the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 21 Oct 2025
The DLR CO2-equivalent estimator FlightClim v1.0: an easy-to-use estimation of per flight CO2 and non-CO2 climate effects
Abstract. As aviation’s contribution to anthropogenic climate change is increasing, the sector aims at reducing its climate effect in accordance with international agreements. The strong and variable non-CO2 effects are complex, making reliable climate effect quantification a necessary first step. To support this, we develop the easy-to-use first-order climate effect estimator for single flights FlightClim v1.0. The tool estimates the flight-specific climate effect with a simplified calculation model, without requiring detailed information on exact routing, amount of fuel burn, or weather conditions.
For this purpose, we first analyze a global flight dataset containing detailed trajectories, associated flight emissions, and climate responses. Similar flights are grouped into clusters, and regression formulas are derived to estimate the Average Temperature Response over 100 years (ATR100) for CO2 and non-CO2 effects. To prevent abrupt changes at cluster boundaries, we apply linear smoothing as postprocessing. Second, we compare a Multiple and Symbolic Regression approach, which differ in effort and complexity but offer similar estimation quality. The choice of method depends on the specific application. Both methods are designed for climate footprint assessments due to their simplicity though not suitable for policy measures. Emission trading or monitoring and reporting systems instead require detailed weather and route data to incentivize operational non-CO2 mitigation. Compared to previous studies, our approach covers more aircraft types, including most commercial airliners, and improves precision through smoothed clustering and a dedicated parameterization of aircraft size influence on the contrail effects.
The resulting climate effect functions are embedded into the Excel-based tool FlightClim v1.0, which implements the formulas of the Multiple Regression approach due to slight qualitative advantages. Requiring only aircraft size and origin-destination airports as input, FlightClim estimates climate effect for CO2, H2O, NOx emissions and contrail-induced cloudiness. It includes per seat allocation and supports different climate metrics.
Competing interests: Volker Grewe and Simon Unterstrasser are members of the editorial board of the journal
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.-
Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
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Supplement
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- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2025-4700', William Collins, 12 Nov 2025
- AC1: 'Reply on RC2', Hannes Bruder, 22 Jan 2026
-
RC2: 'Comment on egusphere-2025-4700', Anonymous Referee #2, 05 Dec 2025
In this study, the authors build the simplified model FlightClim to calculate the climate impact of a flight from the knowledge of aircraft size and origin and destination airports. They build on the work described by Dahlmann et al. (2023) by adding more flights and city pairs to the database used to derive the simplified equations are derived, adding more aircraft types, and clustering flights to help with the regression.
Obviously, we are in the realm of very simplified modelling here. FlightClim is built from many oversimplifying assumptions and from a series of regressions of noisy relationships, so the accuracy of the calculated climate impacts is expected to be very low, as stated by the authors. Still, the proposed tool represents an advance, at least from an atmospheric physics point of view, over the simplest solution of using a global multiplier of CO2 emissions to approximate the climate impact of non-CO2 effects. On that basis, I recommend publication, but it would be important to make a better case for the fitness for purpose of the tool.
The authors suggest that the tool could be of use to the general public that want to estimate the climate impact of their flight, or have it estimated in flight booking platforms, and to compagnies that would like to estimate the total climate impact of their aircraft fleet or business travel. It is true that such use does not require very accurate per-flight estimates, but there are still a couple of important requirements that would need to be demonstrated:
- The first requirement is for the estimation of total climate impact to be reasonably accurate (i.e. that errors compensate across all flights). Lines 60-62 suggest that this aspect was quantified by Dahlmann et al. (2023), so can that comparison be done again here?
- The second requirement is that comparing two flights should give a reasonable change of identifying the flight with the largest impact. That seems limited to comparing flights between clusters but would not work within the same cluster. Is that correct? Is that good enough?
It seems that the accuracy of FlightClim could be easily improved by using seasonal regressions and taking into account the daytime/nighttime nature of the flight, which is important for contrail climate impact. If I understand well, AirClim is able to provide that information. Why not build that in? That would not make the use of FlightClim more complicated.
I am surprised by the very large contribution of NOx to total ATR100 for midlatitude flights in Figure 2. Given the current distribution of air traffic, a large fraction of total flights will be midlatitude flights. It should follow that NOx should represent a large fraction of total non-CO2 effects but that would not be consistent with the assessment of Lee et al. (2021). Is there a way to reconcile those results?
Other comments:
- Lines 131-134: That scenario is ancient! Given that the assumption of increasing emissions is given as a strength of the new method (line 71), it is surprising that the selection of scenario does not warrant more care. Why not base the calculations on recent aircraft manufacturer forecasts, or on the baseline LTAG assumptions?
- Line 139: “for that reason” – Megill et al. 2024 recommends ATR70 yet ATR100 is chosen here, so the justification does not quite work.
- Line 269: “disincentives” for kind of decisions? As stated elsewhere, the tool should only be used for trivial decision making.
- Line 267, Section 3.3: What is the reason for the choice of two different smoothing boundaries? Why not be symmetric in both clusters?
- Lines 379-380: “FlightClim is based on regression formulas, that themselves fit the results of the climate response model AirClim.” – you are missing another clause: “, which itself fit the results of climate model simulations”.
- Lines 381-384: Must repeat here that the tool is not suited for any kind of trajectory optimisation to reduce the climate impact of a flight.
Citation: https://doi.org/10.5194/egusphere-2025-4700-RC2 - AC1: 'Reply on RC2', Hannes Bruder, 22 Jan 2026
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2025-4700', William Collins, 12 Nov 2025
Review of Thor et al. 2025
This paper describes two regression methods for parameterising the outputs of a tool that itself parameterises the CO2 and non-CO2 effects of aircraft flights. It extends a previous parameterisation by allowing for different aircraft types. Given that this study is the parameterisation of a parameterisation is it not obvious that such a detailed regression analysis using two separate methods is warranted.
This study needs to account for any uncertainties in the underlying understanding of the non-CO2 climate effects. From Lee et al. 2021 the uncertainties in CiC, H2O, and NOx are approximately 70%, 60% and 100%. It does not seem justified to fit up to 4th order polynomials to such uncertain data. Any errors in the parameterisation will be small compared to the uncertainties in the physics. The function forms of the dependencies on latitude and distance are ultimately derived from a single climate-chemistry model (E39/C) for atmospheric composition appropriate for the year 2000; hence confidence in the precise forms of the dependencies does not seem high enough to justify anything beyond the simplest parameterisations.
The advance over Dahlmann et al. 2023 seems to be the addition of different aircraft types. It needs to be shown to what extent this study reduces the errors compared to Dahlmann et al. and whether this improvement is significant compared to the overall climate uncertainties. Could a simple modification have been made to Dahlmann et al. to account for aircraft size rather than developing two entirely new parameterisations?
The meaning of the ATR100 metric needs to be explained. My understanding of the text is that this takes a single flight in 2012 and integrates the temperature out to 2111 and divides by 100. So it is not clear how this relates to an increasing emissions over 100 years or depends on future climate scenarios.
Many of the differences between the MR and SR approaches seem to be due to choices made, not due to any inherent features of the approaches e.g. whether to calculate ATR100 per kg fuel or per flight. It is not explained why MR and SR treat aircraft size differently (e.g. use of MTOW vs seat category). Is this because the understanding developed during the course of the study? Or because the regional data became available too late to be included in some of the analysis?
It should be made clear who the intended audience for this paper is, particularly to what extent a reader could apply any of the conclusions more generally beyond the specifics of this particular tool.
Specific points
Line 71: The implications of the increasing emissions needs to be explained since ATR100 seems to be for each flight in 2012.
Line 125: The use of the year 2000 atmospheric composition (particularly NOx) may bias the NOx effect since this will have changed significantly over the last 25 years. Skowron et al. 2021 showed that this can even change the sign of the NOx effect.
Line 132: Why is a future increase in emissions needed if the ATR100 is calculated from flights in 2012? Why is a 1992 scenario used, presumably understanding of future flight patterns was pretty basic 33 years ago?
Line 135: The key atmospheric component will be the NOx rather than CO2 and CH4. As above, Skowron 2021 showed that the NOx effect can change sign depending on the NOX background. It is not clear why a future scenario is needed if the flights are for 2012. Does the ATR100 incorporate a varying CO2 radiative efficiency with time? This would be a very different philosophy to all other climate metrics e.g. GWP100 which assume a fixed radiative efficiency over the 100 year time horizon. It may be a valid criticism that metrics should actually be scenario dependent, but given this is different from current practice this argument needs to be made and explained.
Line 140: Why is the ATR100 used if the recommended metric is ATR70? The ATR metric needs to be explained better here. My understanding is that it is a pulse metric, i.e. the integrated climate effect of a “pulse” emission where the “pulse” can be 1 kg of fuel burned, 1 km flown or an individual flight. If so, then no future scenario is needed if the flights are assumed to occur in 2012.
Line 155: It is not obvious why these six variables should be useful to cluster the flights (presumably the PMO is simply proportional to CH4 and doesn’t add extra information). It seems that the regressions use total NOx rather than split into O3, CH4 and PMO. The aim isn’t to find clusters with different strengths of (e.g.) NOx, but to find clusters where the behaviour of the (e.g.) NOx effect is functionally different.
The latitudinal clustering appears not to be useful for SR, and in MR causes issues at the latitudinal boundary.
Line 265: Since the unclustered results include the short flights which have very different characteristics to the other flights it seems strange to include them in the parameterisations of mid-latitude and tropical. Would it not be better to exclude the short flights to derive the parameterisations for these mid-latitude + tropical flights?
Line 285: This paragraph needs to be explained better. It seems it was the authors’ choice to explicitly separate out the fuel use and NOx emissions in the MR scheme but not in SR. Therefore MR could equally have been designed to directly estimate ATR100 if the authors had chosen to. Similarly use of discrete seat categories in MR rather than MTOW in SR is purely the authors’ choice and is not inherent in the types of regression.
Line 292: The authors have chosen not to directly use the fuel use in the SR approach. They could have done so if this was useful.
Line 297: The authors have chosen to use seat categories in the MR approach, presumably they could just as easily have used MTOW as a variable if they wanted a continuous function.
Line 302: The authors chose to use the absolute error to optimise the SR; they could have chosen the relative error if they wanted to give a better relative estimate for short and medium flights. It might help the reader if the authors explained that the MR are optimised on a per kg fuel or kg NOx basis, whereas the SR are optimised on a per flight basis. Again this is a choice made by the authors and not inherent in the methodologies.
Line 334: It seems worrying that there is a systematic bias to underestimate ATR100 in the MR approach.
Line 357: The discussion need to include consideration of the physical uncertainties in the non-CO2 effects. From Lee et al. 2021 it would seem that these are far higher than the parameterisation errors discussed in this study.
Line 405: A simple way of adding the wingspan to the Dahlmann formulae would have been to multiply eqn 12 of Dahlmann et al. with eqn S2 from this study. This would have been a much simpler procedure than developing two new regression techniques here, and any parameterisation errors would have been likely much smaller than the physical uncertainties.
Corrections
Line 55, “CiC” needs to be defined.
Line 62: Units for 1.18 need to be given.
Citation: https://doi.org/10.5194/egusphere-2025-4700-RC1 - AC1: 'Reply on RC2', Hannes Bruder, 22 Jan 2026
-
RC2: 'Comment on egusphere-2025-4700', Anonymous Referee #2, 05 Dec 2025
In this study, the authors build the simplified model FlightClim to calculate the climate impact of a flight from the knowledge of aircraft size and origin and destination airports. They build on the work described by Dahlmann et al. (2023) by adding more flights and city pairs to the database used to derive the simplified equations are derived, adding more aircraft types, and clustering flights to help with the regression.
Obviously, we are in the realm of very simplified modelling here. FlightClim is built from many oversimplifying assumptions and from a series of regressions of noisy relationships, so the accuracy of the calculated climate impacts is expected to be very low, as stated by the authors. Still, the proposed tool represents an advance, at least from an atmospheric physics point of view, over the simplest solution of using a global multiplier of CO2 emissions to approximate the climate impact of non-CO2 effects. On that basis, I recommend publication, but it would be important to make a better case for the fitness for purpose of the tool.
The authors suggest that the tool could be of use to the general public that want to estimate the climate impact of their flight, or have it estimated in flight booking platforms, and to compagnies that would like to estimate the total climate impact of their aircraft fleet or business travel. It is true that such use does not require very accurate per-flight estimates, but there are still a couple of important requirements that would need to be demonstrated:
- The first requirement is for the estimation of total climate impact to be reasonably accurate (i.e. that errors compensate across all flights). Lines 60-62 suggest that this aspect was quantified by Dahlmann et al. (2023), so can that comparison be done again here?
- The second requirement is that comparing two flights should give a reasonable change of identifying the flight with the largest impact. That seems limited to comparing flights between clusters but would not work within the same cluster. Is that correct? Is that good enough?
It seems that the accuracy of FlightClim could be easily improved by using seasonal regressions and taking into account the daytime/nighttime nature of the flight, which is important for contrail climate impact. If I understand well, AirClim is able to provide that information. Why not build that in? That would not make the use of FlightClim more complicated.
I am surprised by the very large contribution of NOx to total ATR100 for midlatitude flights in Figure 2. Given the current distribution of air traffic, a large fraction of total flights will be midlatitude flights. It should follow that NOx should represent a large fraction of total non-CO2 effects but that would not be consistent with the assessment of Lee et al. (2021). Is there a way to reconcile those results?
Other comments:
- Lines 131-134: That scenario is ancient! Given that the assumption of increasing emissions is given as a strength of the new method (line 71), it is surprising that the selection of scenario does not warrant more care. Why not base the calculations on recent aircraft manufacturer forecasts, or on the baseline LTAG assumptions?
- Line 139: “for that reason” – Megill et al. 2024 recommends ATR70 yet ATR100 is chosen here, so the justification does not quite work.
- Line 269: “disincentives” for kind of decisions? As stated elsewhere, the tool should only be used for trivial decision making.
- Line 267, Section 3.3: What is the reason for the choice of two different smoothing boundaries? Why not be symmetric in both clusters?
- Lines 379-380: “FlightClim is based on regression formulas, that themselves fit the results of the climate response model AirClim.” – you are missing another clause: “, which itself fit the results of climate model simulations”.
- Lines 381-384: Must repeat here that the tool is not suited for any kind of trajectory optimisation to reduce the climate impact of a flight.
Citation: https://doi.org/10.5194/egusphere-2025-4700-RC2 - AC1: 'Reply on RC2', Hannes Bruder, 22 Jan 2026
Peer review completion
Journal article(s) based on this preprint
Hannes Bruder
Robin Niclas Thor
Malte Niklaß
Katrin Dahlmann
Roland Eichinger
Florian Linke
Volker Grewe
Simon Unterstrasser
Sigrun Matthes
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(6080 KB) - Metadata XML
-
Supplement
(9520 KB) - BibTeX
- EndNote
- Final revised paper
Review of Thor et al. 2025
This paper describes two regression methods for parameterising the outputs of a tool that itself parameterises the CO2 and non-CO2 effects of aircraft flights. It extends a previous parameterisation by allowing for different aircraft types. Given that this study is the parameterisation of a parameterisation is it not obvious that such a detailed regression analysis using two separate methods is warranted.
This study needs to account for any uncertainties in the underlying understanding of the non-CO2 climate effects. From Lee et al. 2021 the uncertainties in CiC, H2O, and NOx are approximately 70%, 60% and 100%. It does not seem justified to fit up to 4th order polynomials to such uncertain data. Any errors in the parameterisation will be small compared to the uncertainties in the physics. The function forms of the dependencies on latitude and distance are ultimately derived from a single climate-chemistry model (E39/C) for atmospheric composition appropriate for the year 2000; hence confidence in the precise forms of the dependencies does not seem high enough to justify anything beyond the simplest parameterisations.
The advance over Dahlmann et al. 2023 seems to be the addition of different aircraft types. It needs to be shown to what extent this study reduces the errors compared to Dahlmann et al. and whether this improvement is significant compared to the overall climate uncertainties. Could a simple modification have been made to Dahlmann et al. to account for aircraft size rather than developing two entirely new parameterisations?
The meaning of the ATR100 metric needs to be explained. My understanding of the text is that this takes a single flight in 2012 and integrates the temperature out to 2111 and divides by 100. So it is not clear how this relates to an increasing emissions over 100 years or depends on future climate scenarios.
Many of the differences between the MR and SR approaches seem to be due to choices made, not due to any inherent features of the approaches e.g. whether to calculate ATR100 per kg fuel or per flight. It is not explained why MR and SR treat aircraft size differently (e.g. use of MTOW vs seat category). Is this because the understanding developed during the course of the study? Or because the regional data became available too late to be included in some of the analysis?
It should be made clear who the intended audience for this paper is, particularly to what extent a reader could apply any of the conclusions more generally beyond the specifics of this particular tool.
Specific points
Line 71: The implications of the increasing emissions needs to be explained since ATR100 seems to be for each flight in 2012.
Line 125: The use of the year 2000 atmospheric composition (particularly NOx) may bias the NOx effect since this will have changed significantly over the last 25 years. Skowron et al. 2021 showed that this can even change the sign of the NOx effect.
Line 132: Why is a future increase in emissions needed if the ATR100 is calculated from flights in 2012? Why is a 1992 scenario used, presumably understanding of future flight patterns was pretty basic 33 years ago?
Line 135: The key atmospheric component will be the NOx rather than CO2 and CH4. As above, Skowron 2021 showed that the NOx effect can change sign depending on the NOX background. It is not clear why a future scenario is needed if the flights are for 2012. Does the ATR100 incorporate a varying CO2 radiative efficiency with time? This would be a very different philosophy to all other climate metrics e.g. GWP100 which assume a fixed radiative efficiency over the 100 year time horizon. It may be a valid criticism that metrics should actually be scenario dependent, but given this is different from current practice this argument needs to be made and explained.
Line 140: Why is the ATR100 used if the recommended metric is ATR70? The ATR metric needs to be explained better here. My understanding is that it is a pulse metric, i.e. the integrated climate effect of a “pulse” emission where the “pulse” can be 1 kg of fuel burned, 1 km flown or an individual flight. If so, then no future scenario is needed if the flights are assumed to occur in 2012.
Line 155: It is not obvious why these six variables should be useful to cluster the flights (presumably the PMO is simply proportional to CH4 and doesn’t add extra information). It seems that the regressions use total NOx rather than split into O3, CH4 and PMO. The aim isn’t to find clusters with different strengths of (e.g.) NOx, but to find clusters where the behaviour of the (e.g.) NOx effect is functionally different.
The latitudinal clustering appears not to be useful for SR, and in MR causes issues at the latitudinal boundary.
Line 265: Since the unclustered results include the short flights which have very different characteristics to the other flights it seems strange to include them in the parameterisations of mid-latitude and tropical. Would it not be better to exclude the short flights to derive the parameterisations for these mid-latitude + tropical flights?
Line 285: This paragraph needs to be explained better. It seems it was the authors’ choice to explicitly separate out the fuel use and NOx emissions in the MR scheme but not in SR. Therefore MR could equally have been designed to directly estimate ATR100 if the authors had chosen to. Similarly use of discrete seat categories in MR rather than MTOW in SR is purely the authors’ choice and is not inherent in the types of regression.
Line 292: The authors have chosen not to directly use the fuel use in the SR approach. They could have done so if this was useful.
Line 297: The authors have chosen to use seat categories in the MR approach, presumably they could just as easily have used MTOW as a variable if they wanted a continuous function.
Line 302: The authors chose to use the absolute error to optimise the SR; they could have chosen the relative error if they wanted to give a better relative estimate for short and medium flights. It might help the reader if the authors explained that the MR are optimised on a per kg fuel or kg NOx basis, whereas the SR are optimised on a per flight basis. Again this is a choice made by the authors and not inherent in the methodologies.
Line 334: It seems worrying that there is a systematic bias to underestimate ATR100 in the MR approach.
Line 357: The discussion need to include consideration of the physical uncertainties in the non-CO2 effects. From Lee et al. 2021 it would seem that these are far higher than the parameterisation errors discussed in this study.
Line 405: A simple way of adding the wingspan to the Dahlmann formulae would have been to multiply eqn 12 of Dahlmann et al. with eqn S2 from this study. This would have been a much simpler procedure than developing two new regression techniques here, and any parameterisation errors would have been likely much smaller than the physical uncertainties.
Corrections
Line 55, “CiC” needs to be defined.
Line 62: Units for 1.18 need to be given.