimized routing. Climate Change Functions (CCFs) and algorithmic Climate Change Functions (aCCFs) provide spatially and temporally resolved information on the effect of aviation emissions on the atmosphere, which enable the planning of such eco-efficient flight routes. While CCFs are computationally demanding, aCCFs offer simplified but faster estimates based on correlations with meteorological data, facilitating climate-optimized flight planning applications. As the current applicability of aCCFs is limited to specific regions and seasons according to previously available CCF calculations, this study aims to address these limitations by expanding the spatial and temporal scope of CCFs and by comparing results with existing aCCFs beyond their original temporal and spatial domain. Dedicated contrail and chemistry simulations were accomplished by means of a Lagrangian approach within the ECHAM/MESSy Atmospheric Chemistry (EMAC) climate model to calculate CCFs for a new date and new regions. This study advances aviation non-CO2 climate impact modelling by expanding CCFs to U.S. and European airspaces, to a novel season, enhanced spatial and temporal resolution of contrail effects, refining ozone radiative forcing estimates, and incorporating long-term climate responses over a 100-year time horizon. The new CCFs show consistent magnitudes and spatial gradients with earlier CCFs, but reveal systematic underestimation of contrail radiative forcing due to low optical depths. The comparison of CCFs of the present study with aCCFs outside their design region and season indicates that aCCFs capture general magnitudes and most gradients but underestimate their variability, particularly for contrails and NOx-induced effects, and reveals limitations at certain altitudes and seasons. While aCCFs offer a fast alternative for trajectory planning, they simplify complex processes compared to detailed CCF simulations. The comprehensive model setup presented in this study describes a pathway how further refine aCCF formulations and how to expand datasets to improve accuracy and applicability outside their original domain. The new CCFs from this study expand spatial (EU and continental US) and seasonal coverage (spring) and provide valuable data to advance future aCCF formulations for broader applications.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Journal of Environmentally Compatible Air Transport System.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: final response (author comments only)
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RC1: 'Comment on jecats-2026-7', Anonymous Referee #1, 01 Jun 2026
- AC1: 'Reply on RC1', Christine Frömming, 14 Oct 2026
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RC2: 'Comment on jecats-2026-7', Anonymous Referee #2, 17 Jul 2026
Review of “Expanding spatial and temporal coverage of climate change functions: Assessment and comparison with aCCFs” by Frömming et al
General comments
The paper named “Expanding spatial and temporal coverage of climate change functions: Assessment and comparison with aCCFs” aims at providing an updated version of the climate change functions (CCFs) previously published by Grewe et al. (2014) and Frömming et al. (2021). In parallel, Algorithmic climate change functions (aCCFs) are developed (van Manan and Gewe, 2019; Dietmüller et al., 2023; Yin et al., 2023). The underlying concept of the CCF/aCCF is not described in the paper but the reader is sent to previous paper.
The new developments related to the CCFs update are the extension of the geographical coverage by introduction of the United States and European airspaces, the introduction of a new weather situation, the revision of the horizontal resolution of contrail modelling, the enhancement of the temporal coverage, the improvement of the RF estimation for ozone (O3) and the introduction of the Average Temperature Response overs a time horizon of 100 years (ATR100) climate metric.
The authors claim that the objective of the paper is to advance the current understanding and modelling of aviation’s non-CO2 climate effects but it seems more that the paper is reporting on the intercomparison of a new set of CCFs with previously published CCFs/aCCFs.
Overall, the paper is gathering a significant piece of work regarding the update of the CCFs including the analysis of the new results obtained with those new CCFs in comparison of the results using the previous version of the CCFs/aCCFs.
I must say that the paper is not always easy to read as some sections could be reorganized and details/simplified. Also the conclusions of the work should be clearly highlighted and reported in the abstract. I would therefore suggest some major corrections before the paper can be published into JECATS.
Specific comments
Abstract
L11: I am not sure, the paper really advance aviation non-CO2 climate impact modelling as it is mainly using preexisting codes. Please rephrase.
L15 to 21: This past is confusing. I understand that there is a comparison of the nex CCFs with the old aCCFs, then the authors say that the new CCFs will be use to update the aCCF but is this last point is really done in this work? Please simplified and rephrase.
See also my comment in the conclusion section in relation with the abstract.
Introduction
L7-8: As said before, is it really the objective of the work here. Please rephrase.
Section 2
Subsection 2.1: Please considers reducing massively this section or merge it with the next one as it is optional according to me for this paper.
L85: I suggest to replace “in principe” by “in theory”.
L107: Why those 2 days are selected? Can add some context especially with respect to the previous version of the CCFs and the associated seasons.
L141: How this is affection the CCFs outputs? Any hints?
L142: Why not using Bier and Burkhardt (2022) for the contrails initialization and evolution?
L144-148: Is this part should not belong to the discussion section?
L172-174: Not sure to understand this part related to the pulse. I guess is the explanation on how AirClim is calibrated. Please clarify.
L177 to the end of the section 2: It make an historic of the CCFs/aCCF/paCCFs. Not sure it is appropriate here as it is confusing. I would also reduce 2.3 subsection unless it is justified to keep it and merge 2.3 with 2.4 with a focus on the actual update of the CCS using Table 1.
Section 2.4.2: confusing. It seems that some old simulations are used. Is it still relevant to use it for the CCFs? Also, could you recall why the 2.8°x2.8° is used for the contrails modelling.
Subsection 2.4.3: Any possibility to use ERF? Please discuss this possibility eventually in the discussion section.
Subsection 2.4.4: The shortcomings related to the contrails modelling and their implications in the used of CCFs should be clearly highlighted.
Subsection 2.4.5: This section seems to have been dropped there with no clear connection which the previous section. Either the location of tis subsection is not appropriate or it should be merge a previous subsection. Also, I would consider to use also the GWP100 (ERF-based) as it is considered as a reference metric (e.g. see IPPC reports).
Section 3: It is not clear why those 2 days have been chosen. Please clarify.
Section 4
Subsection 4.2:
L372: New references linked for example to ACACIA project work are available and should be added. Please check in the relevant literature.
Section 5
Overall, section 5 have a lot of results using multiple graphical representation. The description/interpretation is not easy to follow and I would recommend to reorganize/use shorter sentences which will make to paper nicer to read.
L428: only the winter season can be use for contrails?
L437-440: This sentence is for example difficult to understand. Please rephrase.
Subsection 5.1 and 5.2:
l480-484 and l506-507: Following the statement of those line, what is the conclusion of this section about the use of the current ACCs?
Subsection 5.4 and 5.5:
L538 and l553: The overestimation (for O3) /underestimation (for H20) is quite strong. Would you then recommend to use of ACCs for re-routing?
Section 6
My overall understanding for this section is that CCFs/aCCFs capture the general magnitude/variability of the different forcers that were modelled in this work but there are strong underestimation/overestimation are modelled for some of the forcers. If so, could you make a general recommendation on the use of CCFs/aCCFs.
Conclusion:
L645: “novel season”: Is it correct to say that for contrails which were modelled over 2 days only?
L654: Is the used of aCCFs can be recommend if strong over/underestimation is seen for some of the forcers?
L655-l659: This section should be clearly rephrase and reported in the abstract.
Citation: https://doi.org/10.5194/jecats-2026-7-RC2 - AC2: 'Reply on RC2', Christine Frömming, 14 Oct 2026
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- 1
General comments
The authors present a limited evaluation of algorithmic climate change functions (aCCFs) as a method to evaluate the climate impact of specific flights, using revised calculations of climate change functions (CCFs) based on calculations with the ECHAM/MESSy EMAC climate model. The evaluation looks specifically at two days in March 2014, comparing revised CCFs in a limited spatial domain at low resolution (2.8x2.8 degrees) to algorithmic CCFs (aCCFs) derived from the original CCFs. The title promises “[e]xpanding spatial and temporal coverage” with “[a]ssessment and comparison with aCCFs”, two different goals: with regards to the first, the experimental setup makes this rather a case study as it is not clear how to combine the new results with the original CCFs. On the second goal, the paper does not provide any external evaluation of (a)CCFs but rather just compares one set of CCFs to another. More concerningly, seemingly strongly negative results are presented positively in the abstract in a way which seems very misleading. I do not think the conclusions drawn are supported by the study's results, which instead show what appears to be a general failure of existing CCFs and aCCFs to represent variability in results from the same model.
Despite this, I do feel that the work contains some excellent analysis and could potentially provide a useful case study of shortcomings in the general concept of CCFs and aCCFs. Ideally it could present solutions to some of these shortcomings, and provide a set of clear metrics for how future CCFs might be evaluated to show that they are beginning to accurately represent the original model (or ideally to show that they represent broad model consensus). However, the manuscript currently seems to be split between multiple conflicting objectives, seeking on the one hand to extend and support (a)CCF usage while also performing a case study (presented as an extension) which yields overall unfavorable results. As such I cannot recommend the manuscript for publication without either substantially reframing the work to make it clear what the results imply about the (in)accuracy of CCFs and aCCFs, or performing a substantial expansion of scope to address these errors and develop the promised expanded-scale CCFs.
Specific comments
The work is not an extension, but rather a case study: if the exact same model had been used as for the original CCF work, then the argument that this study presents an extension (albeit a very limited one) would be reasonable. Alternatively, the study could have recomputed CCFs for the times and locations of the original study. Instead, we have to consider that the original CCFs are for 36 lat/lon pairs and 4 altitudes, computed using one model, over only the North Atlantic and for 8 different days which are meant to represent specific weather patterns. In this study we have CCFs for 56 lat/lon pairs (none of them matching the original pairs) and 6 altitudes (three of the four from the original study and three news ones) for two seemingly arbitrary days (specifically, three times in one day and two times in the other – none of which match those in the original study – on 2014, 13-14 years later than the original), now simulated using a different model version, at the same coarse resolution, and with nudging rather than free running (with other changes beyond these). This makes it extremely challenging to consider how the two could be used together, as the degree of (dis)agreement between the new and old approaches cannot be directly evaluated. Instead extrapolation of the old CCFs to compare against the new - as indeed is done here – shows that the sets are apparently incompatible. I would recommend that, if the authors wish to “expand” the CCFs, they instead recompute the CCFs with their updated climate model and perturbation structure, and perform a structured evaluation which covers all the target time points (i.e. including the original weather patterns), not just these two days.
The “novel season” argument is not well supported: the authors claim that this is an expansion to a “novel season”, but they simulate only two days in one year. The justification then states that this is close to a winter pattern (lines 310-311), and states that a different paper (specifically Peter et al., 2025) benefited from this simulation – rather than justifying this choice because of, say, its ability to meaningfully represent a novel season. As above, I would recommend that – if the authors wish to argue that a novel season is represented – a dedicated evaluation of the need for a novel season to be represented should be performed along the lines of the original argument for 8 weather patterns to represent two seasons.
The evaluation of (a)CCF accuracy is very limited: it appears that CCFs have three primary shortcomings which have then propagated to aCCFs. First, they cover only a limited geographical scope yet are extrapolated to other regions. Second, they are derived from a single model. Third, they are derived on the basis that eight weather patterns represent the majority of variability – but this has only been shown for the original domain (van Manen and Grewe, 2019). This study does not communicate the implications of its findings that the original CCFs/aCCFs did not accurately predict the new results (the first recommended change), nor does it meaningfully address any of these three shortcomings (the alternative recommended change). A thorough evaluation of aCCFs, or indeed of CCFs, would require more than just comparing results from one model with itself. I would strongly recommend that the authors consider bringing in different models, ideally as independent as possible, to give a meaningful evaluation of the degree to which CCFs or aCCFs represent any sort of consensus. Without this they represent just one model's estimate of the atmospheric response under a very limited set of circumstances.
The abstract and key conclusions of the paper are not supported by the results: the authors argue that the new CCFs “compare well with earlier CCFs” (line 565), and that “aCCFs successfully reproduce the overall magnitudes and most gradients” of CCFs. I do not agree that this accurately represents the rest of the paper, and am confused as to why these conclusions are drawn. Elsewhere the authors state that the aCCFs for NOx “overestimate the climate response by 25-30%” even within the target altitude range, and that the functions should not be used outside that range at all (line 578). The authors note that the estimated contrail RF is low compared to other studies, is likely biased due to a factor of 5 to 15 underestimation of optical depth (line 592), and shows a sign of daytime radiative forcing which disagrees with the scientific consensus (line 596). They also note that their specific example demonstrates how the CCFs and aCCFs derived from winter and summer are inadequate to describe a spring scenario (lines 605-608), meaning that not only are aCCFs not able to represent CCFs, but CCFs are not particularly generalizable. More generally the analysis seems confused; results such as those shown in Figure 6 show a lack of consistency between the old CCFs, the new CCFs (which again cannot be used outside of the two days simulated), and the aCCFs, with neither pattern nor magnitude showing agreement. The text however seems to oscillate between acknowledging this (“correlation between contrail CCFs and aCCFs is weak (r=0.2) and statistically not significant”, line 470) and then framing the results as positive (“we find comparable magnitudes of CCFs and aCCFs”). My takeaway from this study is that aCCFs are not yet fit for use in trajectory planning, being unable to represent the variability even within their source CCFs and with little evidence provided that the CCFs are extensible or in agreement with other models. Phrasing such as “aCCFs offer a fast alternative for trajectory planning” (line 17) imply that it would be appropriate to do so, but based on the results from this work I would expect the abstract to instead strongly discourage the use of aCCFs or CCFs.