Predicting the climate impact of aviation for en-route emissions: the algorithmic climate change function submodel ACCF 1.0 of EMAC 2.53

. Using climate-optimized ﬂight trajectories is one essential measure to reduce aviation’s climate impact. Detailed knowledge of temporal and spatial climate sensitivity for aviation emissions in the atmosphere is required to realize such a climate mitigation measure. The algorithmic Climate Change Functions (aCCFs) represent the basis for such purposes. This paper presents the ﬁrst version of the Algorith-mic Climate Change Function submodel (ACCF 1.0)


Introduction
Civil aviation satisfies modern society's mobility needs and is an essential economic driver.Air transportation demand increases at around 4.4 % yr −1 and is forecast to maintain that growth for the next decades (Airbus, 2018).Though the global COVID-19 pandemic has put a tremendous challenge on the aviation industry, aviation (as a fundamental part of the modern world) will recover eventually.An example from the recent ICAO post-COVID forecast shows that the revenue passenger kilometres (RPK) is expected to grow at an annual average rate of 3.6 % with a low and high range between 2.9 % and 4.2 % over the next 3 decades from 2018 to 2050 (https://www.icao.int/sustainability/Pages/Post-Covid-Forecasts-Scenarios.aspx, last access: 17 May 2023).
On the other hand, the environmental impact of aviation is increasing at an evenly rapid pace.Aviation contributes 2.5 % to global anthropogenic CO 2 emissions and is responsible for about 3.5 % of global warming (Lee et al., 2021).This is because the non-CO 2 effects from aviation in the uppermost troposphere and lowermost stratosphere are as harmful to global climate change as CO 2 emissions (Lund et al., 2017).The non-CO 2 effects include ozone (O 3 ) formation and methane (CH 4 ) depletion (causing the primary mode ozone (PMO) and stratospheric water vapour (SWV) decrease) due to aviation NO x emissions (Stevenson et al., 2004;Köhler et al., 2013;Myhre et al., 2007;Szopa et al., 2021;Terrenoire et al., 2022), contrail cirrus (Heymsfield et al., 2010;Burkhardt and Kärcher, 2011;Schumann and Graf, 2013;Kärcher, 2018) and their alterations by aerosols direct and indirect effects (Kärcher et al., 2007;Penner et al., 2009;Myhre et al., 2013;Chen and Gettelman 2016), and the water vapour (H 2 O) effect (Wilcox et al., 2012).Some recent studies investigated how COVID-19 affects aviation's climate impact per NO x or contrails concerned.For instance, Voigt et al. (2022) conducted a measurement campaign to investigate atmospheric concentration changes.The authors observed a significant reduction in NO x at cruise altitudes, contrail coverage, and the resulting radiative forcing.Furthermore, Gettelman et al. (2021) show that the effect of COVID-19 reductions in flights reduces contrail formation, which is aligned with the other study.However, due to spatial and seasonal variability of contrail radiative forcing, the annual-mean contrail effective radiative forcing shows no significant changes.Since aviation is expected to recover, it is still essential to address various climate effects of aviation with regard to their mitigation.The non-CO 2 effects depend not only on the emission quantity but also on the alti-tude, geographical location, time, and local weather conditions (e.g.Frömming et al., 2021).Therefore, it is possible to mitigate aviation's climate impact via operational measures to avoid climate-sensitive regions associated with non-CO 2 effects (Grewe et al., 2017b;Sridhar et al., 2011;Yin et al., 2018;Matthes et al., 2020).
Information on the climate-sensitive regions, i.e. areas where the non-CO 2 effects are significantly enhanced or reduced, is required to facilitate climate-optimized flight operations.In the earlier research within the EU-project RE-ACT4C (http://www.react4c.eu,last access: 17 May 2023), Climate Change Functions (CCFs) were developed and implemented for flight trajectory optimization.The CCFs are 5D datasets (including longitude, latitude, altitude, time, and emission type) that describe the specific climate impacts, i.e. the average temperature change in kelvin per flown kilometre or per emitted mass of the relevant species (NO x and H 2 O) locally.The high-fidelity CCFs were computed for eight representative weather situations (five winter patterns and three summer patterns classified by Irvine et al., 2013) for the North Atlantic region (Frömming et al., 2021).Grewe et al. (2014a) discussed the development and verification procedure of CCFs thoroughly.Various application studies have demonstrated the effectiveness of the CCFs in climate-optimized trajectory calculations (Grewe et al., 2014b(Grewe et al., , 2017b)).These studies show promising mitigation potential when using CCFs as inputs for flight trajectory optimization (e.g. a 10 % reduction in climate impact for a 1 % cost increase).One of the underlying challenges is that calculating these CCFs is computationally expensive.Thus, with the present computing performance, it is impossible to use CCFs for real-time calculation, which is necessary for future climate-optimized flight planning.
To this end, previous research initiated development (Irvine, 2017;Matthes et al., 2017;van Manen and Grewe, 2019) and tests (Rao et al., 2022) of the so-called algorithmic Climate Change Functions (aCCFs).The aCCFs are algorithmic approximations of the high-fidelity CCFs to represent the correlation of meteorological parameters (e.g.temperature and geopotential) at the time of emission and the respective average temperature response over a time horizon of 20 years (ATR20).Since the aCCFs are essentially mathematical approximations, they can be quickly implemented in numerical weather prediction (NWP) models, thereby serving as a means of advanced meteorological information for flight trajectory planning.
The ACCF submodel version 1.0 (ACCF 1.0) of the European Centre HAMburg general circulation model (ECHAM) and Modular Earth Submodel System (MESSy) Atmospheric Chemistry (EMAC) model is based on the aCCFs version 1.0 (aCCFs 1.0).The ACCF 1.0 calculates the ATR20 from individual emissions and the contrail cirrus effect as a function of the online calculated local weather parameters in EMAC.One can use the ACCF 1.0 in two different ways: (1) to study the sensitivity of non-CO 2 effects (i.e.NO x , H 2 O, contrail cirrus) to weather parameters and (2) to couple it with a flight planning tool (e.g.EMAC/AirTraf; Yamashita et al., 2016Yamashita et al., , 2020) ) for climate-based route optimization.
This paper elaborates on the modelling approach, the characteristics, and the application of ACCF 1.0.Please note that, for the first time, we show a consistent set of aCCF formulas in terms of fuel scenario, metric, and efficacy (aCCFs 1.0).Due to the continuous development of aCCFs, we expect different versions of aCCFs to be released in the future.Accordingly, the ACCF submodel will be updated.
The structure of the paper follows that Sect. 2 provides a roadmap of the ACCF 1.0 development focusing on different considerations when deriving the first version of contrail aCCFs and the NO x and H 2 O aCCFs.Section 3 presents an overview of ACCF 1.0, including the model components and the individual aCCF formulas.The original correlations of the NO x and H 2 O aCCFs were derived in van Manen and Grewe (2019), whereas some coefficients in the equations are updated here for consistency.Furthermore, the contrail cirrus effect is explained in detail here (and in the Supplement).In Sect.4, we evaluate the performance of the ACCF 1.0 outputs via two types of simulations.First, we compare the climatological aCCFs to other literature studies in terms of their latitudinal and vertical variability.Second, we use the tagging chemistry approach (contribution approach, Grewe et al., 2010Grewe et al., , 2017a) ) to evaluate the reduction of NO x -induced O 3 effect through climate-optimized flight trajectories based on the O 3 aCCF formula.Section 5 implements the ACCF 1.0 with the complete sets of aCCFs in the AirTraf 2.0 to demonstrate the usage of ACCF 1.0 for climate-optimized flight trajectories.It has to be noted that the two demonstration exercises are academic case studies, which do not intend to suggest an efficient implementation of such climateoptimized trajectories as we present here the extreme case of only considering ecological effects while completely ignoring economic effects in the optimization (equivalent to a noncombined objective function).One could consider combining the cost and climate objectives in trajectory optimizations to identify eco-efficient flights (e.g.Matthes et al., 2023).Section 6 discusses further developments of aCCFs before concluding in Sect.7.

Roadmap of the MESSy ACCF 1.0 submodel development
The new MESSy submodel ACCF 1.0 consists of a set of aCCFs 1.0, which take relevant local meteorological data as inputs to calculate the ATR20 for a given emission or effect concerning contrails.As introduced above, the roadmap toward the ACCF 1.0 model involves multiple stages of work originating from different research projects.Figure 1 illustrates the development of the ACCF 1.0, including the previous research on the original CCFs development followed by the aCCFs approach, which is the core of the ACCF sub- In this figure, we also demonstrate the major contributions of the current research.While the original CCFs and aCCFs have been developed and published in previous research, the approach of developing contrail aCCFs is only made available in the current ACCF V1.0 paper as the Supplement.Furthermore, one main effort of this research is to evaluate the quality of the aCCFs.
The individual CCFs, the basis of the aCCFs, were developed slightly differently.The CCFs of O 3 , CH 4 , and H 2 O were calculated using a well-established modelling chain within EMAC (Jöckel et al., 2006(Jöckel et al., , 2010)).The model follows a multi-step approach starting with the simulation of the fate of emissions.The impact of pulse emission from a large number of time-region grid points is efficiently calculated by applying a Lagrangian transport scheme (i.e.following the air parcel).The RF caused by these pulse emissions is computed using the online diagnostic of the EMAC radiation scheme.Grewe et al. (2014a) and Frömming et al. (2021) have described details of this approach.
For the contrail CCF, the Lagrangian trajectories were used to determine the lifetime of a contrail, the temperature, and the position along the lifetime of a contrail.The Lagrangian trajectories were computed using the ECMWF reanalysis data (ERA-Interim; Dee et al., 2011) with winds input to a trajectory model (Methven, 1997).Accordingly, the contrail optical depth and solar zenith angle were calculated to obtain the contrail RF.The main discrepancy between contrail CCF and the other CCFs lies in the RF calculation.The contrail RF is calculated using the parametric model described by Schumann et al. (2012), which is different from the EMAC radiation scheme.Knowing the RF, to obtain the ATR20 value, the conversion from RF to ATR20 is calculated using the climate response model AirClim (Grewe and Stenke, 2008;Dahlmann et al., 2016) in a consistent way for all species considered, which was not the case in the earlier studies.
Based on the CCFs, the regression method was then applied to derive the aCCFs of O 3 , CH 4 , H 2 O (van Manen and https://doi.org/10.5194/gmd-16-3313-2023 Geosci.Model Dev., 16, 3313-3334, 2023 Grewe, 2019), and the contrail cirrus aCCFs (Supplement of this paper).The CO 2 aCCF is a constant value, which is determined based on emission scenarios.Note that the values from van Manen and Grewe (2019) and Irvine et al. (2017, Supplement to this publication) are updated by the formulas in the present study, as a more consistent conversion to ATR is employed, using slightly different response functions and consistent future scenarios for all species.

Model description EMAC
ACCF 1.0 is a submodel of the global atmospheric-chemistry model EMAC.EMAC is a numerical chemistry-climate model system that includes submodels describing the tropospheric and middle atmosphere processes and their interaction with oceans, land, and influences from anthropogenic emissions (Jöckel et al., 2010)  The SMIL manages model input-output through the CHANNEL submodel (Jöckel et al., 2010).The SMCL is independent of other submodels and contains the code to solve the relevant equations for the individual aCCFs.The input variables to calculate aCCFs in the ACCF submodel are either from the base model calculation (i.e.temperature, geopotential) or from the other EMAC submodels.For instance, the H 2 O aCCF is a function of potential vorticity (PV) provided by the submodel TROPOP (Jöckel et al., 2006).The daytime contrail aCCF depends on the outgoing longwave radiation (OLR) at the top of the atmosphere from the submodel RAD (Dietmüller et al., 2016).The potential contrail coverage (potcov) calculated from the submodel CONTRAIL (Frömming et al., 2014) is used to determine whether persistent contrails can form and may lead to a climate impact by contrails.The Supplement of this paper includes a user manual of the submodel ACCF.It describes the namelist settings of the ACCF submodel and includes submodels necessary for coupling input-output variables.

Basic mechanisms of submodel ACCF 1.0
This section summarizes the formulas of aCCFs 1.0.For full details of the original derivation, the reader is referred to van Manen and Grewe (2019) and the Supplement of this paper.The complete set of the aCCFs 1.0 computes the ATR20 of CO 2 emissions, H 2 O emissions, NO x emissions (forming O 3 and decreasing CH 4 + PMO), and day/night contrail cirrus.

Synoptic on a selected day
The individual non-CO 2 aCCFs depend on weather parameters, e.g.temperature, geopotential, and potential vorticity.
A 1 d simulation on 18 December 2015 was performed to demonstrate such correlations.Figure 3 shows the geographical distribution of (a) temperature, (b) potential vorticity, and (c) geopotential over Europe at the pressure level of 250 hPa on the same day.These parameters are calculated by running the EMAC model nudged towards the ERA-interim data and will be used to calculate the non-CO 2 aCCFs (see the following sections).

CO 2 aCCF
CO 2 is a long-lived species, and hence, the climate impact of aviation's CO 2 depends only on the amount of CO 2 emitted.Therefore, the CO 2 aCCF is calculated using the nonlinear climate-chemistry response model AirClim, assuming a 1 Tg fuel use in 2017.The CO 2 aCCF then represents the average temperature response of CO 2 for 2017-2036 (in K (kg (fuel)) −1 ) (named P-ATR20 CO 2 ).As a result, a constant value of 7.48 × 10 −16 K (kg (fuel)) −1 was obtained.For the same amount of emission in 2017, but with an annual growth rate according to a business-as-usual (BAU) future scenario as given by Grewe et al. (2021), the ATR20 for CO 2 (named F-ATR20 CO 2 ) was 7.03 × 10 −15 K (kg (fuel)) −1 .A conversion factor of 9.4 was derived from the P-ATR20 CO 2 to F-ATR20 CO 2 .

NO x -induced aCCFs
The aviation NO x emission (NO x = NO + NO 2 ) leads to O 3 formation via a catalytic reaction.NO reacts with HO 2 forming NO 2 .Due to photodissociation, NO 2 forms O( 3 P), leading to the O 3 formation.The O 3 formation, on the other hand, enhances the OH production (e.g.Grewe et al., 2017a), hence causing a shift of the OH/HO 2 ratio towards OH.The additionally formed OH leads to the oxidation of CH 4 .Furthermore, the destruction of CH 4 leads to a reduced O 3 production rate as feedback to the O 3 concentration.This O 3 change is called primary mode ozone (PMO) (Wild et al., 2001).The effect of PMO is much smaller than the initial O 3 production.However, PMO has a longer lifetime (is bound to the CH 4 perturbation) than the initial O 3 production.Furthermore, because of the CH 4 oxidation, less CH 4 enters the stratosphere, which again reduces the SWV.Since H 2 O is a greenhouse gas, the decrease in SWV reduces the warming effect of H 2 O (Myhre et al., 2007).The overall aviationinduced NO x effects include the short-term O 3 increase and long-term CH 4 reduction (also CH 4 -related PMO and SWV decrease).The current NO x aCCF addresses the impact of short-term O 3 production and CH 4 destruction and PMO reduction.SWV decrease is not taken into account because of its low magnitude.The corresponding formulas are presented below. https://doi.org/10.5194/gmd-16-3313-2023 Geosci.Model Dev., 16, 3313-3334, 2023 NO x -induced O 3 -aCCF Earlier research showed the impact of weather patterns and related transport processes on the contribution of aviation NO x emissions to O 3 and CH 4 concentrations (Grewe et al., 2017c;Frömming et al., 2021;Rosanka et al., 2020).For instance, Grewe et al. (2017c) and Frömming et al. (2021) showed that a unit NO x emission within a high-pressure blocking situation leads to more O 3 -induced RF than a NO x emission west of this high-pressure area because the transportation pathways differ significantly.Air parcels starting within the high-pressure system are transported to the tropics and lower altitudes, experiencing a more active chemical regime and faster O 3 production (Rosanka et al., 2020).The analysis by van Manen and Grewe (2019) independently looked at correlations of CCF data describing the atmospheric state (meteorological and chemical data) at the time of emission.They found the best correlation representing the impact of ozone changes caused by a local NO x emission with the geopotential and temperature.This indicates that the weather regime at the time of emission essentially controls the air parcel's fate in which NO x is emitted.Thereby, the O 3 -aCCF (in K (kg (NO 2 )) −1 ) is developed based on temperature (T ) (in K) and geopotential ( ) (in m 2 s −2 ).For an atmospheric location (x, y, z) at time t with T = T (x, y, z, t) and = (x, y, z, t), the O 3 -aCCF can be found in Eq. ( 1).Please note that the coefficients in Eq. ( 1) differ from those derived in van Manen and Grewe (2019) in order to have a consistent set of formulas representing ATR20 for a pulse emission scenario (P-ATR20).Based on this, other metrics, for instance, ATR20 for future emission scenarios (F-ATR20), can be derived (e.g.Table 1).For the same reasons, corrections are also applied for coefficients of methane formulas (Eq.2) and water vapour formulas (Eq.5).
where P-ATR20 O 3 is the ATR20 for a pulse emission.Figure 4a shows an example of the O 3 -aCCF (in K (kg (NO 2 )) −1 ) on 18 December 2015 over Europe at 250 hPa.The contour lines indicate the geopotential, and it is noticeable that the O 3 -aCCF strongly follows the geopotential distribution.Overall, the changes in O 3 concentration caused by NO x emissions have warming effects.

NO x -induced CH 4 -aCCF
The analysis by van Manen and Grewe (2019) showed the highest correlation of the CH 4 response to NO x emissions with geopotential and the mean incoming solar radiation, i.e. combining the initial transportation pathway with an indicator for both seasons and available incoming radiation.Therefore, the CH 4 -aCCF (in K (kg (NO 2 )) −1 ) is based on geopotential ( ) (in m 2 s −2 ) and incoming solar radiation at the top of the atmosphere as a maximum value over longitude (F in ) (in W m −2 ).For an atmospheric location (x, y, z) at time t with = (x, y, z, t), the CH 4 -aCCF can be found in Eq. (2).
where S is the total solar irradiance; θ is the solar zenith angle; ϕ is latitude; and d is the declination angle, defined by the time of year via the day of the year N.

NO x -induced PMO-aCCF
The effects of PMO and SWV decrease are not included in Eq. ( 2) but might be simply regarded as an offset of the CH 4 -aCCF with a linear scaling factor (e.g.Skowron et al., 2013), as they are primarily driven by the CH 4 change.Here we apply a constant factor of 0.29 to the CH 4 -aCCF calculated in Eq. ( 2) to account for the PMO effect (Dahlmann et al., 2016).The PMO-aCCF is then described by Eq. ( 4).
aCCF PMO = 0.29 × aCCF CH 4 aCCF PMO ≈ P-ATR20 PMO (4) Figure 4b shows an example of the combined CH 4 -CCF and PMO-aCCF (in K (kg (NO 2 )) −1 ) on 18 December 2015 over Europe at 250 hPa.The overlaid contour lines represent the geopotential on the same pressure level and time step.We can see that the decrease in CH 4 concentration caused by NO x emissions has cooling effects.Here, the cooling effects are overcompensated by the warming effects of O 3 .The overall effects of NO x emissions are expected to be warming, as seen in Fig. 4c, which shows the summation of O 3 -aCCF, CH 4 -aCCF, and PMO-aCCF.

H 2 O-aCCF
The H 2 O emission's climate impact largely depends on its residence time.The likelihood of removing (rain-out) the emitted H 2 O decreases with altitude up to the tropopause.Or vice versa, the H 2 O emission's residence time increases with height and shows a sharp gradient at the tropopause (Grewe and Stenke, 2008;Wilcox et al., 2012).Hence the distance to the tropopause is already a good indicator of the H 2 O's lifetime.There are different tropopause definitions, for instance, temperature lapse rate (including the World Meteorological Organization (WMO), thermal tropopause, WMO, 1957) and potential vorticity (PV) (Kunz et al., 2011).The WMO thermal tropopause and the PV dynamical tropopause may differ locally (Grewe and Dameris, 1996).van Manen and Grewe (2019) showed that PV is a better indicator for the H 2 O-aCCF, since PV can also be used as a definition between tropospheric and stratospheric air masses.The H 2 O-aCCF (in K (kg (fuel)) −1 ) is based on PV in standard potential vorticity units (PVUs).For an atmospheric lo-cation (x, y, z) at time t with PV = PV(x, y, z, t), the H 2 O-aCCF can be found in Eq. ( 5).
(5) Figure 5 shows an example of the H 2 O aCCF (in K (kg (fuel)) −1 ) on 18 December 2015 over Europe at 250 hPa.One can notice that the H 2 O has warming effects in general, and the highest values occur at the location where the potential vorticity is also high (see Fig. 3b).

Contrail cirrus aCCF
Contrail cirrus is short-lived.Because of its contrasting effects on shortwave and longwave radiation, contrail cirrus's radiative and climate effects distinguish between daytime and night-time.Thus, the specific radiative forcing of contrail cirrus (in W m −2 ) per flight distance has been developed for the daytime and night-time conditions by Emma Irvine (now Klingaman) based on reanalysis data (Klingaman and Shine; see Supplement).Note that, in the Supplement, the contrail coverage is assumed to be either 1 or 0, which is reasonable for higher horizontal resolutions.Therefore contrail distance equals flight distance in a grid box.Here, however, we deal with lower horizontal resolutions of T42 (Sect.3.1), and the conversion of flight distance to contrail distance requires the multiplication of the potential contrail coverage value of the regarded grid box.This approach ensures that Grewe et al. (2014a) and the Supplement are consistent.Unlike the other aCCF formulas in calculating the P-ATR20 value directly, the algorithm of contrail cirrus estimates the global-and annual-mean specific RF per flight distance using the parametric equation of Schumann et al. (2012).Accordingly, the contrail-cirrus aCCF (an approximation of ATR20) for pulse emissions (P-ATR20 contrail ) is obtained as a product of the specific RF per flight distance value and a constant of 0.0151 K W m −2 derived using the AirClim model.

Night-time contrail aCCF
Night-time contrails refer to contrails with their entire (6 h in this paper) lifetime occurring at night.Since these contrails only exist during hours of darkness, they cause only longwave RF, so their net RF must be positive (warming).The scatterplot of relevant meteorological variables against the net RF of night contrails was used to identify which parameters had the strongest relationships with the net RF (see Klingaman and Shine; see Supplement).It was found that the local temperature can provide reasonable approximations for the night contrails' radiative effects.By using the nonlinear regression method, the specific RF per flight distance of night-time contrails (RF contrails-night ) (in W m −2 km −1 ) is derived based on temperature (T ) (in K).For an atmospheric location (x, y, z) at time t, with T = T (x, y, z, t), the specific RF per flight distance of night-time contrail cirrus can be https://doi.org/10.5194/gmd-16-3313-2023Geosci.Model Dev., 16, 3313-3334, 2023 found in Eq. ( 6).Please note that correlation is not valid for temperatures less than 201 K.For temperatures below 201 K, the value should be set to 0.
By multiplying the factor of 0.0151 K W m −2 , the night-time contrail aCCF (in K per flown km) is calculated in Eq. ( 7).As explained in Sect.2, the conversion factor from specific RF to ATR20 for contrails is obtained using the climate response model, AirClim (Grewe and Stenke, 2008;Dahlmann et al., 2016).We apply a consistent set of global emission inventory for a given scenario, for which the specific RF and ATR20 are calculated.The ratio between specific RF and ATR20 is then derived as 0.0151 K W m −2 , hence used here as a conversion factor.Similarly, the daytime contrail aCCF in kelvin per flown kilometre is calculated in Eq. ( 9).
aCCF contrails-day = RF contrails-day × 0.0151 aCCF contrails-day ≈ P-ATR20 contrails-day (9) Please note that in the ACCF submodel, the contrail aCCF is only activated when the potential contrail coverage is larger than zero and the flight distance is converted to contrail distance by multiplying with the potential contrail coverage (see also above).Depending on the time of the contrail cirrus occurring, either day-or night-contrail-cirrus aCCF calculation is used.Figure 6 shows an example of the day-and night-time contrail aCCF on 18 December 2015 over Europe at 250 hPa: (a) 12:00 UTC and (b) 00:00 UTC.One can see that the contrail aCCF depends on the formation time.For instance, at the exact location (e.g. over Ireland), a contrail formed at 12:00 UTC has a cooling effect, whereas at 00:00 UTC it has a warming impact.

Physical climate metric and efficacy applied in the ACCF submodel
The aCCF formulas provided in Sect.3.3 calculate the climate impact of O 3 , CH 4 , PMO, H 2 O, and contrail cirrus consistently in P-ATR20, i.e. for a pulse emission.With pulse emission, one could compare, for instance, the future impact of emissions in a given year.When a non-pulse emission is considered, for example, an increased emission scenario representing the growth of air traffic, the metrics of pulse emission can be converted (Fuglestvedt et al., 2010).Here we demonstrate an example of converting the P-ATR20 to the ATR20 of the future BAU emission scenario (F-ATR20) derived by Grewe et al. (2021).We determined the climate metric conversion factors for the aCCFs of O 3 , CH 4 , PMO, H 2 O, and contrail cirrus using the AirClim model.We performed two simulations with pulse emissions in 2017 and future emission scenario BAU, respectively.For Table 1.Example values of climate metrics conversion factors from ATR20 of a pulse emission in 2017 (P-ATR20) to ATR20 of future BAU emission scenario (F-ATR20) and efficacies of different species/contrail-cirrus effect.The efficacies are taken from Lee et al. (2021).

Descriptions
Metric conversion factors Efficacy (P-ATR20 →F-ATR20) both simulations, we calculate the factor between ATR20 and RF for each effect and use the ratio between these values as conversion factors.Table 1 shows the conversion factors from the P-ATR20 to the F-ATR20 metric.In the namelist of the ACCF 1.0, these metric conversion factors can be changed depending on the chosen scenario for different purposes (see Supplement).
The efficacy of the individual forcing agents (O 3 , CH 4 , PMO, H 2 O, and contrail cirrus), which consider the different effects of these forcing agents in producing global temperature change (e.g.Hansen et al., 2005), are not included in the aCCF formulas in Sect.3.3.However, they can be easily included via namelist settings of the ACCF submodel (see the user manual in the Supplement for namelist settings).The present study implemented the forcing efficacies in Lee et al. (2021), as shown in Table 1.The final output of the ACCF submodel is a product of the output of aCCF formulas in Sect.3.3, the metric conversion factor, and the efficacies.

ACCF model simulations
In this section, we present the application of the submodel ACCF, how it describes the climate effects of aviation emissions, and how it can be used for aircraft trajectory optimization.This section also presents the quality check of ACCF submodel outputs.Firstly, we compare the climatology of the prototype aCCFs for O 3 , CH 4 , H 2 O, and contrail cirrus to results from the literature.Secondly, we study the O 3 RF change caused by the air traffic emissions through the AirTraf submodel calculated online for cost-and climate-optimized flights, respectively.The climate-optimized flights minimized the NO x -induced O 3 effect computed using Eq.(1).

Climatology of aCCFs
The climatological aCCFs are calculated for all meteorological situations emerging over a 1-year nudged simulation in 2016.The climate metric conversion factors and the efficahttps://doi.org/10.5194/gmd-16-3313-2023 Geosci.Model Dev., 16, 3313-3334, 2023 cies in Table 1 are considered.Figure 7a-c show the annual and zonal mean aCCF from O 3 , CH 4 combined with PMO, and total NO x (O 3 + CH 4 + PMO), respectively.The considered region is over the Northern Hemisphere and between 150-300 hPa.
The warming effects of O 3 increase with the altitude and towards the lower latitudes, which is in line with other studies.For instance, Fig. A2 of Dahlmann et al. (2016) shows that the global annual-mean RF of aviation NO x -induced O 3 increases with the pressure altitude.Figure 8 of Grewe and Stenke (2008) shows the global mean temperature change of NO x -induced O 3 for 2100, considering a constant emission from 2050-2100.Due to different emission scenarios, the absolute value in Fig. 7 of this study is much lower (orders of magnitude).However, when comparing the vertical and lateral variability in the vertical range of 150 and 300 hPa (typical flight corridor range), a similar pattern can be observed.
In comparison, the cooling effect of CH 4 (including PMO) increases towards lower altitudes but shows less dependency on latitude than O 3 at the lower altitude.That is to say, if the flight altitude is reduced, one would expect more substantial cooling effects due to NO x -induced CH 4 depletion.Such phenomena are in line with the study of Frömming et al. (2012), where it was shown that the CH 4 mean RF reduces when flying lower.Furthermore, when comparing Fig. 8 of Grewe and Stenke (2008) and Fig. A2 of Dahlmann et al. (2016) in the same vertical range, we notice some discrepancies in the CH 4 aCCF pattern in the latitudinal directions.Both Figs. 8 and A2 show that the cooling effects of CH 4 increase towards lower latitudes.This was also observed in Köhler et al. (2013).However, Fig. 7b shows an opposite trend, which needs further diagnosis in future studies.Since the value of CH 4 aCCF is about 5 times smaller than the O 3 aCCF, one can consider the mismatch of CH 4 aCCF to be of minor importance.
Figure 7d shows the annual zonal mean H 2 O aCCF.The warming effects of H 2 O increase with altitude and towards the polar region, which matches well with the previous study of Grewe and Stenke (2008), confirming that ACCF accurately represents the variations in global climate change of aviation H 2 O emissions at the different regional locations and different altitudes.
Figure 8 shows the zonal mean climatological value of contrail cirrus aCCFs (in K km −1 ) by combining the day and night effects.The RF and hence the F-ATR20 are calculated at the location where contrails could be formed.We compare the climatological contrail-cirrus aCCF with the values presented in the previous literature (Fig. A2 of Dahlmann et al., 2016, where the annual zonal mean contrails RF per flown km are calculated using normalized emissions).We notice that the order of magnitude and the profile of the contrail aCCF match the study of Dahlmann et al. (2016).

Radiative forcing calculation of aircraft emissions using EMAC submodels
To demonstrate the usage of the ACCF 1.0 in aircraft trajectory optimization considering non-CO 2 climate effects, we use the O 3 aCCF to calculate the RF due to aviation NO x -induced O 3 by combining ACCF with AirTraf, TAG-GING, and RAD (EMAC submodels).Figure 9 shows how an aircraft trajectory from the departure to the arrival airport is guided through climate-sensitive regions, described with the help of the ACCF submodel.Providing atmospheric perturbations in reactive species to the TAGGING submodel calculates associated ozone changes, and eventually, radiative impacts are characterized in the RAD submodel.For the demonstration, we optimize the flight trajectories of a subset of daily European flights concerning either minimum cost (simple operating cost option in the AirTraf submodel; Yamashita et al., 2020) or minimum climate impact from only  In line with the simulation scheme above, we configured the EMAC model with a list of EMAC submodels.In addition to the standard submodels, we use AirTraf 2.0 (Yamashita et al., 2020) to calculate the air traffic emissions from different flight trajectories, MECCA (Module Efficiently Calculating the Chemistry of the Atmosphere; Sander et al., 2005) and SCAV (SCAVenging; Tost et al., 2006a), to represent the chemical kinetics of EMAC.We also use TAG-GING 1.0 (Grewe et al., 2017a) to tag the contributions of emissions to concentrations.The radiation flux change of the NO x -induced O 3 change is calculated using the submodel RAD (Dietmüller et al., 2016).The complete list of used https://doi.org/10.5194/gmd-16-3313-2023 Geosci.Model Dev., 16, 3313-3334, 2023 EMAC submodels in this simulation can be found in Table A1 of the Appendix.
The simulation setup for trajectory optimization is given in Table 2.A total of 85 daily European flights are used.The constant flight Mach number 0.82 combined with the wind speed will result in different ground speeds.For costoptimized flight trajectories, simple operating cost calculated using Eq. ( 10) is the objective function.For climateoptimized flight trajectories, the F-ATR20 of NO x -induced O 3 is used as the objective function.There are 11 design variables to express a flight trajectory.Five variables control the vertical change between flight levels of 8839 m (29 000 ft, FL290) and 12 497 m (41 000 ft, FL410), and six variables control the lateral shift.The Adaptive Range Multi-objective Genetic Algorithm (ARMOGA version 1.2.0,Sasaki and Obayashi, 2005;Sasaki et al., 2002) is implemented for trajectory optimization.
where t is the flight time in hours, m fuel is the fuel consumption in kilograms, C t is the flight time related cost in euros (EUR) per hour, and C f is the fuel related cost in EUR per kilogram of fuel).
Figure 10 shows the calculated flight trajectories on a single day for the minimal cost (red) and the minimal NO x -O 3 climate impact (green).Figure 10a shows the changes in flight altitudes, and Fig. 10b shows the lateral shifts of flight trajectories aggregated along the vertical direction.For costoptimized flights, the aircraft tends to fly as high as possible within the vertical constraints to maximize aerodynamic efficiency, reducing fuel consumption and the associated operational cost.As for the climate-optimized routine, the situation is much more complicated.The climate impact of O 3 attributed to NO x emissions depends on multi-criteria, e.g. the emitted quantity, time, location, and weather.On aver-age, the altitudes of climate-optimized flights are lower than those of cost-optimized flights.We also notice from Fig. 10b that some flights tend to shift northward to reduce the NO x -O 3 climate impact.
The flight characteristics and performance data are summarized in Table 3.Compared to the cost-optimized flights, the fuel consumption of the climate-optimized flights is 11 % higher, and the NO x emissions are 15 % higher.The total cost of climate-optimized flights is about 5 % higher than that of cost-optimized flights.
Having the flight trajectories and their respective performance calculated with AirTraf using ACCF values (Fig. 10), NO x emissions from cost-and climate-optimized trajectories are then integrated into the global EMAC model as tagged species by the EMAC/TAGGING submodel.This allows the contributions of different NO x emission sources to the atmospheric changes of the NO x and O 3 concentrations to be identified.This showcase simulation using tagging chemistry was run for 3 months, from January to March 2016.Figure 11 shows relative changes in monthly mean mixing ratio distribution of (a) NO x (in mol mol −1 ) and (b) O 3 (in mol mol −1 ), comparing effects caused by NO x emissions from climate-optimized flight trajectories with the effect of cost-optimized trajectories (baseline) in March 2016.The figure is presented in the vertical cross-section.The climateoptimized trajectories emit NO x at a lower altitude than the cost-optimized trajectories; therefore, we see an increase in the NO x mixing ratio at the lower altitude (indicated by the red colour in Fig. 11a).As a result, the O 3 production is shifted downwards (see Fig. 11b).The residence time of O 3 at the lower altitude is shorter due to a more efficient washout.Therefore, the calculated RF of the NO x -induced O 3 for the climate-optimized flights (13.3 mW m −2 ) is about 2 % less than that of the cost-optimized flights, which confirms  that the climate-optimized flight trajectories based on the O 3 aCCF reduce the associated NO x -O 3 climate effect.

Application of the ACCF submodel for trajectory optimization
This section demonstrates the application of the ACCF submodel to assess the aviation climate effects during trajectory optimization.In previous research, Yamashita et al. (2020) implemented the ACCF submodel in AirTraf 2.0 to obtain climate-optimized trajectories.Here, we update the ACCF submodel outputs using the physical climate metric F-ATR20 and consider the efficacy of radiative effects.

Simulation setup
We couple the ACCF 1.0 with the AirTraf 2.0 in this simulation.In AirTraf 2.0, two optimization objectives are considered, respectively: cost-and climate-optimized.The simulation setup can be seen in Table 4.In this section, the climate-optimized trajectory minimizes the total F-ATR20 of CO 2 , NO x (summation of O 3 , CH 4, and PMO), H 2 O, and day/night contrail cirrus, including the efficacies of individual species/contrail cirrus as shown in Table 1.

Optimized flight trajectories
We compare the F-ATR20 values of cost-optimized (red) and climate-optimized (green) trajectories in Fig. 12. Costoptimized trajectories are characterized by higher flight altitudes to maximize aerodynamic efficiency, which is similar to what was described in Sect.4.2.On the other hand, climate-optimized trajectories considering non-CO 2 effects fly at lower altitudes at most locations to reduce the impact of the total NO x , H 2 O, and contrails.Table 5 summarizes the flight characteristics.Compared to the cost-optimized flights, the climate-optimized trajectories (ignoring economic costs while only minimizing climate effects) tend to increase fuel consumption by 17 % and NO x emissions by 25 %.On the other hand, the total F-ATR20 is reduced by 51 % driven by the contrails effect (−89 %), followed by the combined CH 4 and PMO impact (−41 %).The impact of CO 2 and H 2 O is characterized by lower orders of magnitude than the impacts from NO x emissions and contrails; therefore, they are not crucial properties during the optimization process, but they are affected by changes due to higher fuel consumption (causing higher CO 2 impact (+17 %)) and lower mean flight altitudes (leading to lower H 2 O impact (−33 %)).
Furthermore, one can observe that the contribution of CO 2 to the overall climate impact is relatively low compared to the non-CO 2 effects.This could be caused by choice of the physical climate metric and the radiation scheme used to develop https://doi.org/10.5194/gmd-16-3313-2023 Geosci.Model Dev., 16, 3313-3334, 2023  the original CCFs and the following aCCFs characteristics.
While ongoing research investigates how to best define an adequate climate metric reflecting short-term and long-term effects to a certain extent, we expect to develop a better understanding with further diagnosis.

Discussions
This research implements a consistent set of prototype algorithmic climate change functions as the submodel ACCF 1.0 of EMAC, enabling quantifying aviation emission climate effects.The demonstration simulations confirm that the developed aCCFs can predict the characteristic patterns of ATR20 from H 2 O, NO x -induced O 3, and contrail cirrus.The NO xinduced CH 4 pattern shows a slight discrepancy in terms of latitudinal variabilities when compared to previous studies (Grewe and Stenke, 2008;Frömming et al., 2012;Köhler et al., 2013).As the total NO x aCCF is dominated by the positive O 3 , we expect that the combination of O 3 and CH 4 captures the feature of aviation NO x adequately.Further development of the CH 4 aCCF formula is required to address the latitudinal discrepancy.Furthermore, the ACCF submodel has been implemented in a comprehensive tagging chemistry simulation chain to evaluate mitigation gains because of modified aviation emissions.By coupling the ACCF submodel with the AirTraf sub-model, NO x emissions are calculated from cost-optimized and climate-optimized flights considering only the NO xinduced O 3 effect.The NO x emissions are then fed into the tagging chemistry scheme to estimate the resulting RF due to changes in O 3 mixing ratios.The results confirmed that the climate-optimized trajectories reduce the RF of O 3 by 2 % compared to the cost-optimized flights.
The case study on trajectory optimization for cost-and climate-optimized flights indicates a relatively low contribution of CO 2 to the overall climate impact compared to the non-CO 2 effects.Our first thoughts are that this might be related to the metrics we are using, the radiation scheme in developing the original CCFs models, and the regional effects.Ongoing work in the metric diagnosis and the geographical analysis will help us better understand the reasons.

Climate metrics conversion
Regarding the physical climate metric used in this study, the aCCF formulas in Sect. 3 calculate the average temperature response over 20 years for a pulse emission (P-ATR20).Based on the P-ATR20, it is possible to obtain different physical climate metrics for any other emission scenario by applying a climate response model, for example, AirClim.Though the flexibility of the ACCF namelist setup allows the user to convert the climate metrics, the metric selection involves different factors, for example, the perspective ques- tion (Fuglestvedt et al., 2010;Grewe and Dahlmann, 2015).We want to stress that we consider it essential that any optimization study carefully defines the physical climate metric used, the type of strategic decision envisaged, constraints given, and assumptions on policy and regulations accepted.
For instance, one should identify the application scenario (or the perspective question) as the specific application scenario is critical for defining the adequate reference, the physical climate metric, and the emission scenario.A pulse emission would compare the future climate impact in a given year.A future emission scenario would compare the effect of varying emissions over a period in the future.From the perspective question, an adequate climate indicator and time horizon can then be deduced.

Uncertainties of contrail aCCFs
While the aviation-induced contrail-cirrus effects play essential roles in aviation's climate impact, the level of scientific understanding on contrail cirrus climate effects is moderate or low (see, for example, Lee et al., 2021), which implies a large uncertainty.The uncertainties of contrail-cirrus climate impact are subject to different aspects, including the natural variability of the atmosphere and modelling uncertainties.
Both uncertainties propagate to contrail-cirrus aCCF.For instance, contrail aCCF is only calculated when potential contrail coverage (potcov) is greater than zero.The potcov varies strongly with the local atmospheric temper-ature and relative humidity over ice, which again depend on specific models (e.g. an Earth system climate model vs. a weather forecast model with higher resolution).While comparing the temperature field calculated from the EMAC model on 18 December 2015 nudged towards the ECMWF reanalysis data (ERA-Interim) with the original ERA-Interim datasets at three pressure levels of 200, 250, and 300 hPa, we observed that the temperature calculated from the EMAC model is on average 3 K lower than the reanalysis data.This temperature difference affects the predicted potcov and the calculated contrail-cirrus aCCF (see Eq. 6). Figure 13 shows a comparison between the values of F-ATR20 calculated from contrail-cirrus aCCF on 18 December 2015 at 250 hPa. Figure 13a shows the geographical pattern using the original EMAC temperature, and Fig. 13b shows the geographical pattern when artificially correcting the 3 K temperature bias from the EMAC temperature.Two effects are observed: (1) the areas where the contrails might form are reduced for a warmer temperature, and (2) the maximum value of ATR20 increases indicating a more substantial warming effect.From this preliminary analysis, we could see that the uncertainties related to the inputs of aCCFs play an essential role in the robustness of the aCCFs results.
Furthermore, for a given model resolution, one might expect a latitude dependency of contrail aCCF as the flight distance per grid box varies with latitude, which is currently under investigation.

Ongoing research on the robustness of aCCFs
The aCCFs 1.0 used in this study represent a prototype formulation and face different aspects of uncertainties.The aC-CFs are based on simulations performed for the North Atlantic Flight Corridor during summer and winter.While applying the aCCFs at European airspace, we observe that the climatological pattern of aCCFs in vertical and latitudinal variability matches other studies (Dahlmann et al., 2016).Nevertheless, using them at other locations and seasons should be done cautiously and carefully evaluated.We would like to note here that the development of the aCCFs is an ongoing research activity, and an expansion of their geographic scope and seasonal representativeness is under investigation.Furthermore, a concept toward robust aCCFs is under development, which will additionally integrate information about uncertainties arising from low-level understanding of climate science (Matthes et al., 2023).This robust aCCFs will rely on a set of aCCFs that consider educated guess es-timates of individual climate impacts.The basis of this educated guess can be, for example, the conservative estimates of the individual RF (see Lee et al., 2021).Additionally, the second set of aCCFs will be provided to perform individual risk analyses originating from different sources of uncertainty.This will be done by quantitatively estimating the error if a lower or higher climate impact is assumed.With that, we add up to low-or high-range aCCF estimates, respectively.This concept of robust aCCFs can be applied in aircraft trajectory optimization studies with EMAC/AirTraf.The corresponding experiment design would rely on one reference optimization using the educated guess aCCFs and sensitivity optimization experiments using the low-or high-range aC-CFs estimates.A robust trajectory would be characterized by not losing overall benefits (mitigation gains) even if lower or upper estimates of aCCFs are applied.Technically, this could be solved by calling the ACCF submodel several times within the same simulation, using the range of different aCCFs estimates.

Conclusions
We developed the submodel ACCF 1.0 of the chemistryclimate model EMAC to estimate the climate impact of aviation emissions in the flight corridor of the Northern Hemisphere, representing an implementation of aCCF 1.0 formulas.The submodel ACCF 1.0 was developed according to the MESSy standard and was thoroughly presented in this paper.This submodel calculates aviation's climate impact of CO 2 emissions and non-CO 2 effects, such as from NO x -induced O 3 , NO x -induced CH 4 (including PMO), H 2 O, and contrail cirrus based on a consistent set of aCCFs.The mathematical formulation of the individual prototype aCCFs 1.0 is provided.
The climatological profile of the NO x -induced effect on ozone (O 3 aCCF) shows that the warming effects of NO xinduced O 3 increase with altitude between 150-300 hPa and towards lower latitudes, while the climatological distribution of H 2 O aCCF shows that the warming effect of H 2 O increases towards higher altitudes or latitudes.By comparison to the literature, we conclude that the vertical and latitudinal structure within the flight corridor of the Northern Hemisphere of the NO x -induced O 3 and H 2 O is well represented by the aCCFs.
The NO x -induced effect on methane (CH 4 aCCF) shows that cooling effects increase towards lower altitudes and higher latitudes.Although the latitudinal variation of CH 4 aCCFs is less pronounced than for other species, it is somewhat of the opposite tendency to the literature.Since the absolute value of CH 4 aCCF is mostly overcompensated for by the O 3 aCCF, the total NO x aCCF could still capture the vertical and latitudinal variability of the overall NO x effects.
For the contrail-cirrus aCCF, the climatological pattern follows the potential contrail coverage.The calculated F-ATR20 value also matches the literature, except that contrailcirrus aCCF generates values at low altitudes where contrails are not expected to be formed.This might be related to the threshold of temperature and humidity used for calculating the potential contrail coverage and the temperature bias in the EMAC model.
Using the tagging chemistry approach, we were able to show that climate-optimized trajectories based on O 3 aCCF indeed reduce the radiative forcing contribution from aviation NO x -induced O 3 compared to the cost-optimized trajectories.
Finally, the trajectory optimization results confirm that the total F-ATR20 of climate-optimized flights is about 51 % lower than the cost-optimized flights, with the largest contribution from contrail cirrus., 2023).The version presented here corresponds to ACCF 1.0.The status information for ACCF will be available on the website.
Supplement.The Supplement related to this paper includes the development of contrail-cirrus aCCF and the user manual for the ACCF submodel setup.The supplement related to this article is available online at: https://doi.org/10.5194/gmd-16-3313-2023supplement.
Author contributions.FY and VG designed the submodel ACCF V1.0.FY implemented the coupling of ACCF V1.0 with the Modular Earth Submodel System (MESSy).VG, SM, KD, EK, and KS developed the algorithmic Climate Change Functions (aCCFs).KD calculated the metric conversion factor.CF calculated the Climate Change Functions (CCFs).HY and VG designed the submodel Air-Traf V2.0.BL and FL provided the traffic sample for this study.PR, SD, SM, and PP contributed to the discussions.FY and FC performed the simulations and analysed the results presented in this paper.
Competing interests.At least one of the (co-)authors is a member of the editorial board of Geoscientific Model Development.The peer-review process was guided by an independent editor, and the authors also have no other competing interests to declare.
Disclaimer.Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.Review statement.This paper was edited by Jason Williams and reviewed by two anonymous referees.

Figure 1 .
Figure 1.Overview of conceptual development and relevant projects (i.e.REACT4C, ATM4E, and FlyATM4E) leading to the algorithmic Climate Change Functions (aCCFs) and the ACCF submodel.

Figure 2
Figure2illustrates the structure of ACCF 1.0 and its interactions with other EMAC submodels.The ACCF 1.0 includes two layers: the sub-model interface layer (SMIL) and the submodel core layer (SMCL).The SMIL manages model input-output through the CHANNEL submodel(Jöckel et al., 2010).The SMCL is independent of other submodels and contains the code to solve the relevant equations for the individual aCCFs.The input variables to calculate aCCFs in the ACCF submodel are either from the base model calculation (i.e.temperature, geopotential) or from the other EMAC submodels.For instance, the H 2 O aCCF is a function of potential vorticity (PV) provided by the submodel TROPOP(Jöckel et al., 2006).The daytime contrail aCCF depends on the outgoing longwave radiation (OLR) at the top of the atmosphere from the submodel RAD(Dietmüller et al., 2016).The potential contrail coverage (potcov) calculated from the submodel CONTRAIL(Frömming et al., 2014) is used to determine whether persistent contrails can form and may lead to a climate impact by contrails.The Supplement of this paper includes a user manual of the submodel ACCF.It describes the namelist settings of the ACCF submodel and includes submodels necessary for coupling input-output variables.

Figure 2 .
Figure 2. Overview of EMAC/ACCF submodel structure, the calculation process in the ACCF submodel, and its interaction with the other MESSy submodels.SMIL (submodel interface layer) and SMCL (submodel core layer) are components of MESSy coding standards.
aCCF contrails-night = RF contrails-night × 0.0151 aCCF contrails-night ≈ P-ATR20 contrails-night (7) Daytime contrail aCCF Daytime contrails refer to contrails that form and dissipate during daylight or have a part of their 6 h lifetime during the day.The specific RF per flight distance of daytime contrails (RF contrails-day ) (in W m −2 km −1 ) is based on the OLR (in W m −2 ) at the top of the atmosphere at the time and location of the contrail formation.Therefore, for an atmospheric location (x, y) at time t with OLR(x, y, t), the RF of daytime contrail cirrus can be found in Eq. (8).Please note that Eq. (8) will predict negative specific RF per flight distance for OLR < −193 W m −2 and positive specific RF per flight distance for any larger OLR values.RF contrails-day = 10 −10 × (−1.7 − 0.0088 × OLR) (8)

Figure 9 .
Figure 9. Sketch of the radiative forcing calculations for ozone changes caused by online air traffic NO x emissions for cost-and climateoptimized flight trajectories.Cost-optimized aircraft trajectories minimize the simple operating cost of the flight, while climate-optimized aircraft trajectories minimize the climate impact (here only the NO x -induced O 3 effect is included).

Figure 10 .
Figure 10.Calculated daily flight trajectories in (a) vertical variation and (b) lateral variation using AirTraf for cost-optimized (red) and climate-optimized flights considering only the NO x -O 3 effects (green).

Figure 11 .
Figure 11.Changes of (a) NO x mixing ratio and (b) resulting changes in O 3 mixing ratio caused by NO x -O 3 -optimized flight trajectories using only O 3 aCCF.The baseline is cost-optimized flights.

Figure 12 .
Figure 12.Comparison of (a) vertical shift and (b) lateral shift between cost-optimized (red) and climate-optimized (green) trajectories on 18 December 2015.

Figure 13 .
Figure 13.Geographical distribution of contrail aCCF (in K km −1 ) on 18 December 2015 at 250 hPa for (a) the original EMAC temperature and (b) the bias-corrected EMAC temperature.

Acknowledgements.
The computing resources to conduct simulations with the ECHAM/MESSy Atmospheric Chemistry (EMAC) model were provided by the TU Delft High Performance Cluster (HPC12).This work used resources of the Deutsches Klimarechenzentrum (DKRZ) granted by its Scientific Steering Committee (WLA) under project IDs bd0781 and bd1062.Financial support.The current study has been supported by the previous ATM4E project and the current FlyATM4E project.Both projects have received funding from the SESAR Joint Undertaking under grant agreement nos.699395 (ATM4E) and 891317 (Fly-ATM4E) under European Union's Horizon 2020 Research and Innovation programme.
Grewe (2019)ile, we demonstrate the different processes between the CCF and aCCF model development.For instance, van Manen andGrewe (2019)analysed the relation of weather data to different aviation climate effects, for example, NO x -induced O 3 , NO x -induced CH 4 , and H 2 O based on the CCF datasets.Accordingly, the aCCFs were developed.Please note that though the aCCFs have been developed based on the CCF data, the formality is generalized beyond the weather pattern in CCFs.The work in Sect.4.2 of this study attempts to evaluate the applicability of aCCFs by implementing the NO x aCCFs on arbitrary-day weather conditions concerning European flights.By evaluating the resulting emissions utilizing the EMAC model, the simulations confirmed the effectiveness of using the O 3 aCCF model for climate-optimized trajectories to reduce the radiative forcing (RF) of aviation NO x -induced O 3 .Please see the details of the work in Sect.4.2 of this paper.

Table 2 .
AirTraf simulation setup for trajectory optimizations considering cost minimum and climate minimum (only NO x -O 3 effect), respectively.• in latitude and longitude, 31 vertical pressure levels up to 10 hPa, a time step of 12 min)

Table 3 .
Daily sum over the flight-plan of the characteristics of the cost-optimized and the NO x -O 3 -optimized flights.

Table 4 .
AirTraf simulation setup for trajectory optimizations considering cost minimum and climate minimum.

Table 5 .
Daily sum of flight characteristics over the cost-optimized and the climate-optimized trajectories on 18 December 2015.

Table A1 .
https://doi.org/10.5194/gmd-16-3313-2023Geosci.Model Dev., 16, 3313-3334, 2023 F. Yin et al.: Development of ACCF 1.0 Appendix A: A list of EMAC submodels used in the chemistry simulation Summary of MESSy submodels used in the chemistry simulation.Code and data availability.ACCF 1.0 has been published for the first time as a submodel of the Modular Earth System Submodel System (MESSy) since version 2.53.MESSy is continuously further developed and applied by a consortium of institutions.The usage of MESSy and access to the source code are licensed to all affiliates of institutions members of the MESSy Consortium by signing the MESSy Memorandum of Understanding.More information can be found on the MESSy Consortium website (http: //www.messy-interface.org,MEESy