Influence of the actual weather situation on non-CO2 aviation climate effects: The REACT4C Climate Change Functions

Abstract. Emissions of aviation include CO2, H2O, NOx, sulfur oxides and soot. Many studies have investigated the annual mean climate impact of aviation emissions. While CO2 has a long atmospheric residence time and is almost uniformly distributed in the atmosphere, non-CO2 gases, particles and their products have short atmospheric residence times and are heterogeneously distributed. The climate impact of non-CO2 aviation emissions is known to vary with different meteorological background situations. The aim of this study is to systematically investigate the influence of different weather situations on aviation climate effects over the North Atlantic region, to identify the most sensitive areas and potentially detect systematic weather related similarities. If aircraft were re-routed to avoid climate-sensitive regions, the overall aviation climate Impact might be reduced. Hence, the sensitivity of the atmosphere to local emissions provides a basis for the assessment of weather related, climate optimized flight trajectory planning. To determine the climate change contribution of an individual Emission as function of location, time and weather situation, the radiative impact of local emissions of NOx and H2O to changes in O3, CH4, H2O and contrail-cirrus was computed by means of the ECHAM5/MESSy Atmospheric Chemistry model. 4-dimensional climate change functions (CCFs) were derived thereof. Typical weather situations in the North Atlantic region were considered for winter and summer. Weather related differences in O3-, CH4-, H2O-, and contrail-cirrus-CCFs were investigated. The following characteristics were identified: Enhanced climate impact of contrail-cirrus was detected for emissions in areas with large scale lifting, whereas low climate impact of contrail-cirrus was found in the area of the jet stream. Northwards of 60° N contrails usually cause climate warming in winter, independent of the weather situation. NOx emissions cause a high positive climate impact if released in the area of the jet stream or in high pressure ridges, which induces a south- and downward transport of the emitted species. Whereas NOx emissions at, or transported towards high latitudes, cause low or even negative climate impact. Independent of the weather situation, total NOx effects show a minimum at ∼250 hPa, increasing towards higher and lower altitudes, with generally higher positive impact in summer than in winter. H2O emissions induce a high climate Impact when released in regions with lower tropopause height, whereas low climate impact occurs for emissions in areas with higher tropopause height. H2O-CCFs generally increase with height, and are larger in winter than in summer. The CCFs of all individual species can be combined, facilitating the assessment of total climate impact of aircraft trajectories considering CO2 and spatially and temporally varying non-CO2 effetcs. Furthermore they allow the optimization of aircraft trajectories with reduced overall climate impact. In most regions NOx and contrail-cirrus dominate the sensitivity to local aviation emissions. The findings of this study recommend, to consider weather related differences for flight trajectory optimization in favour of reducing total climate impact.


tematically studies the effects and weather related differences in detail for various locations (latitude, longitude, altitude) and time of emission within the Northern Atlantic region. We have chosen the North Atlantic region as a study domain because the flight trajectories are not as constrained as over the continents. There are long distance flights which allow studying detours, there is sufficient air traffic making it worthwhile to study re-routing. But the traffic is not too dense to enable rerouting without generating too many conflicts with other flights. Additionally this study region is characterised by synoptical scale archetypical 100 weather patterns, which allow creating a set of representative weather situations.
In the present study, first the methodology is presented how the weather related impact of a local emission on climate is calculated in a comprehensive climate chemistry model (Section 2). The weather situations which were used in the present study are described in Section 3. The resulting climate change functions (CCFs) are presented in Section 4. The results are discussed and an outlook is given how the CCFs could be used for planning of climate optimized aircraft trajectories (Section 5). Section 6 105 concludes with a short summary and ideas for future studies.

Model description
The ECHAM/MESSy Atmospheric Chemistry Model (EMAC, Jöckel et al. (2010Jöckel et al. ( , 2016) is a numerical chemistry climate model system which implements submodels describing physical and chemical atmospheric processes, ranging from the tropo-110 sphere up to the middle atmosphere and their interactions with the biosphere, hydrosphere and geosphere. The Modular Earth Submodel System (MESSy) couples the various submodels to the core atmospheric model ECHAM5 (Roeckner et al., 2006).
Here, EMAC is used in a T42L41 spectral resolution, corresponding to a quadratic Gaussian grid of ∼2.8 • ×2.8 • in latitude and longitude, and 41 vertical layers from the surface to 5 hPa, which is a compromise between the level of detail within the simulation and the computational expense. the companion model development paper of Grewe et al. (2014a), while in the present study we resume only the relevant information and focus on the results. To derive these CCFs, a 4-dimensional time-region grid is defined. This time-region grid covers cruise altitude relevant pressure levels from 400 hPa to 200 hPa over the North-Atlantic area, in total yielding 168 grid points (see Table 1). At each of these time-region grid points, a pulse emission of NO x and H 2 O is released within one model timestep of 15 minutes. This is done for a number of representative weather situations (see Section 3). As the weather situation 130 changes slightly during day, 3 different emission times (6, 12, and 18 UTC) are considered. An emission of 5×10 5 kg NO (=2.33×10 5 kg N) is released at each time-region. Regarding water vapour, 1.25×10 7 kg H 2 O is emitted at each time-region.
H 2 O loss is included proportionally to the precipitation rate. The emissions are distributed on 50 air parcel trajectories, which are (randomly distributed) started from within the EMAC grid box in which the time-region grid point lies. The air parcel trajectories transport the emissions and their products in a Lagrangian manner, while diffusive processes are considered by 135 mixing of the air parcel trajectories with a multitude of background trajectories. More information about this mixing process, calculated by the submodel LGTMIX, can be found in the paper by Brinkop and Jöckel (2019). The Lagrangian approach has been chosen, as it facilitates the calculation of many time-regions in parallel. The background chemistry is calculated by the submodel MECCA (v3.2, Sander et al. (2011)), photolyis rates by the submodel JVAL (Sander et al., 2014). Non-methane hydrocarbon (NMHC) chemistry (up to four carbon atoms plus isoprene( is employed, reproducing the main features of the 140 tropospheric chemistry (Houweling et al., 1998). The chemical loss and production rates are calculated for the unperturbed background, while the proportional contributions of the emitted species to the atmospheric mixing ratios of NO y (all active nitrogen species), HNO 3 , O 3 , H 2 O, OH, and CH 4 are calculated for each air parcel trajectory based on a tagging scheme (Grewe, 2013;Grewe et al., 2014aGrewe et al., , 2017. Atmospheric processes such as wash-out and dry deposition, are proportionally taken into account on the air parcel trajectories. The potential contrail coverage is calculated according to Burkhardt et al. (2008) and 145 Burkhardt and Kaercher (2009). It indicates whether atmospheric conditions with respect to temperature and humidity enable the formation of persistent contrails for a representative kerosene fuelled aircraft with an overall propulsion efficiency of 0.3. This ability is transferred onto the air parcel trajectories. Then the actual contrail coverage is determined in dependency whether actual air traffic occurs in the respective grid box. Spreading, sublimation and sedimentation of ice particles are parameterized.
Details are given by Grewe et al. (2014a) and Frömming et al. (2014). Because of its long perturbation life time, emissions of 150 CO 2 are assumed to be equally mixed within the atmosphere, the temporal evolution of the change in mixing ratio is calculated following Fuglestvedt et al. (2010) and Forster et al. (2007) as detailed by Grewe et al. (2014a).
This approach leads to a 4-dimensional distribution of mixing ratios of trace gases, coverage and optical properties of contrails following a local pulse emission over an integration time of 90 days, covering most of the short-term responses, while longer term responses are covered by extrapolation. The impact of the perturbations in the energy balance are quantified by 155 the radiation imbalance at the tropopause (radiative forcing, RF, Shine et al. (1990)). Positive RF will lead to climate warming and vice versa. The instantaneous radiative forcing at the tropopause is calculated directly within the submodel RAD4ALL (Dietmüller et al., 2016) for O 3 , H 2 O and contrails. The stratosphere-adjusted RF, which allows stratospheric temperatures to adjust to the new equilibrium following the radiative imbalance, is derived as described in detail by Grewe et al. (2014a). The RF from CH 4 is determined from the CH 4 perturbation following the method described by Shine et al. (1990) and the RF from 160 primary mode O 3 (PMO) is derived by applying a constant factor of 0.29 to the CH 4 RF as suggested by Dahlmann (2012).
Regarding contrails, the difference between the adjusted and the instantaneous RF is marginal , hence within the present study, the instantanous RF is used. Because of the overall setup of the experiment, in some cases very small ice water contents were simulated. Several other radiation parameterisations are limited to ice water contents or optical depths (τ ) exceeding a certain threshold (personal communication R. R. de Leon, MMU). Although for the model used here, no such 165 validity range exists, in the present study, only contrails with τ ≥0.01 are included, as it is suspected, that in some cases, very small optical depths in combination with small coverages may not yield correct short wave radiative forcings. The RF calculation for CO 2 is based on Fuglestvedt et al. (2010) and includes a simple linearised conversion factor between the change in its atmospheric mass and the RF as provided by Grewe et al. (2014a).
From RF various climate metrics can be derived by means of the climate-chemistry response model AirClim (Grewe and Stenke,170 2008; Grewe and Dahlmann, 2015;Dahlmann et al., 2016). We use the average temperature response (ATR, Schwartz Dallara et al. (2011), which is based on the global mean temperature change integrated over a certain time horizon. The ATR is defined in Eq. 1, with the global mean temperature change ∆ T (K), the time t (years) and the time horizon H (years).
We choose a time horizon of 20 years, as we focus on the short-term effect of a climate-optimized re-routing strategy.

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Based on the RF calculations, other climate metrics could be calculated for other time horizons e.g. 20, 50, or 100 years (Fuglestvedt et al., 2010), such as the absolute global warming potential (AGWP), or the absolute global temperature potential, which would give a wide range of CCFs. A temperature based climate metric has the advantage that it is both, used within the climate modeling community, but also understood by nonexperts. A discussion on the suitability of various metrics and time horizons regarding different research questions is given by Grewe et al. (2014a) and Grewe and Dahlmann (2015).  situations (W1-W5) and three summer situations (S1-S3) as simulated with EMAC using the classification of Irvine et al. (2013). The black dots mark the regions discussed in Section 4.2 and listed in Table A1. Please note that the maps in Figure 1  Five specific types are defined in winter time. Weather situation W1 shows a strong zonal jet stream and a low pressure trough is dominating the North Atlantic. Weather situations W2 and W3 represent a meridionally tilted jet stream with either a weaker or stronger jet, respectively. Weather situation W4 is characterized by a ridge over the Eastern North Atlantic and the jet is confined to the western part of the North Atlantic. W5 shows the least similarity to the NAO and EA teleconnection patterns 190 and the jet is weak and confined to the US coast. W5 is the most frequent weather situation in winter (26 days per season).
Types W1 to W4 occur on average 15-19 days per winter (Irvine et al., 2013). In summer only three types are defined, because of weaker teleconnection patterns and a smaller variability of the jet. Weather pattern S1 represents a strong zonal jet stream, although the jet is weaker than in winter. Weather pattern S2 is characterized by a jet, which is weakly tilted towards northeast.
Weather pattern S3 shows a weak, but strongly tilted jet. Weather patterns S1 and S3 occur with similar frequency (19 and 18 195 days per summer, respectively). S2 is the most frequent type in summer (55 days per summer). For each of these 8 weather situations a representative day is selected, for which the weather dependent climate change functions were calculated. First results of CCFs for one specific weather situation (W1) were exemplarily shown by Grewe et al. (2014b). Here, an overview of the climate change functions for all representative winter and summer weather situations are presented and analysed in detail, with particular focus on the differences between the weather situations.

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The climate change functions were calculated for eight representative weather situations and 168 emission regions listed in  Figure 2 shows the potential contrail formation for the eight representative winter and summer weather situations as simulated with the EMAC model. The potential contrail coverage indicates the probability of atmospheric conditions enabling the formation of persistent contrails. When averaged over the year (not shown) maximum potential contrail coverage is found in 220 the stormtrack region and over Greenland, whereas minimum potential coverage is found over Newfoundland. In our study region, the mean potential contrail coverage ranges from 20% -36% at 250 hPa between the weather situations. The actual magnitude and distribution of potential contrail coverage depends on season and weather situation. Highest potential coverages are found in weather situations W4, W5 and S2 between 250 and 300 hPa. Minimum contrail formation is found at 400 hPa independent of the weather situation, since the temperature threshold for contrail formation is more frequently surpassed at that 225 level, particularly at low latitudes. Common features found in the weather situations studied here, are an enhanced potential contrail coverage in the vicinity of Greenland, where saturation is induced by orographic lifting. Furthermore, enhanced potential contrail coverage is also found south of the jet stream, where the tropopause is higher, and in areas with strong meridional transport, e.g. around ridges, where air masses are lifted, which also leads to saturation. In contrast, comparably low potential coverages can be observed in the area of the jet stream (see Figure 2 e.g. W2, W3).

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As described in section 2, aviation emissions are released in every time-region in our study area, resulting in contrail coverage if atmospheric conditions allow for it. The contrail coverage and ice water content is transported and evolves according to  spreading, sedimentation and sublimation. The span of contrail lifetimes ranges from 15 minutes to more than 24 h. A mean lifetime of contrails of 3.5±5.3 h was found for all considered weather situations. In winter, contrails exist on average 4.0 h, with mean lifetimes ranging from 1.9 h for W2 to over 5 h for W4 and W5. In summer, the mean lifetime of contrails is shorter

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(2.5 h) and similar for all weather situations. 78% of all contrails live less than 5 h, and only 7% of all contrails live longer than 10 hours. Contrail net RF is the sum of positive longwave and negative shortwave RF of similar magnitude (Ponater et al., 2002). Figure 3 shows the probability density function of contrail net RF, emphasizing that the majority of contrails within the 9 https://doi.org/10.5194/acp-2020-529 Preprint. Discussion started: 18 August 2020 c Author(s) 2020. CC BY 4.0 License.  present study causes a mean positive net RF. The scatterplot of net RF versus contrail lifetime for all contrails in Figure 4 shows that a negative net RF may only occur for contrails with lifetimes less than 10 hours independent of the weather situation. This 240 is due to the fact, that contrail RF may only be negative during daytime within a short timeframe (during and close to twighlight, Meerkötter et al. (1999)), and the longer a contrail lives, the higher is the probability, that a larger amount of its lifetime lies outside this timeframe. The scatter plot in Figure 5 shows the instantaneous net radiative forcing relative to the actual, local day-/night-time for all timesteps over the whole contrail lifetime for all time-regions for weather pattern W2. At night (net top solar radiation = 0, horizontally spread for better readability), contrails cause only positive net radiative forcing. During 245 twighlight and daytime with low incoming solar radiation (up to ∼500 Wm −2 ), the largest spread of net radiative forcing is found, which can be both positive and negative, resulting from positive longwave and negative shortwave RF of similar extent.
The strong shortwave cooling during twighlight is caused by the flat angle of incidence and a comparably longer way through the contrails and therefore higher reflective impact (Meerkötter et al., 1999).

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To enhance the spatial resolution of the contrail-cirrus CCFs, the contrail RF, which is initially available on the resolution of the time region grid (15 • ×5-20 • ), is masked with the information whether contrail-cirrus formation is possible at all (i.e. the potential contrail coverage), which is available at the finer spatial resolution of the EMAC model (∼2.8 • ×2.8 • ). Figure 6 shows the climate change functions of contrail-cirrus in terms of ATR20 for all weather situations exemplarily at 250 hPa for an emission time of 12 UTC. Contrail-cirrus CCFs for other pressure levels and times are shown in the supplementary material.   latitude of trajectories starting west of the high pressure ridge is close to the latitude of the emission. The ozone gain altitude 315 and time (Figure 9, mid and bottom) shows a main mode at 6 km and 10 days for trajectories starting in the high pressure ridge (red curve) and 7.5 km and ∼15 days for trajectories starting west of the ridge (blue curve), respectively. Note that the shape of the pdfs differs significantly. The air parcels starting in the high pressure ridge experience the ozone gain earlier and at lower altitudes than the air parcels starting west of the ridge, which experience ozone gain for a much longer period and at higher altitudes. As known from general meteorology, the transport pathways are controlled by the location of air parcels relative to 320 the Rossby waves, leading to transport into different chemical regimes, such as the tropical mid troposphere or the mid to high latitude lowermost stratosphere, which are characterised by a high or low chemical activity, respectively. In a companion paper  leads to a bi-modal distribution (15 • N and 35 • N) of the main ozone gain latitude, whereas in W1, which is characterized by 330 a strong zonal jet stream the pdf is unimodal and very narrow with a peak at 30 • N. This again emphasizes the importance of analyzing location and weather dependent aviation effects, and at the same time supports the potential of finding similarities  Similarities between the pattern of NO x -CCF and the weather pattern ( Figure 1) are found, with high positive values in the area of the jet stream and in the area of high pressure ridges, and low or even negative CCFs at high latitudes and in the area of low pressure troughs. The variability of the pattern is somewhat less pronounced than for O 3 . Total NO x effects show a minimum 340 at ∼250 hPa, increasing towards higher and lower altitudes, with a higher (more warming) impact in summer than in winter (see supplement).  in the lowermost stratosphere, where they have a longer residence time and thus a higher climate impact. In summer (S1, S2, 350 S3), the H 2 O-CCF is considerably smaller than in the winter weather patterns, because of a higher tropopause height, stronger convective overturning, and thus shorter H 2 O lifetimes. In general, the distance of the emission altitude to the actual tropopause largely controls the climate impact of H 2 O emissions, as will be discussed in Section 5. Generally, H 2 O CCFs increase with height, and are higher in winter than in summer (see supplement).

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In the previous sections we have shown that there exist large weather related differences of non-CO 2 aviation climate effects.
We could identify systematic weather related similarities. Regarding contrail-cirrus, we found enhanced potential coverage in areas where largescale lifting of air masses occurs. Close to the jet stream low potential coverage was observed. These general findings are supported by the study of Irvine et al. (2012), who analysed the distribution of ice-supersaturated regions (ISSRs) in similar weather situations within 20 years of ERA Interim Data (European Centre for Medium-Range Weather Forecasts 360 RE-analysis Interim Data, Dee et al. (2011)). The exact manifestation of potential contrail coverage varies with the characteristic features of the weather situation. In general, our findings correspond well with the potential contrail cirrus coverage simulated by Burkhardt et al. (2008), given that their numbers (17%-21%) for 230-275 hPa comprise only 30-60 • N. Regarding contrail lifetimes, our mean lifetimes of 3.5±5.3 h agree well with the estimates of Gierens and Vazquez-Navarro (2018), who determined the complete lifetime of persistent contrails to be 3.7±2.8 h by applying an automatic tracking algorithm 365 in combination with statistical methods to one year of Meteosat-SEVIRI data over Europe and the North-Atlantic. In their example, 80% of contrails had a lifetime smaller than 5 h and 5% lived longer than 10 h. Figure 12 compares the cumulative probability density function of lifetimes of both studies, illustrating that in the present study, a comparably larger fraction of contrails has lifetimes below 3 h. Nevertheless, both, the initial as well as the final stages of contrail lifetimes, had to be estimated by Gierens and Vazquez-Navarro (2018), as they could not be observed by satellite platforms. Ice water contents and 370 optical depths for contrails of the REACT4C study were already presented in Grewe et al. (2014a), and were found to compare well with other studies, e.g. Kärcher et al. (2009);Frömming et al. (2011);Voigt et al. (2011).
Whether the climate impact of contrails and contrail cirrus is warming or cooling in the respective situation is complex and involves detailed knowledge about e.g. contrail optical properties, contrail lifetimes, solar zenith angle, ambient cloud coverage and surface properties below the contrail (e.g. Schumann et al., 2012). In General, enhanced climate impact of contrail-cirrus 375 (irrespective if positive or negative) was detected south of the jet stream, in the vicinity of Greenland and in areas with strong meridional transport, whereas comparably low contrail-cirrus climate impact is found close to the jet stream.
Regarding O 3 -and total NO x -CCFs, we identified high positive values in the area of the jet stream and in the area of high pressure ridges, whereas low or even negative CCFs were found at high latitudes and in the area of low pressure systems.

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In general, the climate impact is higher in summer than in winter, because of reduced photochemistry due to missing sunlight in winter. These findings are in qualitative agreement with earlier climatological studies showing higher responses for NO x emissions at low latitudes and lower or even negative effects at high latitudes (e.g. Berntsen et al., 2005;Köhler et al., 2008;Grewe and Stenke, 2008;Köhler et al., 2013) and comparable seasonal effects (e.g. Gauss et al., 2006). A correlation between the climatological response of O 3 and CH 4 to NO x emissions has been shown in many studies (e.g. Lee et al.,  Figure 13 shows the O 3 -CCFs and the combined CH 4 -PMO-CCFs for all weather situations. A clear correlation is found, indicating that actual weather influences both effects in a similar way, with large or small positive values of O 3 -CCFs correlated with large or small negative CH 4 -and PMO-CCFs. However, the variability of the O 3 -CCFs (± 1.5 10 −12 K/kg(NO 2 ) is about a factor of 3 larger than the combined CH 4 /PMO variability (± 0.5 10 −12 K/kg(NO 2 ).

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The H 2 O-CCFs were also found to be closely related to the actual weather pattern. In regions with higher tropopause altitudes the emitted water vapour has a shorter atmospheric residence time and thus a lower climate impact, whereas in regions with lower tropopause height, the emitted water vapour has a longer residence time and a higher climate impact. In the summer situations, the H 2 O-CCFs are generally smaller than in winter because of enhanced convective activity (larger vertical mixing) and subsequent rainout of H 2 O and a generally higher tropopause height. Figure 14 shows the correlation of H 2 O-CCFs to the 395 emission altitude relative to the tropopause. The H 2 O emission from 1 kg fuel occuring below the tropopause, yields a warming of approximately 0.5·10 −15 K, whereas the same emission above the tropopause leads to a warming of around 1 to 3·10 −15 K.
In general, the distance of the emission altitude to the actual tropopause largely controls the climate impact of H 2 O emissions.
The higher the water vapour emissions are released (relative to the tropopause), the longer it takes until this water vapour enters the troposphere and will eventually be rained out, i.e. the longer is its residence time. These findings are supported by earlier 400 studies regarding the climate effect of water vapour emissions from aviation in a climatological sense (e.g. Grewe and Stenke, 2008;Fichter, 2009;Frömming et al., 2012;Wilcox et al., 2012).
Our findings are in agreement with earlier studies, which investigated the altitude and latitude dependency of annual mean or seasonal non-CO 2 aviation effects (e.g. Gauss et al., 2006;Köhler et al., 2008;Grewe and Stenke, 2008;Fichter, 2009;Frömming et al., 2012;Köhler et al., 2013). Furthermore, as far as comparable, our findings are also in qualitative agreement 405 with studies which investigated the avoidance of contrails (e.g. Mannstein et al., 2005;Sridhar et al., 2011;Chen et al., 2012;Figure 14. Correlation of water vapour climate change functions [K/kg(fuel)] with emission altitude difference relative to the actual tropopause. Pressure levels of the various emission altitudes are distinguished by different colours. A fit function is indicated by the red line. Irvine et al., 2014;Zou et al., 2016;Hartjes et al., 2016;Yin et al., 2018a), although the present study does not optimize trajectories but is only setting the scene. These previous studies indicated a strong reduction potential but were only valid for the actual situation and could not be transferred to other situations.

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The weather situations which were selected in our study occured in the months December to February and June and July.
Although our findings might be transferable to other seasons, future studies should look at special features, which might occur in other months. In the present study, we have explicitely excluded the direct and indirect climate impact of aviation aerosols.
The status of knowledge on indirect aerosol effects is not considered being mature enough to be included in such a study. This will be covered in future projects.

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It is essential to note that uncertainties are associated with individual climate change functions presented in this study. However, for the application of these data in terms of optimisation of flight trajectories not the exact value of climate impact is crucial, but the relation of the individual components and their spatial and temporal variability. A detailed study on the sensitivity of routing changes to uncertainties in the climate change functions had been performed by Grewe et al. (2014b), who found differences in the reduction potentials but similar optimal routes.

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The CCFs of the individual species show the sensitivity of the atmosphere to non-CO 2 aviation emissions. If flight trajectories were rerouted to reduce climate impact by avoiding the most sensitive regions, possible tradeoffs between individual species need to be considered. With the present study, these tradeoffs can be estimated in a consistent way as the effects of all species are represented by means of a consistent metric. For the first time, a comprehensive data set is available for various species, pressure levels, emission times and a multitude of weather situations. During optimization, the characteristic effects of all all CCFs are converted to K/kg(fuel). We multiply the contrail-cirrus CCF by a typical specific range value for transatlantic flights of 0.16 km/kg(fuel) (Graver and Rutherford (2018) and personal communication F. Linke, DLR). Similarly, the total NO x -CCF is converted using a typical emissions index of NO x of 13 g(NO 2 )/kg(fuel) (Penner et al., 1999). Figure 15 shows the merged CCFs of contrail-cirrus, total NO x and H 2 O exemplarily for weather situation W4 at 250 hPa and 12 UTC. When 430 comparing these merged CCFs to individual components reveals clearly, that contrail-cirrus and O 3 -CCFs are the dominating non-CO 2 effects. A hypothetical climate optimized transatlantic flight (which will stay on this pressure level for simplification) would certainly try to avoid the area with high positive CCFs in the eastern Atlantic between 30 and 40 • N, which is due to warming contrail-cirrus. Further this flight trajectory will probably find a compromise between avoiding long distances through enhanced climate warming areas and at the same time avoiding long detours as these would induce a penalty with respect to 435 CO 2 -CCF. However, situations are conceivable, where extensive areas with cooling contrails occur (similar to the negative CCF area in the central Atlantic), which flight trajectories might purposely seek during optimization to minimize their overall climate impact. We emphasize, that this is a very simplified example to illustrate the concept. The optimization of weather dependent flight trajectories with respect to minimum climate impact is much more complex. However, such an optimization goes clearly beyond the scope of the present study. Nonetheless, the data from the present study are a comprehensive and valuable basis for 440 weather dependent flight trajectory optimization with minimum climate impact. Some of the studies, based on the present data have already been published (e.g. Grewe et al., 2014b;Niklass et al., 2017;Yin et al., 2018b;Yamashita et al., 2019), others are in preparation.

Conclusions
The model configuration and methodology to generate spatially and temporally resolved information on the sensitivity of the atmosphere to local aviation emission, which has been employed in this research paper, is, to our knowledge, unique. We inves-460 tigated the influence of different weather situations on non-CO 2 aviation emissions' climate impact. Our results are 4D-climate change functions, which describe the climate impact of flown distance and local emissions of NO x and H 2 O, affecting contrailcirrus and the mixing ratios of the greenhouse gases O 3 , CH 4 and H 2 O. We studied the impact of local emissions for eight different representative weather situations and for three points in time per day, resolving the temporal evolution of the weather system. The main objective was to derive systematic relationships between aviation climate impact and prevailing weather 465 situation and emission location. For all non-CO 2 species included in the study, we found distinct weather related differences in their associated CCFs. We found an enhanced significance of the position of emission release in relation to high pressure systems, in relation to the jet stream, in relation to the altitude of the tropopause, and in relation to polar night. The results of this study represent a comprehensive dataset for studies aiming at weather dependent flight trajectory optimization reducing total climate impact. The dominating non-CO 2 effects were found to be contrail-cirrus and impacts induced by NO x emissions 470 on average, however, this might deviate temporally and regionally.
For an implementation of climate change functions in actual flight planning it would be necessary to accurately predict the sign and magnitude of individual CCFs for the actual weather situation. This can possibly be persued by means of more generic aC-CFs, which facilitate the prediction of CCFs by means of instantaneous meteorological data (e.g. Matthes et al., 2017). These aCCFs have to be verified and first verification results for the O 3 -aCCFs are promising (Yin et al., 2018b). However, to improve 475 the quality of these predictions, more knowledge has to be gained, particularly with repect to the transition of warming to cooling climate effects from contrail-cirrus and total NO x impacts. Further evaluation and quantitative estimates on uncertainties require additional comprehensive climate-chemistry simulations. Furthermore, better understanding of the tradeoffs between different effects (e.g. transport versus chemistry) or different species is essential. It might also be useful to focus on evaluating what might be the most promising regions to bypass, in other words, where total climate impact is highest and easiest to avoid 480 or at lowest additional cost. The main ozone gain latitude (φ j ) of an emission location (identified with the index j) is defined as the mean latitude at which the air parcel trajectories experience most of the ozone increase. Accordingly, the main ozone altitude and time are defined as the mean altitude and time at which the air parcel trajectories experience most of the ozone increase, respectively. In the following, we exemplarily define how the ozone gain latitude is derived, the other quantities are obtained by replacing latitude by altitude and time, respectively. The air parcel trajectories (identified with the index i) will contribute different shares to the 495 total ozone gain latitude. The ozone gain (O Gaini 3 (t)) along an air parcel trajectory is defined as the increase in O 3 from the previous to the current time step t (for a decrease in O 3 , the ozone gain is set to 0). The contribution A j,i of a single trajectory i to the latitude of the main ozone gain (=ozone gain latitude ) for the emission location j is given by where φ i (t) is the latitude of the trajectory i at time t. By taking the sum of the contributions A j,i of all trajectories i starting 500 at emission location j, the latitude of the main ozone gain is The weights (w j,i ) for each trajectory to the ozone gain latitude are calculated by combining Equation (A1) and (A2): A similar procedure is used to calculate the latitude of ozone gain for each single trajectory φ j,i : The main difference between φ j and φ j,i is the weighting of the latitude. For φ j,i the ozone gain of a single trajectory is taken into account, whereas for φ j the ozone gain of all trajectories started at the emission region j is taken into account.
Equation (A3) and (A4) define a data set containing the contribution and the latitudinal location of the main ozone gain for each trajectory. Based on these data a weighted probability density function (PDF) is derived in Eq. (A5). For a bin size of ∆φ, 510 a center φ of this bin, and n air parcel trajectories (i = 1, ..., n), which have their main ozone gain φ j,i in this bin, the PDF is: The sampling size of this PDF would be rather small, if only a single emission location was taken into account (50 trajectories).
In order to enhance the data basis, trajectories from various emission grid points are sampled for different meteorological features (High Pressure Ridge, West of High Pressure Ridge, and Near Jet Stream). In case 1 ("High Pressure Ridge"), the 515 maximum of the O 3 -CCFs is analyzed for W3 and W4 which are both in the region of a high pressure ridge. In case 2 ("West of High Pressure Ridge"), the same weather situations (W3 and W4) are analyzed, but the emission locations evaluated lie further west compared to the points of case 1. In this case, the O 3 -CCFs are significantly lower. In both cases the same emission latitudes are taken into account but different longitudes. The last case ("Near Jet Stream") considers the location of high O 3 -CCFs in the vicinity of the jet stream. For this case weather patterns W1, W4 and W5 are analyzed. A summary of all 520 emission locations taken into account is given in Table A1. Results are discussed in section 4.2.
Author contributions. CF, VG and SM designed the study. CF and PJ developed the relevant EMAC submodels with input from VG and SB. CF and SB performed the EMAC simulations. AH calculated the CCFs from the EMAC output with contributions from CF and VG. CF analysed the data with contributions from VG, SR, JVM. CF prepared the manuscript with contributions from all co-authors.
Competing interests. Author PJ is a member of the editorial board of the journal.