As mentioned in the Introduction, aCCFs were developed to provide a computationally fast way to calculate the climate effect of individual non-CO2 aviation emissions as a function of their geographical location, altitude, time, and weather. Correlations and statistical methods were used to derive the individual prototype aCCFs of water vapor, NOx-induced ozone (production), NOx-induced methane (destruction), and contrail cirrus. For water vapor, ozone, and methane aCCFs, this was done by linking a large range of climate change function (CCF) data, which were calculated in a detailed chemistry–climate model simulation , to selected meteorological data, such as temperature or geopotential height . The algorithm for contrail aCCFs was developed differently. Contrail aCCFs are obtained from contrail radiative forcing calculations, which are based on European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis and contrail trajectory data . A short overview of the mathematical formulation of these emission-type-dependent prototype aCCFs is given in Appendix A of this document. For a detailed description of the first complete and consistent set of prototype aCCFs (aCCF-V1.0) the reader is referred to . Moreover, within the EU project FlyATM4E an updated set of aCCFs (aCCF-V1.0A) was developed that considers the current level of scientific understanding of aviation's climate effects: for more details, readers are referred to and . Overall, for the development of the aCCF a number of assumptions and simplifications were necessary, e.g., in the statistical approach or in the calculation of the CCF data in a climate–chemistry model. Nevertheless, it was shown that these aCCFs are in broad agreement with the climate change metric of earlier studies (e.g., ).

To build the merged non-CO2 aCCFs, all individual aCCFs are consistently converted to the same physical units of [K kg(fuel)-1]. In order to be independent of the aircraft type the individual aCCFs (except the water vapor aCCF) are given in specific units, i.e., K km-1 for contrail aCCFs or K kg(NO2)-1 for the NOx-induced ozone and methane aCCF. By simply multiplying the NOx-induced aCCFs (aCCFO3, aCCFCH4 and aCCFPMO) by the NOx emission indices (EINOx in g(NO2) kg(fuel)-1) and the contrail-cirrus aCCF (aCCFcontrail) by flown distance per kilogram burned fuel (Fkm in [km kg(fuel)-1]) all individual aCCFs are converted to the same unit (K kg(fuel)-1), and in a second step the converted individual aCCFs are combined into a merged aCCF (see Eq. 1). Note that the water vapor aCCF formula is already fuel-related and thus does not need to be multiplied by the emission index of water vapor. Typical transatlantic fleet mean values of EINOx and of Fkm are available from the literature: the transatlantic fleet mean value for Fkm is 0.16 km kg(fuel)-1 ( and Florian Linke, TU Hamburg, personal communication, 2020) and for EINOx it is 13 g(NO2) kg(fuel)-1 (e.g., ), respectively. Another possibility is to take specific emitted amounts of NOx emissions and fuel consumption values from an engine performance model. In this study we also provide altitude-dependent mean emission indices for NOx and flown distance per kilogram of burned fuel for aggregated aircraft and engine classifications (e.g., regional, single-aisle, and wide-body; see Sect. 2.3) and combine that with the choice of climate metric (Sect. 2.4) and the use of forcing efficacies (Sect. 2.5) to merge non-CO2 aCCFs: 1aCCFmergednon-CO2(t,x,y,z,iac,ir,iCM)=aCCFO3(t,x,y,z)×EINOx(iac,z)×rO3(ir)×CMO3(iCM)+aCCFCH4(t,x,y,z)×EINOx(iac,z)×rCH4(ir)×CMCH4(iCM)+aCCFPMO(t,x,y,z)×EINOx(iac,z)×rPMO(ir)×CMPMO(iCM)+aCCFcontrail(t,x,y,z)×Fkm(iac,z)×rcontrail(ir)×CMcontrail(iCM)+aCCFH2O(t,x,y,z)×rH2O(ir)×CMH2O(iCM), where aCCFX represents the algorithmic climate change functions for species X, i.e., water vapor (H2O), ozone (O3), methane (CH4), primary-mode ozone (PMO), and contrail cirrus. The variables t,x,y, and z indicate the three spatial variables (x,y,z) and time (t). iac is the identifier for three mean aircraft and engine classes: regional, single-aisle, and wide-body (see Sect. ). rX(ir) is the efficacy (see Sect. ) of the species X with the switch ir∈{0,1} for disregarding or using the efficacies (i.e., rX(0)=1), and CMX(iCM) is the climate metric conversion factor (see Sect. ) for species X and the choice of currently four climate metrics iCM∈{0,1,2,3}.

By additionally including the aviation climate effect of CO2 the total merged aCCF is given. 2aCCFmergedtotal(t,x,y,z,iac,ir,iCM)==aCCFCO2×CMCO2(iCM)+aCCFmergednon-CO2(t,x,y,z,iac,ir,iCM) Note that the CO2 aCCF is independent of the location x,y,z, efficacy (rX), and aircraft class.

For a merged aCCF it is required that the individual aCCFs are based on the same physical climate metric, emission scenario, and time horizon. The recent publication of comprises such a consistent set of individual updated prototype aCCFs. Note that earlier publications (e.g., ) provided mathematical formulations that assumed different emission scenarios for water vapor and NOx aCCFs as well as for contrail aCCFs, as they were developed separately.

Overall, merged aCCFs are a function not only of time and location, but also of aircraft- and engine-specific data, climate metric, and efficacy. For an efficient and flexible provision of such merged aCCFs we developed the Python library CLIMaCCF.

The calculation of merged non-CO2 aCCFs requires knowledge about the emission index of NOx, EINOx, and the flown distance per kilogram of burned fuel, Fkm (see Eq. 1). As these indices vary depending on the actual aircraft–engine combination (iac) and the cruise altitude (z), the use of global mean emission indices should be avoided. Moreover, there is a strong altitude dependency of the NOx emission index and flown distance Fkm, which should be considered as well. Aggregated values for altitude-dependent emission indices are derived from trajectory simulation and emission inventory data. Similarly, aggregated values for the specific range (i.e., flown distance per kilogram of burned fuel) Fkm are obtained.

For instance, analyzing the 10 most frequented routes in the North Atlantic flight corridor (NAFC) with the 10 most used aircraft types in 2012 yields an average flown distance per kilogram of burned fuel of 0.16 km kg(fuel)-1 (Florian Linke, personal communication, 2020) for transatlantic flights. More differentiated values are obtained by analyzing available emission inventory data from the DLR project “Transport and Climate” (TraK). These data contain the air traffic emission distribution in the year 2015 and can be evaluated separately per aircraft type, altitude, or region. The basis for the development of these emission inventories was a database of reduced emission profiles within the Global Air Traffic Emission Distribution Laboratory (GRIDLAB, ). Those profiles were created by simulating aircraft trajectories for various ranges and load conditions with aircraft performance models from EUROCONTROL's Base of Aircraft Data (BADA, ) model families 3 and 4. Along those trajectories engine emissions were calculated using the EUROCONTROL-modified Boeing fuel flow method 2 applied to engine certification data for the landing and take-off cycle (LTO) taken from the International Civil Aviation Organization (ICAO) engine emission database. In order to create the reduced profiles, those trajectory emission data were finally resampled to only consider key points along the profile such as transitions between flight phases. The emission inventory contains gridded data at a resolution of 0.25∘ × 0.25∘ × 1000 ft. Associated with each grid cell are the amounts of the individual emission species as well as the flown distance in that grid cell. The aggregated mean EINOx value at a given altitude is calculated by dividing the sum of the amounts of emissions per species in all grid cells at that altitude by the sum of burned fuel at that altitude. The specific range is calculated accordingly. We evaluated aggregated fleet-level values for EINOx(iac, z) and the specific range Fkm(iac, z) for a variety of aircraft and engine classes. As the aircraft-specific values are similar for certain aircraft and engine classes, we group those aircraft classes and provide their average fleet values and their standard deviation in Tables  and . Three different aircraft types are given: regional (small aircraft with a short range, up to 100 seats), single-aisle (short- to medium-range narrow-body aircraft), and wide-body (medium- to long-range aircraft, 250–600 seats).

Table  clearly shows that average EINOx values increase with increasing aircraft class and size, while EINOx values decrease with increasing altitude. NOx emissions are produced during combustion due to high combustion temperatures, which are connected to high thrust settings and engine load conditions. In general, the thrust requirement increases with the aircraft size. Increasing the thrust requirement leads to an increase in the combustion temperature and therefore an increase in NOx emissions. Below cruise altitude, e.g., during climb, the aircraft is operated with climb thrust and during descent with nearly idle conditions, leading to higher average engine loads at lower altitudes than during cruise. The flown distance in Table  increases with altitude, as the aircraft is operated in nearly fuel-optimal conditions during cruise. On the other hand, larger aircraft tend to have a lower specific range than aircraft with shorter range, as they become less fuel-efficient on longer ranges, on which they have to carry additional fuel solely for the purpose of transporting a higher fuel mass over a long distance.

Physical climate metrics can be understood as methods to directly compare the climate effect of different forcing agents or different sectors and sources . A climate metric is a combination of a climate indicator (e.g., average temperature response – ATR – or global warming potential – GWP), time horizon (e.g., 20, 50, or 100 years), and emission scenario . For the time development of aircraft emissions a pulse (emission at a certain time), sustained (emission sustained at a certain time), or future increasing (emission continue to develop) scenario might be considered . The choice of an adequate climate effect metric depends on the specific question of climate effect (e.g., what is the contribution to the current climate effect? What is the long-term climate effect?) to be answered . Thus, depending on the question different climate effect metrics should be used.

The aCCFs were developed based on the climate metric of average temperature response over a time horizon of 20 years (ATR20). The emission scenario assumed was either based on pulse emission (P) or on the future business-as-usual emission scenario (F). This inconsistency has been discovered, and a revision of the aCCFs is given in the recent publication of . Now all direct outputs of aCCF formulas are given in P-ATR20 (ATR20 based on pulse emission). P-ATR20 may not be well suited for all questions; e.g., for the question of the climate effect reduction of steadily applying a certain routing strategy, future emission scenarios are more suitable. Thus, we introduced conversion factors CMX(iCM) (see Eq. 1) which make it possible to switch from the P-ATR20 metric (which is the basis of the aCCF-V1.0 formulas in the Appendix A) to other physical climate metrics, such as ATR based on the future emission scenario (i.e., business as usual) with different time horizons (i.e., F-ATR20, F-ATR50, or F-ATR100). To calculate these conversion factors we use the nonlinear climate response model AirClim and perform several simulations with different emission scenarios. A first set of conversion factors for four different metrics (iCM) is presented in Table . Note that for the conversion factor the time development of the forcing is important. As we use the impact on an annual basis the time development of O3 and H2O forcing is the same. Therefore, the conversion factors for O3 and H2O are also the same. The conversion factors of PMO and CH4 are the same, as the time development (and forcing) of PMO is coupled with the time development (and forcing) of CH4. Conversion factors for other emission scenarios and other climate indicators will be presented in an upcoming publication.

Radiative forcing (RF, in W m-2) describes the change in the planetary energy balance. RF is often used as a metric for comparing the global climate effect of specific forcing components (e.g., CO2, ozone, aerosols). What makes RF so useful for comparison is its empirically based linear relationship to the steady-state global mean near-surface temperature change (e.g., ). The model-dependent constant, which relates these two parameters, is the so-called climate sensitivity parameter λ (e.g., ). This relation is a good approximation for many spatially homogeneously distributed climate forcing components, such as CO2. However, for radiatively active gases with a distinctly inhomogeneous structure (vertically and horizontally), like ozone change patterns from precursor emissions of the aviation sectors and contrail cirrus, the relation with the constant climate sensitivity parameter fails (e.g., ). Thus, RF of some non-CO2 forcing agents may be more or less effective in changing global mean temperature per unit forcing compared to the response of CO2 forcing. As pointed out by, e.g., and , this can be explained by the fact that such nonhomogeneous forcings trigger feedbacks that differ from those induced by CO2 (giving a climate response different from CO2). A way to account for this is to introduce a forcing-dependent efficacy parameter, which is defined as warming per unit global average forcing divided by the warming per unit forcing from CO2. By considering this efficacy , a better prediction of the expected global mean temperature change is given.

As mentioned before, aCCFs are based on the climate metric average temperature response (ATR) over a certain time horizon, a useful metric to assess the aviation-induced climate effect . However, here ATR was calculated without taking the efficacy of the different non-CO2 forcing components into account. Integrating the efficacies rX of water vapor, ozone, methane, and contrail cirrus into the merged aCCFs (see Eq. 1) has the potential to make the predictions of aviation-induced temperature change and climate effect more reliable. Efficacies were recently summarized in and are shown in Table . The efficacy of the NOx-induced short-term ozone and NOx-induced methane is larger than 1. This means that ozone and methane RFs have a higher impact on the temperature response than CO2. However, the efficacy values provided by may require updates, e.g., other values for ozone efficacies were provided by , using a more realistic ozone change pattern from aviation emission. Moreover, assume the PMO efficacy to be equal to that for methane, although the PMO change pattern is largely unknown and there are no dedicated PMO climate sensitivity simulations available. For contrails, the efficacy given in is lower than 1, meaning that contrail RF has a lower impact on the global temperature response than CO2. Note that the contrail efficacy of 0.42 in is based on three different contrail efficacy estimates from earlier studies, including an estimate of 0.59 , an estimate of 0.31 , and an estimate of 0.35 . Efficacies strongly deviating from unity (as in the case of contrail cirrus) can substantially affect the assessment of mitigation measures (e.g., ), but it would be desirable to have more model studies on the subject to establish more reliable values.

Within the input block (left box in Fig. ), the meteorological input data needed to calculate aCCFs are specified by the user. All meteorological input data needed to calculate the individual aCCFs are summarized in Table . The current implementation of the library is compatible and tested with several data products of the European Centre for Medium-Range Weather Forecasts (ECMWF) (i.e., reanalysis data ERA5 and ERA-Interim, forecast). These user settings include the selections of geographical area, horizontal resolution, and several output options (e.g., the output file can include merged aCCFs, individual aCCFs, and the input data used). Besides the specification of meteorological input data, users can select the version of aCCFs they aim to use. These options include aCCF-V1.0, which is the first consistent and complete set of aCCFs , aCCF-V1.0A, in which the aCCF-V1.0 is calibrated to the climate response model AirClim (see ). Additionally user-defined scaling factors can be applied to the selected aCCF version. These scaling factors are set to 1 by default; however, if a scaling of the aCCFs (to higher or lower values) is desired (e.g., for sensitivity studies) the user can adopt them accordingly. User settings for the generation of individual and merged aCCFs can also be selected. Here, the user can choose different assumptions for aircraft-specific parameters and the physical climate metric (emission scenario, physical climate indicator, time horizons). Moreover, the user can decide if the aCCF calculation is performed with or without consideration of efficacy. As for efficacy, users can use the values reported by or use efficacy values provided by other studies. As the selection of aircraft and engine classification is an important factor in determining reliable merged aCCF (see Sect. ), we have implemented an initial set of specific emission indices for some selected aircraft–engine combinations. By selecting an aggregated aircraft and engine type, tabulated flight-level-dependent NOx emission indices and flown distance per burned fuel values are used to calculate the merged aCCFs. An additional functionality is the identification of areas that are very sensitive to aviation emission, in the following called “climate hotspots”. To quantify these areas, a threshold value is used to identify the regions with very large effects induced by aviation. The threshold to determine these climate hotspot areas is also considered an adjustable parameter (for details, see Sect. ). In the end, the users can specify output parameters such as merged aCCFs or the aCCFs of each species. In the case of using ensemble forecasts, one can also receive the ensemble mean and ensemble spread of the resulting individual or merged aCCFs from CLIMaCCF. The user can select the output format (either netCDF or PICKLE). There is also a possibility to output the climate hotspots in the GeoJSON file format.

The processing block (upper right box in Fig. ) performs the aCCF calculations using the given weather data and the user settings described above. The processing block includes, for the aCCF calculation, preprocessing of input variables, the calculation of individual and merged aCCFs, and the calculation of climate-sensitive regions (climate hotspots). A more detailed description of these calculations is given in the following.

Before calculating individual and merged aCCFs, preprocessing of several input data is needed.

Processing weather data. In an initial step, based on the user preferences, the geographical areas where the merged aCCFs are calculated can be reduced, or the default resolutions can be changed. In these cases, some modifications are applied to the original input weather data. Notice that the horizontal resolution cannot be increased, and the decrease in resolution is a factor i of natural numbers. For instance, if the resolution of meteorological input data is 0.25∘ × 0.25∘, the resolution can be reduced to i×0.25∘×i×0.25∘ for i∈N.

In the output block (lower right box in Fig. ), the processed aCCFs are saved. In the current version, for saving aCCFs (e.g., individual aCCFs, merged aCCF, and climate hotspots) and weather variables (if selected), NetCDF and PICKLE file formats can be selected. In addition, the user can choose the GeoJSON format for storing polygons of climate-sensitive regions (i.e., climate hotspots).

As an application example we show typical summer patterns of water vapor, NOx-induced (including ozone, methane, and PMO), contrail-cirrus, and merged non-CO2 aCCFs at 12:00 UTC (under daytime conditions) on 15 June 2018 over the geographical region of Europe (15∘ W–30∘ E, 35–60∘ N) at a pressure level of 250 hPa. With this analysis we aim to give an impression of the typical structure and of gradients of the specific aCCFs over the European airspace. Note that in this subsection, we generated individual and merged aCCFs using aCCF-V1.0A and by assuming the climate metric of F-ATR20 with inclusion of efficacies. For merging we used typical transatlantic fleet mean parameters (see Sect. ). In the case of merged aCCFs we will focus on the merged non-CO2 aCCFs (Eq. 1), as the merged aCCF pattern does not change if including the CO2 aCCF, which has a constant value in time and location. But of course, for climate-optimal trajectory optimization, fuel consumption also has to be taken into account, as this is directly linked to CO2 emissions.

As mentioned above, the merged aCCFs can be used as advanced MET information for flight planning, as CLIMaCCF enables quantifying the total non-CO2 climate effect as a four-dimensional data set (latitude, longitude, altitude, and time) that is necessary for a climate-optimized trajectory. In Sect. 4.1, we showed the merged aCCF constructed with CLIMaCCF assuming the climate metric of F-ATR20 (the efficacies included) as well as the transatlantic fleet mean value of the NOx emission index and the specific range. However, as described in Sect. , there are several choices for generating the merged aCCFs. These choices are related to the climate objective (climate metric) and the emission behavior of the aircraft type, and they depend of course on a user objective. In the following, we investigate how sensitive the merged non-CO2 aCCFs are to different assumptions. Table  summarizes the different considerations of merged non-CO2 aCCFs that were performed with CLIMaCCF. The reference calculation is the same as shown in Sect. 4.1 (using the climate metric F-ATR20, inclusion of efficacies, and emission indices of typical fleet mean values of transatlantic flights). Additionally, we conducted three sensitivity calculations with height-dependent emission indices and specific ranges of different aircraft types (i.e., regional, single-aisle, and wide-body), as well as one sensitivity calculation with a different climate metric of F-ATR100.

In the first three sensitivity calculations (SENS-AC1, SENS-AC2, and SENS-AC3), we varied the emission indices by using different aircraft types. By choosing different aggregated aircraft types (i.e., regional, single-aisle, and wide-body), the respective values of Fkm and EINOx were used (see Tables  and ). Note, moreover, that, in contrast to the mean fleet value used for the reference calculation, EINOx and specific range values are flight-altitude-dependent. These sensitivity calculations are used to investigate how the aircraft type influences the overall climate effect in terms of the average temperature change. Figure  shows the merged aCCFs for the reference calculation (REF) and for the aircraft-dependent sensitivity calculations (SENS-AC1, SENS-AC2, and SENS-AC3) on 15 June 2018 at a pressure level of 250 hPa. Additionally, Fig.  in Appendix B provides aircraft- and engine-dependent merged aCCF patterns together with the respective water vapor, NOx, and contrail-cirrus aCCFs, all given in the same unit (K kg(fuel)-1). Generally, for all aggregated aircraft types, the highest climate effect is found in the areas of contrail formation. Comparing the aircraft-type-dependent merged aCCFs reveals that contrails are more dominant for the regional and single-aisle aircraft types. In the case of regional (SENS-AC1) and single-aisle (SENS-AC2) aircraft types, the merged aCCFs have very high contrail aCCF values (see Fig. ), leading to the high absolute merged aCCF values. The maximum merged aCCF values are smaller if the transatlantic fleet mean (REF) and the wide-body (SENS-AC3) aircraft type emission indices are chosen. Moreover, in regions where no contrails form, the NOx-induced aCCF (i.e., the sum of the ozone, methane, and PMO aCCFs) shows relatively high values for REF and SENS-AC3 compared to those for SENS-AC1 and SENS-AC2. Compared to the aircraft- and engine-dependent NOx emission indices and flown distances at a flight altitude of 35 000 ft (roughly corresponding to the pressure layer of 250 hPa) in Tables  and , these differences can be explained: at this cruise altitude the aggregated regional aircraft type shows the lowest EINOx (7.968 g(NO2) kg(fuel)-1) but the highest flown distance values Fkm (0.488 km kg(fuel)-1).

To generate a merged non-CO2 aCCF, it is necessary to choose a consistent climate metric for all individual aCCFs. As mentioned in Sect. , there are many metrics used in the literature to assess the climate effect; however, the choice of the metric depends on the objective of the study (e.g., ). CLIMaCCF provides the possibility to choose between a set of different climate metrics. Thus, we can show how different metrics influence the merged non-CO2 aCCF. As an example we compare the reference calculation (REF), which is based on F-ATR20 (Fig. a), to the SENS-M1 calculation, which assumes the climate metric of F-ATR100 (Fig. b). For the F-ATR100 metric, the focus lies more on long-term mitigation effects, whereas the choice of the F-ATR20 metric focuses on the short-term mitigation effect. Choosing the time horizon of 100 years for the F-ATR largely impacts the absolute values of the merged aCCF, as the metric conversion factor of all species is higher for F-ATR100 (see Table ). Moreover, in Fig.  (Appendix B) the individual aCCFs for these two metrics are shown in terms of the same unit (K kg(fuel)-1), and we see that the climate effect of NOx-induced emissions gets more important compared to the contrail aCCFs in the case of ATR100.

Any trajectory planning tool capable for planning climate-optimized aircraft trajectories (see ) can use the information on the location-, altitude-, and time-dependent climate effect of non-CO2 emissions and aim to avoid such highly sensitive regions by planning for an alternative, climate-optimized, or eco-efficient aircraft trajectory. CLIMaCCF offers the possibility to identify regions with a large climate effect, called climate hotspots. Threshold values that define these climate hotspots have to be provided. These threshold values are based on the merged non-CO2 aCCF values: if the merged aCCF exceeds a certain threshold value of the merged aCCF the region is defined as a climate hotspot. As the merged aCCFs highly vary with season, flight altitude, geographical latitude, daytime and nighttime conditions, and synoptic weather situation, these threshold values should be determined dynamically for every time step and flight altitude over a certain geographical region (e.g., European airspace). To do so, we calculate the percentile (e.g., 95th percentile) of the merged aCCF distribution over all grid points spanning, e.g., the European airspace (in our example we use the geographical region of 35–60∘ N, 15∘ W–30∘ E). This percentile then provides the time step and level-dependent threshold of the merged aCCF. As mentioned above, regions are defined as climate hotspots if the corresponding merged aCCF lies above this threshold. Thus, e.g., in the case of the 95th percentile the highest 5 % of the merged aCCFs are declared as climate hotspots. In CLIMaCCF the user has the possibility to select the geographical region over which the percentile of the merged aCCF is calculated as well as the percentage (e.g., 90 %, 95 %) of the percentile.

Figure  illustrates such climate hotspots (in red) over the European airspace at the different cruise altitudes of 200, 250, and 300 hPa for 15 June 2018 at 12:00 UTC. The underlying merged non-CO2 aCCF used here is based on the REF calculation (see Table  and Fig. ). By selecting the 95th percentile for the calculations we get different threshold values for different altitudes: 2.945×10-13 K kg(fuel)-1 for 200 hPa, 3.256×10-13 K kg(fuel)-1 for 250 hPa, and 2.687×10-13 K kg(fuel)-1 for 300 hPa. The threshold at 250 hPa has the highest value, meaning that aviation's climate effect (in terms of merged non-CO2 aCCFs) is generally larger here. Comparing the climate hotspot patterns in Fig. , it is clear that these regions vary a lot for different altitudes.

With the open-source Python library CLIMaCCF we provide a simple and easy-to-use framework for quantifying the spatially and temporally resolved climate effect of aviation emissions by making use of the aCCFs that are published in the studies of , , , and . CLIMaCCF is easy to install and to run, and it efficiently calculates the individual and merged non-CO2 aCCFs, taking the actual meteorological situation into account. Merged non-CO2 aCCFs are generated by combining the individual aCCFs of water vapor, NOx-induced ozone, methane, and contrail cirrus by making assumptions on the technical specification of the engine–aircraft combination (i.e., EINOx and Fkm) and on an appropriate physical climate metric. With this newly developed Python library, the user has the possibility to investigate merged aCCFs for three different aggregated aircraft types (regional, single-aisle, wide-body) that provide flight-level-dependent values of EINOx and Fkm (for details see Tables  and ). This novel feature of calculating merged aCCFs by considering the flight-level- and aircraft-dependent values of EINOx and Fkm, rather than using the transatlantic fleet mean values, leads to a better representation of aviation's non-CO2 climate effect. Compared to the study of , which showed aviation's merged climate effect (in terms of CCFs) by using transatlantic fleet mean values, this is a real improvement, as merged aCCFs vary significantly for different aircraft types as also shown in Fig. .

Moreover, CLIMaCCF offers the possibility to calculate aCCFs for a set of different physical climate metrics. For instance, the user has the flexibility to calculate the aCCFs for the climate metric of global average temperature response (ATR) with pulse emission or future emission scenario over the time horizons of 20, 50, and 100 years. However, we want to point out here that any optimization study has to carefully choose an adequate physical climate metric (i.e., its climate indicator, emission scenario, and time horizon) so that it is suitable for the specific application, which depends on strategic decisions, on given constraints, and on policy assumptions (e.g., ). For example, a pulse emission compares the future climate effect in a given year, whereas a future emission scenario compares the effect of increasing emissions over a future time period. This leads to different estimates of the ATR, as also shown in Fig. .

Besides the wise selection of an appropriate climate metric, other configuration parameters also have to be chosen carefully by the user. Thus, if using the Python library CLIMaCCF for calculating the climate effect of contrails the user has to pay special attention to defining the threshold of relative humidity for ice-supersaturated regions (ISSRs). In the case of contrail aCCFs we need to determine these ISSRs, as persistent contrails can only form in these regions, and the contrail aCCF is calculated only for these regions. These ISSRs are identified by two conditions: the temperature is below 235 K (in order to avoid identification of mixed-phase regions ), and the relative humidity with respect to ice (RHice) exceeds 100 % (see, e.g., , their Supplement on contrail aCCFs). However, for considering the sub-grid-scale variability in the relative humidity field in numerical weather forecast model data, e.g., ERA5, RHice thresholds below 100 % are needed. For example, showed that the relatively coarse resolution of the ERA-Interim data leads to a grid box with a grid mean humidity slightly below 100 %, as it is likely within this grid box that some air parcels show relative humidity values above 100 %. In the following we explain how we derive the threshold value of RHice in order to consider the sub-grid-scale variability for the data product ERA5 HRES (see Sect. ). To do so we calculated the annual mean (2009–2010) ISSR frequency over the European region (5∘ W–30∘ E, 40–60∘ N) using the ERA5 data set. For the ISSR frequency calculation we varied the threshold value of RHice (i.e., taking 90 % and 95 %), but leaving the temperature threshold of 235 K constant, and compared the results to the observationally based ISSR frequency values of the study of . This study used in situ measurement data for temperature and RHice from the full MOZAIC program

The MOZAIC (Measurement of Ozone, Water Vapour, Carbon Monoxide and Nitrogen Oxides by Airbus In-Service Aircraft) program was designed to collect trace gases by using automatic equipment installed on board five long-range Airbus A340 aircraft operated by European airlines. See .

It is also essential to note here that CLIMaCCF is facing limitations. An important limitation is the prototype character of the aCCFs. As described in Sect.  the aCCF algorithms were developed based on a set of detailed comprehensive climate model simulations for meteorological summer and winter conditions with a focus on the North Atlantic flight corridor . We do not recommend off-design use of these aCCFs, especially using the aCCFs for tropical regions or for spring and autumn. However, the development of the aCCFs is a current research activity, and an expansion of their geographic scope and seasonal representation is ongoing. New developments and improved understanding in aCCF algorithms will provide updated aCCF formulas that will be included in future versions of CLIMaCCF as soon as they are published. As the current version of CLIMaCCF provides the possibility to chose between different aCCF versions, it will be easy to implement further aCCF versions.

Moreover, aCCFs are associated with different aspects of uncertainties, as current scientific understanding still recognizes uncertainties in the quantitative estimates of weather forecast and climate effect prediction. The uncertainty range of the individual aviation climate effects was recently specified in (see the confidence interval of the RF estimates in their Fig. 3). They showed that large uncertainties of individual non-CO2 effect (i.e., contrail cirrus, NOx, water vapor, and the indirect aerosol effect) estimates still exist. Within the EU project FlyATM4E, a concept is developed that incorporates these uncertainties in order to generate robust aCCFs . Thus, for this purpose, aCCF-V1.0A was developed in order to calibrate the individual aCCF quantities to the state-of-the-art climate response model AirClim. The option to choose aCCF-V1.0A is included in CLIMaCCF and can be selected in the configuration script. A more detailed description on aCCF-V1.0A is given in and . Besides choosing between two different aCCF versions (i.e., aCCF-V1.0, aCCF-V1.0A), the individual aCCFs (either version 1.0 or version 1.0A) can be modified by being multiplied by any factors specified by the user. By using these alternative factors the user has the possibility to generate upper- and lower-limit estimates of the aCCF. With that the different degrees of level of scientific understanding can be reflected.

CLIMaCCF was successfully applied to ERA5 HRES reanalysis data. Obtained results show the characteristic patterns of the individual and merged aCCFs for a single day in June 2018 over the European airspace. The patterns of the individual aCCFs show the overall positive climate effect of NOx and water vapor emissions as well as negative and positive values for the daytime contrail aCCFs. These features were found in several studies before (e.g., ). Looking at the merged aCCFs it is clear that NOx and contrail aCCFs dominate the magnitude of merged aCCFs, while the water vapor aCCF only plays a minor role for the total non-CO2 aCCF. Overall, the merged aCCF pattern is highly dominated by the very variable contrail aCCF pattern, and thus avoiding the contrail climate effect leads to the most promising mitigation potential. This is in line with earlier studies that also showed the dominating effect of contrail cirrus (e.g., ).

Applying CLIMaCCF to data sets other than ERA5 HRES can influence the aCCF patterns in magnitude and granularity. This depends on how the meteorological input data and also their vertical and horizontal resolution differ from the ERA5 HRES data set used in this study.