| 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.
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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.