A multi-method assessment of the regional sensitivities between flight altitude and short-term O3 climate warming from aircraft NO x emissions

Flight altitude is relevant to the climate effects resulting from aircraft emissions. Other research has shown that flying higher within the troposphere leads to larger warming from O3 production. Aircraft NO x emissions are of particular interest, as they lead to warming via the short-term production of O3, but also to reduced warming via processes like CH4 depletion. We focus on short-term O3 production, as it constitutes one of aviation’s largest warming components. Understanding how O3 formation varies altitudinally throughout the upper troposphere/lower stratosphere is essential for designing climate-compatible aircraft and routing. We quantify this variation by performing simulations with a global atmospheric chemistry model for three representative cruise altitudes, five regions and two seasons using three methods: Eulerian tagging, perturbation and Lagrangian tagging. This multi-method, regional approach overcomes limitations of previous studies that utilize only one of these methods and apply global emission inventories biased towards present-day flight distributions, thus limiting their applicability to future aviation scenarios. Our results highlight that underrepresenting emissions in areas with growing flight activity (e.g. Asia Pacific) may lead to significant, regional underestimations of the altitudinal sensitivity of short-term NO x -related O3 warming effects in certain cases. We find that emitting in Southern regions, like Australasia, leads to warming larger by a factor of two when compared to global averages. Our findings also suggest that flying lower translates to lower warming from short-term O3 production and that this effect is strongest during the local summer. We estimate differences ranging from a factor of 1.2–2.6 between tagging and perturbation results that are attributable to non-linearities of NO x -O3 chemistry, and derived regional correction factors for a widely-used sub-model. Overall, we stress that a combination of all three methods is necessary for a robust assessment of aviation climate effects as they address fundamentally different questions.


Introduction
Aircraft emissions trigger a radiative imbalance in Earth's energy budget that leads to both warming and cooling effects.These stem from carbon dioxide (CO 2 ) and non-CO 2 emissions, with the latter accounting for almost 70% of aviation's total effective radiative forcing (RF).Jointly, they equate to ∼4% of anthropogenic global warming (Kärcher 2018, Grewe et al 2019, Lee et al 2021).The aviation industry's recovery to near pre-pandemic levels (Boeing 2023) is a strong indication that this share will likely increase if mitigation measures are not implemented in time (Lee et al 2009).Here, we focus on nitrogen oxide (NO x ) emissions given their potential to instigate one of aviation's largest warming effects via short-term, indirect ozone (O 3 ) formation, a process that bears large uncertainty across NO x -related processes (Lee et al 2021).Furthermore, NO x emissions can degrade air quality (Yim et al 2015, Quadros et al 2020) and are projected to outpace the growth in fuel consumption, making them a pressing concern, especially as they cannot be effectively mitigated even with the use of sustainable aviation fuels (Hamilton 2019).More efficient engine technologies also fall short in this regard as they often equate to larger pressure ratios and turbine inlet temperatures that reduce CO 2 , but at the cost of increasing NO x (Miller et al 2022, Quadros et al 2022a).
Varying the flight altitude, however, is an operationally feasible mitigation option for the near-term.Research has shown that flying lower within the upper troposphere and lower stratosphere (UTLS≡ here referring to altitudes between 9-12 km) leads, overall, to smaller non-CO 2 climate effects (Grewe et al 2002, Fichter et al 2005, Frömming et al 2012, Matthes et al 2021).Several of these studies, however, are limited, since their emission inventories were based on flight patterns from the early 2000s, when routes in the North American and European airspace represented roughly 80% of all air traffic (Gauss et al 2006, Skowron et al 2013, Søvde et al 2014, Matthes et al 2021).These analyses thus underrepresent spatial sensitivities of NO x -O 3 climate effects in regions that are projected to grow in terms of air traffic, like Asia Pacific, thereby limiting their applicability to future aviation scenarios given aviation's spatially heterogeneous growth (Gössling and Humpe 2020, Airbus 2023).
To quantify such regional sensitivities to aviationinduced short-term NO x -O 3 impacts, two main calculation methods are available: source apportionment (tagging) and sensitivity analysis (perturbation).The former estimates the contribution of different sources to a total pollutant concentration by labeling pertinent chemical species and tracking them across relevant reaction pathways, thereby guaranteeing a closed budget.The latter, on the other hand, is not additive and calculates the impact from an emission change using two simulations: one with a particular emission and another without (Grewe et al 2010, 2019, Grewe 2013, Mertens et al 2018, Thunis et al 2019).Here, we perform source apportionment via a tagging approach (Wang et al 2009, Grewe et al 2017, Rieger et al 2018) and conduct a sensitivity analysis (Blanchard 1999) via a perturbation method.If the relationship between emission and concentration is linear, then both methods yield identical results (Grewe et al 2010, Clappier et al 2017).Given the strong non-linearity of NO x -O 3 chemistry (Cohan et al 2005, Grewe et al 2012), large differences ranging from a factor of 2-5 have been previously reported (Emmons et al 2012, Grewe et al 2012, 2019, Kranenburg et al 2013, Mertens et al 2018, Thunis et al 2019, Dedoussi et al 2020).These differences highlight each method's suitability to address distinct research questions.Tagging addresses 'what is a sector's contribution towards O 3 ?' while perturbation addresses 'what is the marginal impact of a sector on O 3 if its NO x emissions are changed?' .Both questions should be addressed concurrently when assessing mitigation options for aviation's climate impact as it is insufficient to quantify a sector's contribution to total O 3 (tagging) without also gauging the impact of an emissions reduction (perturbation).
In this study, we use the ECHAM/ Modular Earth Sub-model System Cycle (MESSy) Atmospheric Chemistry (EMAC) model to compute the shortterm O 3 produced from aviation NO x for both methods.We run Eulerian and Lagrangian simulations, where the former calculates physical processes on an Earth-fixed frame and the latter along trajectories of advected air parcels (Brasseur and Jacob 2017).The computational cost of conducting the high-fidelity Eulerian tagging simulations increases significantly when having to analyze multiple emission scenarios.A more efficient approach to tagging is provided by the reduced-order Lagrangian sub-model AIRTRAC (supplement to Grewe et al 2014), which has been used to create the climate change functions (CCFs) (Grewe et al 2014, Frömming et al 2021) that estimate the climate impact of a local emission.With the upcoming requirement imposed by the European Union to include non-CO 2 effects in the monitoring, reporting and verifying initiative (MRV) (Scheelhaase et al 2024), AIRTRAC-derived CCFs could become an integral part of this reporting workflow.AIRTRAC is, however, limited by its simplified and linearized chemistry scheme, which is why we calculate correction factors to improve its accuracy.
This article has three main objectives: firstly, to understand how short-term NO x -induced O 3 production from aviation and consequent RF vary geographically, altitudinally and seasonally, especially when compared to studies that assume present-day flight traffic distributions.Secondly, to quantify the differences between tagging and perturbation, which address distinct questions.We lastly compare the linearized Lagrangian tagging sub-model AIRTRAC with the non-linear TAGGING sub-model (Grewe et al 2017, Rieger et al 2018) to derive regional correction factors that can leverage AIRTRAC's computational efficiency for decision-making applications.

Methodology
We perform all simulations with the EMAC model (MESSy version 2.55.2) using three approaches: Eulerian tagging, perturbation and Lagrangian tagging.Overall, 74 simulations are run, totaling approximately 218 000 CPU hours.Altogether, these simulations currently form one of the most extensive datasets to assess short-term climate warming effects from aviation NO x -induced O 3 .The full dataset is openly available (Maruhashi et al 2023).Newtonian relaxation is used to nudge the sea surface temperature, the wind divergence, the vorticity and the logarithm of the sea-level pressure towards ERA-Interim reanalysis data corresponding to the simulation year.Lastly, all three methods have a common limitation: plume-scale chemical processes are disregarded, leading to a possible overestimation of the short-term O 3 impact by about 20%-30% (Meijer et al 1997, Kraabøl and Stordal 2000, Cameron et al 2013, Fritz et al 2020).

NO x emissions
A pulse emission of 5 × 10 5 kg of nitric oxide (NO) 3 is introduced at 0600 UTC within a 15 min interval at each of the 28 points per region across five regions (North America, Eurasia, South America, Africa and Australasia) and three pressure altitudes (200, 250 and 300 hPa) on 1 January and July 2014.This NO emission per point represents on average ∼40% of total annual NO emissions by commercial aircraft flying over North America (Maruhashi et al 2022, Quadros et al 2022b).Each simulation tracks the production of O 3 from NO emitted on one of these two days for three months.The coordinates of all emission points (28 points × 5 regions × 3 altitudes = 420) are displayed in figure 1 (see section S1.1 of the supplement for exact coordinates).An overview of the methodology is provided in figure 2.
3 Amount chosen for comparability with Grewe et al (2014)

Eulerian simulations
The Eulerian tagging method applies the TAGGING sub-model, which has been improved for this study by reducing the signal-to-noise ratio for small emissions (section S2 of the supplement).A set of 30 simulations based on the coordinates in figure 1 were performed, with an additional 12 simulations to assess the altitudinal variability of the O 3 production efficiency in North America for different NO emission amounts in July (section S3 of the supplement).The simulation setup resembles that of Jöckel et al (2016).
TAGGING is unable to independently consider multiple emission scenarios in parallel within one simulation since the chemical interaction between neighboring emissions is non-zero.Instead, due to computational constraints, each Eulerian simulation simultaneously emits NO at the 28 emission points per region.In doing so, however, we introduce interaction effects between emissions.The O 3 production efficiency from each Eulerian simulation, O Eul 3,Net , is normalized by the emission amount of 28 × 5 × 10 5 kg (NO).
This scaled mean Eulerian net O 3 production, O Eul 3,Net (equation ( 1)), includes seven production, five loss and one interaction term, which represents the non-linearity arising from interactions between emissions and saturation effects, O 3,Int (not explicitly part of the model output).The source-specific factor γ represents one of the main differences between tagging and perturbation as the former will scale the non-linear effects according to the mass contribution of each emission category (Clappier et (1) The perturbation method is applied also using an Eulerian reference frame.The net O 3 produced using this approach is the difference between two simulations: 1. NO is simultaneously emitted at 28 points in figure 1  The net O 3 production, O Pert 3,Net , is given by equation ( 2), where a disturbance of δNO per emission point is introduced in the perturbed simulation that reflects the full chemical processes of EMAC.The result is normalized by the NO disturbance 28 × 5 × 10 5 kg (NO): We again acknowledge the existence of the interaction term O 3,Int , however, unlike tagging, it attributes all non-linearities to the source from which the emission change is assumed to emanate, ergo γ = 1.

Lagrangian simulations
Lagrangian simulations are performed via a setup nearly identical to the one in Maruhashi et al (2022).AIRTRAC computes O 3 contributions from aviation NO x emissions along air parcel trajectories via a tagging approach.An advantage of this sub-model is the possibility to simultaneously consider 28 emission scenarios in parallel within a single simulation, since there is no chemical interaction with neighboring NO x emissions.This therefore makes it the most computationally efficient approach.It also allows for greater ease in the quantification of NO x -O 3 uncertainties as more independent scenarios may be studied.As a shortcoming, however, the linearized reaction rates in AIRTRAC (constant O 3 production efficiency) and its simplified chemistry mechanism (fewer chemical processes tracked) are likely to provide less accurate estimates for the highly nonlinear NO x -O 3 chemistry.AIRTRAC uses only one production term from nitrogen compounds, P O3N , and two loss terms: L O3N (loss from nitrogen compounds) and L O3Y (loss from non-nitrogen compounds) for each emission point.These are then averaged across the 28 emission points and normalized by the emitted NO ( 5 (3) To determine the contribution of the NO emission to atmospheric concentrations of active nitrogen species (NO y ), AIRTRAC scales the production and loss terms from relevant background species (e.g.HO 2 ) according to volume mixing ratio fractions computed by the tagging methodology of Grewe et al (2010), see section S4 of the supplement.

Method comparison metrics
To compare O 3 production efficiencies (i.e.emissionscaled O 3 production) across methods, the area ratios of their respective O 3 production efficiency curves as a function of time (i.e.O 3 curves) are evaluated.A M1,M2 (equation ( 4)), is defined in terms of two integrals: one for method 1 (M 1 ) and another for method 2 (M 2 ) being compared.M 1 and M 2 can correspond to Lagrangian tagging (Lg), Eulerian tagging (Eul), or the perturbation approach (Pert).The integration bounds encompass the full simulation period T of ∼90 days.We refer to A Lg,Eul as correction factors, We follow the RF definition of Maruhashi et al (2022), where it is expressed as the change in the net instantaneous long-and shortwave radiative fluxes from a pulse emission.Additionally, we scale down our RF estimates by a factor of 4 to make our estimate from a three-month pulse emission comparable to annual values from literature.
In all simulations, RF is computed online by the RAD sub-model and subsequently mapped to the climatological tropopause by the VISO sub-model (Jöckel et al 2010).To obtain a point estimate per scenario, we compute area-weighted medians, as they are unaffected by extreme values, thereby making them a more robust indicator.We additionally compute area-and time-averaged means (calculation method in section S5 of the supplement).To visualize the spread of the RF time series, we compute kernel density estimators (KDEs) for all cases (section S6 of the supplement).

Comparison of O 3 production between methods
We first compare the O 3 production efficiency between the Eulerian tagging and perturbation methods.Figure 3(a) displays the case when NO is emitted at 300 hPa in North America during January.The former method (blue curve) leads to larger O 3 production when compared to the latter (orange curve).According to table 1, the Eulerian tagging estimates for this case are larger than the perturbation by a factor of 1.48.Across all simulations (see sections S7 and S8 of the supplement for all O 3 curves), we also find that Eulerian tagging is larger by a factor of A Eul,Pert ranging from 1.16 to 2.55 with a mean of 1.83.This is consistent with past studies, where differences ranging from a factor of 2 to 5 were reported for road traffic and shipping (Grewe et al 2012, Mertens et al 2018) and around 1.6 for short-term aviation O 3 effects (Dahlmann et al 2011, Grewe et al 2019).The tagging method, however, will not always overestimate relative to the perturbation approach, ] as estimated by the Lagrangian tagging (green), Eulerian tagging (blue) and perturbation (orange) methods for NO emitted at 300 hPa in January.The AIRTRAC and TAGGING sub-models were applied for the Lagrangian and Eulerian tagging methods, respectively.No specific sub-model is required for the perturbation method.The shaded green area represents the range of Lagrangian O3 estimates for 28 independent emission scenarios based on the coordinates shown in figure 1.The green curve is the average of these 28 scenarios.The dotted gray line denotes the range of O3 estimates (13.75 days after emission) obtained by Grewe et al (2014) using AIRTRAC to also study 5 × 10 5 kg of NO released at 200, 250, 300 and 400 hPa during 06h00, 12h00 and 18h00 UTC in January.The gray 'X' marks the mean value.(b) Application of the correction factor A Lg,Eul = 4.6 from table 1 to the same emission scenario shown in (a).The green curve is the original O3 estimated by the Lagrangian tagging curve, the purple curve is the corrected green curve and the blue curve is from the Eulerian tagging method.
Table 1.Calculation of the ratio of O3 curve areas for the tagging and perturbation methods for all emission altitudes (200, 250 and 300 hPa), regions (NA = North America, SA = South America, EU = Eurasia, AF = Africa and AU = Australasia) and emission days (1 January and July 2014).Area ratios A Lg,Eul and A Eul,Pert refer to the application of equation ( 4) to the different methods (Lg = Lagrangian Tagging, Eul = Eulerian Tagging and Pert = Perturbation).

Emission on 1 January 2014
Emission on 1 July 2014 Differences between Lagrangian and Eulerian tagging sub-models, are however, mainly attributable to AIRTRAC's simplifications.The green shaded area indicates the range of O 3 estimates from 28 independent emission scenarios considered by the Lagrangian approach, contrasting with only one scenario of the Eulerian alternative.Likely, the difference by a factor of 4.6 between the areas of the green and blue O 3 curves in figure 3(a) arises from the lack of chemical interaction between Lagrangian air parcels (O 3,Int = 0), simplified chemistry and AIRTRAC's linearized reaction rates that translate to constant O 3 production efficiencies.Unlike the Eulerian tagging and perturbation methods, where O 3 production efficiencies vary with the amount of emitted NO, AIRTRAC's O 3 production efficiency is invariant to emission strength (i.e.amount emitted, see section S3 of supplement).This equates to discarding shifts in the local NO x regime from varying the amount of NO emitted as there is no feedback between emission and background.However, to leverage the computational efficiency of AIRTRAC despite these simplifications, we derive correction factors A Lg,Eul in table 1. Figure 3(b) illustrates the application of a correction factor (A Lg,Eul = 4.6) for the scenario of figure 3(a), where the corrected Lagrangian curve (purple) now more closely resembles the Eulerian tagging curve (blue).More simulations would be required, however, to capture O 3 behavior in other aviation emission scenarios considered in Grewe et al (2014), as is indicated by the gray line in figure 3(a).

Altitudinal variation of short-term RF from aviation NO x -O 3 interactions
The variation between short-term O 3 median RF from aviation NO x with emission altitude for all three methods is presented in figure 4. For the Eulerian tagging and perturbation methods, emitting at higher altitudes always leads to a larger median RF per Tg (N).The Lagrangian tagging method also largely predicts a similar relation, but displays some cases of inversions, e.g. in North America the RF is largest at 250 hPa.Frömming et al (2021) also report a nonmonotonic relation with altitude for aviation's net NO x warming effect using AIRTRAC while Matthes et al (2021), via a multi-model approach involving EMAC, also found a non-monotonic relation for lower altitudes (∼300 hPa).One of the inversions in figure 4(a), for instance, may be explained by larger O 3 production efficiency maxima occurring at 250 hPa during January for North America (see figure S7.1(b) in the supplement).The predominant trend, however, is to witness warming effects from aircraft NO x emissions increase with altitude within the troposphere, as there is a more efficient accumulation of NO at higher altitudes from fewer removal processes (Grewe et al 2002, Köhler et al 2008, Frömming et al 2012, Matthes et al 2021).
We note significant regional and seasonal variations in the estimated RF.During January, figure 4(a) presents larger values in the southern hemisphere (SA, AF and AU) while in July (figure 4(b)), warming in NA and EU increases, but decreases for the remaining three southern regions.Such a seasonal shift occurs from the strong photochemical dependence of O 3 production (Stevenson et al 2004, Gauss et al 2006, Frömming et al 2021, Maruhashi et al 2022).Seasonality also significantly impacts the altitudinal sensitivity of O 3 RF.Flying higher in Eurasia during January from 250 to 200 hPa leads to an increase in short-term O 3 warming by ∼20% according to the Eulerian tagging approach (figure 4(a)).In July, the same altitudinal shift would lead to an increase of 50% (figure 4(b)).This suggests that altitudinal measures for the short-term mitigation of NO x -O 3 impacts are most effective during the local summer.Across all methods, Australasia generates the largest RF for a January emission (as is also seen by the wider spread of the RF KDEs in section 6 of the supplement), which is explained by the lower background NO concentrations in its vicinity (Gilmore et al 2013, Skowron et al 2015, Maruhashi et al 2022).
Comparing our RF perturbation estimates in figure 4 with Lee et al (2021) reveals regional differences, particularly for low-altitude emissions in North America and Eurasia.For a January emission at 300 hPa in North America (figure 4(a)), for example, our RF value is smaller by a factor of 3 relative to their lower bound estimate of 16 (mW m −2 )/Tg (N).When juxtaposed with Eulerian tagging estimates by Matthes et al (2021), our Eulerian tagging results from July emissions (figure 4(b)) compare well, albeit with larger discrepancies observed at the highest emission altitude.Even larger differences of a factor of 2 emerge when comparing our Eulerian tagging estimates with Matthes et al (2021) for January in Southern regions (SA and AU).Our study therefore underscores that estimates based on global emission inventories, if used to evaluate the effects of increasing emissions in underrepresented regions, could overor underestimate aviation NO x -O 3 warming impacts depending on the region and method.A robust, global assessment of aviation's evolving non-CO 2 effects should take into account the dynamic shift in air traffic distribution given the heterogeneity in regional NO x -O 3 responses.
These disparities also bring to light the large uncertainties surrounding aviation NO x -O 3 effects that arise from distinct methods and may increase further from adopting additional model types like chemical-transport models (CTMs) or climateresponse models (CRMs) (Cameron et al 2017).Comparison with our mean RF values leads to similar conclusions (section S9 of supplement).Relative to our tagging estimates, we lastly note that TAGGING consistently exhibits larger RF in Pacific regions when compared to AIRTRAC, which may explain some magnitude differences in figure 4.During a northern emission in January for instance, TAGGING estimates larger warming in the southern Pacific relative to AIRTRAC (figures S10.1(d)-(f) and (j)-(l) of the supplement), leading to smaller differences between their RF estimates for NA and EU in figure 4(a).
Figure 4 should also be interpreted in terms of the distinct research questions that the tagging and perturbation approaches address.Eulerian tagging is represented by the black line and indicates aviation's sectoral contribution to the overall O 3 budget and how this varies with altitude, region and season.In figure 4(b), for instance, flying higher from 250 to 200 hPa in Eurasia could lead to a strong increase in aviation's contribution to total O 3 via an increase in its short-term O 3 production, assuming the amount emitted by other sectors is unchanged.In contrast, perturbation (shown in blue) investigates the impact on RF that would result at each corresponding scenario if aviation emissions were regionally increased by 28 × 0.5 Gg.A discussion of how to combine these two methods is found in Mertens et al (2018).Annualized, area-weighted median radiative forcing point estimates (section S5 of supplement for calculation method) from short-term NOx-induced O3 for emission altitudes of 300 hPa (∼9.2 km), 250 hPa (∼10.4 km) and 200 hPa (∼11.8 km) across all five regions (North America (NA), South America (SA), Eurasia (EU), Africa (AF) and Australasia (AU)) during (a) 1 January and (b) 1 July of 2014.The solid gray line represents the corresponding mean RF estimate for short-term O3 effects from Lee et al (2021) using a perturbation approach.The dotted gray lines demarcate the 90% confidence interval of the same study, where the 5% lower limit is 16 and the 95% upper limit is 39 mW m −2 .The purple triangles depict the tagging estimates in mWm −2 of Matthes et al (2021), who calculated 43 for a base flight altitude (equated to our 250 hPa), 46 for a flying higher and 40 for a flying lower scenario, which were compared to our 200 and 300 hPa estimates, respectively.For clarity, these values are not labeled above.All RF estimates presented in (a) and (b) have been scaled to represent the equivalent value of a 1 Tg of nitrogen (N) emission.

Summary and conclusions
The variation between aircraft NO x emission altitude and short-term climate warming from O 3 production has been assessed using three methods (Eulerian tagging, perturbation and Lagrangian tagging), all within the framework of the EMAC model.We performed 74 simulations across five regions and three altitudes during the summer and winter seasons to account for seasonal and regional differences.This study does not include NO x terms that lead to a reduced warming, which, when combined with the short-term O 3 warming component, may lead to a negative net-NO x forcing (Holmes et al 2011, Terrenoire et al 2022).
In the process, differences between estimates from these approaches were discussed, in the context of the questions that they can be used to answer, and a set of correction factors A Lg,Eul (table 1) was calculated for the widely-used Lagrangian AIRTRAC sub-model (used in e.g.CCFs (Grewe et al 2014, Frömming et al 2021)) that may be useful for Europe's new MRV initiative.
Our results regarding the altitudinal relationship of aircraft climate effects from short-term NO x -O 3 interactions only partly confirm past studies, which conducted their analyses based on emission inventories that are influenced by more numerous flights in the Northern Trans-Atlantic.Their approach may still significantly underestimate the altitudinal sensitivity of RF for Southern regions, like Australasia, particularly for emissions in January.We have, however, verified that the proportional relationship between O 3 RF and altitude holds regionally for all five regions during both seasons according to the Eulerian tagging and perturbation approaches.A few exceptions were found for the Lagrangian method, but certain non-monotonic trends have also been found in earlier studies (Frömming et al 2021, Matthes et al 2021).We have also found that the change in short-term O 3 RF with altitude is more impactful when flying higher (or lower) during the season in which greater solar radiation is available.
Differences between the Eulerian tagging and perturbation approaches range from a factor of 1.16 to 2.55 with a mean of 1.83 for the O 3 mass curves.These estimates agree well with the range of 2-5 provided by literature (Emmons et al 2012, Grewe et al 2012, 2019, Kranenburg et al 2013, Mertens et al 2018, Thunis et al 2019, Dedoussi et al 2020, Matthes et al 2021).The Lagrangian tagging sub-model exhibits larger differences likely due to a combination of reasons: the lack of inter-parcel chemical interaction effects, the relatively simplified chemistry scheme and the linearization of the NO x -O 3 response.To correct for these shortcomings, we compute and provide correction factors.
Although O 3 mass estimates from tagging and perturbation methods can differ by almost a factor of 3, both should still be considered in tandem for a comprehensive assessment of aviation climate effects, given that they address distinct questions.Each of the three methods presented here can play a unique role in the mitigation decision-making process.Tagging identifies mitigation opportunities by determining the share of each sector to the total O 3 budget.The perturbation method may be applied to evaluate an emissions reduction measure of a certain sector.Lastly, the corrected Lagrangian tagging method can help us efficiently gauge the uncertainty levels in these estimates by providing more data for more scenarios and better understand transport-related phenomena (Maruhashi et al 2022).When addressing technological, operational or regulatory decisions, these methods would provide valuable, complementary insights.

Figure 2 .
Figure 2.Summary of features across calculation methods (tagging and perturbation), questions addressed by each method, reference frames (Eulerian and Lagrangian) and comparison metrics (x area ratios of O3 production efficiency curves and y RF median (RF mean in supplement)).

Figure 3 .
Figure 3. Normalized NOx-induced O3 production in North America.(a) Comparison between emission-scaled O3 mass curves [kg(O3)/kg(NO)] as estimated by the Lagrangian tagging (green), Eulerian tagging (blue) and perturbation (orange) methods for NO emitted at 300 hPa in January.The AIRTRAC and TAGGING sub-models were applied for the Lagrangian and Eulerian tagging methods, respectively.No specific sub-model is required for the perturbation method.The shaded green area represents the range of Lagrangian O3 estimates for 28 independent emission scenarios based on the coordinates shown in figure1.The green curve is the average of these 28 scenarios.The dotted gray line denotes the range of O3 estimates (13.75 days after emission) obtained by Grewe et al (2014) using AIRTRAC to also study 5 × 10 5 kg of NO released at 200, 250, 300 and 400 hPa during 06h00, 12h00 and 18h00 UTC in January.The gray 'X' marks the mean value.(b) Application of the correction factor A Lg,Eul = 4.6 from table 1 to the same emission scenario shown in (a).The green curve is the original O3 estimated by the Lagrangian tagging curve, the purple curve is the corrected green curve and the blue curve is from the Eulerian tagging method.

Figure 4 .
Figure 4. Annualized, area-weighted median radiative forcing point estimates (section S5 of supplement for calculation method) from short-term NOx-induced O3 for emission altitudes of 300 hPa (∼9.2 km), 250 hPa (∼10.4 km) and 200 hPa (∼11.8 km) across all five regions (North America (NA), South America (SA), Eurasia (EU), Africa (AF) and Australasia (AU)) during (a) 1 January and (b) 1 July of 2014.The solid gray line represents the corresponding mean RF estimate for short-term O3 effects from Lee et al (2021) using a perturbation approach.The dotted gray lines demarcate the 90% confidence interval of the same study, where the 5% lower limit is 16 and the 95% upper limit is 39 mW m −2 .The purple triangles depict the tagging estimates in mWm −2 of Matthes et al (2021), who calculated 43 for a base flight altitude (equated to our 250 hPa), 46 for a flying higher and 40 for a flying lower scenario, which were compared to our 200 and 300 hPa estimates, respectively.For clarity, these values are not labeled above.All RF estimates presented in (a) and (b) have been scaled to represent the equivalent value of a 1 Tg of nitrogen (N) emission.
al 2017, Matthes et al 2021).Further details in section S2 of the supplement.