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Greater fuel efficiency is potentially preferable to reducing NOx emissions for aviation’s climate impacts


Aviation emissions of nitrogen oxides (NOx) alter the composition of the atmosphere, perturbing the greenhouse gases ozone and methane, resulting in positive and negative radiative forcing effects, respectively. In 1981, the International Civil Aviation Organization adopted a first certification standard for the regulation of aircraft engine NOx emissions with subsequent increases in stringency in 1992, 1998, 2004 and 2010 to offset the growth of the environmental impact of air transport, the main motivation being to improve local air quality with the assumed co-benefit of reducing NOx emissions at altitude and therefore their climate impacts. Increased stringency is an ongoing topic of discussion and more stringent standards are usually associated with their beneficial environmental impact. Here we show that this is not necessarily the right direction with respect to reducing the climate impacts of aviation (as opposed to local air quality impacts) because of the tradeoff effects between reducing NOx emissions and increased fuel usage, along with a revised understanding of the radiative forcing effects of methane. Moreover, the predicted lower surface air pollution levels in the future will be beneficial for reducing the climate impact of aviation NOx emissions. Thus, further efforts leading to greater fuel efficiency, and therefore lower CO2 emissions, may be preferable to reducing NOx emissions in terms of aviation’s climate impacts.


Emission standards for aircraft NOx are set by the Committee on Aviation Environmental Protection of the International Civil Aviation Organisation (ICAO-CAEP). In the past, aircraft NOx emissions standards have been set to protect local air quality and have been assumed to have co-benefits for climate protection, as aircraft NOx results in an overall warming effect at present1,2. Emissions of NOx, whether from aviation or other sources, result in the short-term formation of ozone (O3) (a warming) and the long-term destruction, via hydroxyl (OH) production, of small amounts (~a few percent) of ambient methane (CH4) (a cooling)1. In addition, the methane reduction results in a long-term reduction in O3 (cooling)3 and a long-term reduction in H2O in the stratosphere (cooling) from reduced oxidation of methane4. The net balance of these components ranges from positive for aviation NOx, to negative for shipping and surface NOx4,5,6.

The general scientific advice given to the ICAO-CAEP to date has been to reduce emissions of both NOx and CO2. However, reducing both is problematic because of a technological trade-off between aviation NOx and CO27,8,9. Furthermore, one has to be very careful trading short-lived climate forcers against long-lived greenhouse gases, e.g. the reduction of NOx emissions might result in a fuel penalty that in fact can lead to a net climate disbenefit10. Here, we present a new analysis of future aviation emission scenarios and the balance of NOx from surface and aircraft sources, that makes this recommendation uncertain in terms of climate benefits and we suggest that the scientific evidence for reducing aircraft NOx needs to be revisited.

At subsonic aircraft cruise altitudes of 8–12 km, the atmosphere is sensitive to aircraft NOx emissions where O3 production is four times more efficient than near the ground11 and the aviation net NOx effect also depends on the state of the atmosphere into which NOx is emitted12. Changes in emissions of any surface source that take place as a result of various air quality and climate policies may have impacts on background conditions, and consequently might have an impact on the climate effect of aviation NOx emissions, which is not independent of background conditions. The changes in the tropospheric composition and global radiative forcing (RF) for various scenarios of anthropogenic O3 precursor emissions have been widely explored13,14,15. However, the impact of changing surface emissions on aircraft NOx climate effects has been virtually left out of discussions and sensitivity experiments can only be found in one study3. This present study aims to fill this gap and start the discussion on how future anthropogenic background emissions can affect the aviation climate impact.

Using a suitable three-dimensional chemistry transport model (CTM) of the global atmosphere (MOZART3)16,17, we examine the changes in the tropospheric composition and the net RF from aviation NOx emissions for 30% reductions in the most recent present-day inventories available (2006) of O3 precursor emissions (NOx, carbon monoxide - CO, non-methane volatile organic compounds - NMVOC) and for a future (2050) range of Representative Concentration Pathways (RCP) scenarios together with ICAO-CAEP aviation emission projections (see Methods for details of models used and simulations). These simulations allow an analysis of the relative benefits to reducing aviation impacts from reducing aviation and background NOx emissions.


Aviation net NOx radiative forcing in 2050

The resulting RFs (Table 1) highlight that an aviation net NOx RF can vary greatly depending on the background condition, and both anthropogenic surface and aircraft emissions affect the aviation net NOx RF. At present, all scenarios predict increased aircraft NOx emissions in the year 2050 that reach 2.17 Tg(N) year-1 for the low air-traffic growth and optimistic technology development and 5.59 Tg(N) year-1 for high air-traffic growth and low technology development: which compared with the year 2006, 0.71 Tg(N) year-1, are significant increases. In contrast, reductions of surface O3 precursor emissions are projected under each of the applied RCP scenarios for the year 2050, for which the cleanest background is predicted under RCP 2.6. The total aircraft net NOx RF in 2006 is 3.5 mW m-2 and it increases to between 5.8 and 12.5 mW m−2 in 2050 for low- and high-growth scenarios, respectively; within each RCP scenario, the net aviation NOx RF can differ by ~23%, depending on background conditions. The largest aviation net NOx RF is observed under RCP 8.5 and the smallest for RCP 2.6 (for equal aviation NOx emissions). This significant increase in the aviation net NOx RF for 2050 is driven mainly by an intense rise of aviation NOx emissions; however, reduced surface emissions resulting in a cleaner background atmosphere in the year 2050 to some extent mitigates the aviation impact (Fig. 1). For instance, if the anthropogenic surface emissions were kept constant at present levels, the 2050 aircraft net NOx RF of the high air-traffic growth would be 17.5 mW m−2, that is 48% greater than under the 2050 RCP 2.6 and 28% greater than under 2050 RCP 8.5 background conditions.

Table 1 Aircraft NOx radiative forcing (RF, mW m−2) for different background and aircraft emission scenarios in 2006 and 2050. Net NOx RF is a sum of a short-term O3 (sO3), CH4, CH4-induced O3 (lO3) and SWV.
Fig. 1: Net NOx radiative forcing by emission rate, original CH4 parameterisation.
figure 1

Aviation net NOx radiative forcing (RF) (the sum of the short-term positive O3 RF perturbation and the negative RF terms caused by a reduction in CH4 lifetime, see Methods), by aviation NOx emission rate according to a range of background emission scenarios, utilising the IPCC Fifth Assessment Report59 simplified expression for the calculation of CH4 forcing. Aviation net NOx RF systematically increases with increasing NOx emissions from aviation, showing a variation according to the background surface emissions, with high mitigation (RCP 2.6) having a smaller aviation net NOx RF than, lower mitigation scenarios (RCP 4.5, RCP 8.5) for the same aviation NOx emission. Overall uncertainties are indicated by the grey shading, which is one standard deviation (68% confidence interval) from the ensemble of 20 NOx studies presented in Supplementary Fig. 1.

This observed increase of aviation net NOx RFs in the future is in agreement with other studies that have explored the climate impact from aviation NOx emissions in 2050. Global CTMs and chemistry-climate models (CCMs) using 2050 aviation emissions derived from the Aviation Environmental Design Tool (AEDT) and the RCP 4.5 background scenario have been employed18,19,20. Unger et al.19 calculated that both the positive short-term O3 and negative CH4 RFs in 2050 increased by ~80% for the AEDT Base scenario (4.0 Tg(N) year−1), whereas Khodayari et al.20 estimated the 2050 short-term O3 RF to be 48–75% greater than in 2006, and the 2050 CH4 RF increased by 57–80%. From these studies, the available 2050 short-term O3 RF ranged from 30 to 162 mW m−2 and the CH4 RF varied from −36 to −72 mW m−2 (all estimates are for AEDT-Base and RCP 4.5 scenarios)18,21. The 90.7 and −48.6 mW m−2 calculated in this study with the RCP 4.5 background emissions are in line with estimates found in the literature. The existing spread in the calculated aviation NOx-induced effects is the result of both differences in the projections of aircraft emissions and the inter-model differences. The latter difference raises an important level of uncertainty3, for which the differences in model chemistry schemes and the treatment of physical processes play an important role. Also, due to the inclusion of more feedback processes and coupled interactions (particularly aerosol and cloud coupling processes), different responses between the offline models (CTMs) and the fully coupled models (CCMs) can be observed18. However, based on the reported net NOx RFs available in the literature any systematic differences between CTMs and CCMs cannot be identified (Supplementary Fig. 1 and Supplementary Note 2).

The impact of surface emissions on aviation net NOx radiative forcing

Not only does the overall reduction of background emissions (i.e. different RCP scenarios) change the aircraft impact (same aircraft emissions), but also the mix of these reductions can have an impact. This is demonstrated by reducing individual precursors by −30% (NOx, CO, NMVOC), and all together (ALL), which changes the oxidative capacity of the atmosphere (Fig. 2). Figure 2 illustrates that a reduction of background NOx emissions (alone) leads to a significant decrease in hydroxyl radical (OH) concentrations, while the reduction of CO and NMVOC emissions (individually) increases OH concentrations as their oxidation process becomes limited, leading to a reduced production of hydroperoxy radicals (HO2). As a result of the above, the reduction in surface NOx emissions increases CH4 lifetime and decreases the concentration of tropospheric O3, while the reductions of CO and NMVOC cause the decrease of both tropospheric O3 and CH4, an observation that is consistent with other studies5,22. These dependencies are observed not only near the ground but also in the upper troposphere–lower stratosphere (UTLS) region, where most of aviation emissions occur; therefore, affecting aviation effects (Supplementary Fig. 2). In general, reducing surface emissions of NOx, CO and NMVOC individually decreases the net aviation NOx RF by up to 43%, the most effective being a reduction in surface NOx emissions alone, and the least effective being a reduction in CO, which results in a reduction of aviation net NOx RF of 14% (Table 1). A simultaneous reduction of all surface emissions by 30% decreases the aviation net NOx RF by 37% (for the same aircraft emissions). The reduction of surface NOx has the greatest potential in affecting the aviation net NOx RF; any 1% change of surface NOx emissions, modifies aircraft net NOx RF by ~1.5% (this estimate is inventory-dependant and here it varies from 1.4% to 1.6% for REACT4C 2006 data and high NOx 2050 scenario, respectively).

Fig. 2: The oxidative capacity of the troposphere under different background conditions.
figure 2

By reducing emissions of individual precursors by 30% (NOx, CO, NMVOC), and all together (ALL) changes the concentrations of hydroxyl radical and hydroperoxyl. The oxidative capacity of the atmosphere to a great extent controls the abundance of most trace gas species, hence affecting CH4 lifetime and concentration of O3 (see text for details). Values are averaged globally within the vertical domain extending from surface to 100 hPa and modelled by MOZART-3 CTM.

There is a well-known increase in O3 production (per unit of emitted N) as background NOx levels decrease and this is what we observe here as well. However, we also calculate a strong dependence of aircraft CH4 lifetime reduction on surface emissions that becomes more efficient with decreasing NOx. So, for a cleaner NOx background the positive short-term O3 RF increases, as expected, but the associated CH4 RF (and all the CH4-induced RFs) reduction increases even more, explaining why the net NOx RF decreases, rather than increasing3 for a cleaner NOx background. This strong CH4 response is possibly triggered by increased CH4 lifetime due to reduced oxidative capacity (Fig. 2). The 30% reduction of surface NOx increases the positive short-term O3 RF by 16%; however, the magnitude of the negative long-term CH4 RF increases even more, by 28%. Thus, less background NOx reduces the net NOx effect from aviation (for the same aviation NOx emissions). Moreover, it turns out that decreasing surface NOx emissions plays a larger role in reducing the aviation net NOx RF than decreasing aircraft NOx emissions (Fig. 3) in percentage terms. Figure 3 shows a steeper slope in the reduction of net NOx RF from percentage changes in surface emissions than from aviation emissions themselves. For example, in order to reduce the global climate impact of aviation NOx by 1 mW m−2, a 17% reduction in present levels of surface NOx emissions is needed; in the case of aviation NOx, it requires the reduction of emissions by 35%. Reducing aviation NOx emissions by such a large amount (35%) for, e.g. a 1 W m-2 net NOx RF reduction could be quite technologically challenging and have a strong risk of increasing aircraft CO2 emissions with a potentially perverse total RF outcome10. If a scenario is envisaged of falling surface NOx emissions, reducing aircraft NOx emissions at the expense of either missed opportunities to reduce CO2 emissions or even actually increasing CO2 emissions could be exactly the wrong thing to do and induce perverse climate outcomes.

Fig 3: Aviation net NOx radiative forcing change versus percentage change in NOx emission rates from surface and aviation sources.
figure 3

The aviation NOx response has been explored for varying, both, surface (red) and aviation (blue) emissions (dots are individual experiments, lines are the best fit lines). In the red case whilst surface NOx emissions are changing, aircraft NOx emissions are kept constant and this has been analysed for the highest and lowest projected range of aircraft NOx emissions, 2050 HighNOx-LowTech scenario (red dashed line; n = 2, r2 = 1.00) and 2006 REACT4C (red dotted line; n = 4, r2 = 1.00, p < 0.05). In the blue case whilst aircraft NOx emissions are changing, the surface NOx emissions are kept constant and this has been analysed for the highest and lowest projected range of surface NOx emissions, 2005 IPCC AR5 (blue dotted line; n = 4, r2 = 0.998, p < 0.05) and 2050 RCP 2.6 (blue dashed line; n = 3, r2 = 0.998, p < 0.05). The exact experiments that are used here are presented in Supplementary Table 1.


The short-term O3 RF is very sensitive to changes in all explored changes in surface precursor emissions (NOx, CO and NMVOC). The long-term CH4 RF is mainly affected by the reduction in surface NOx emissions and it changes very little in the case of the reductions of surface CO and NMVOC alone (probably due to the decrease in OH consumption by CO). This is in agreement with responses from other sensitivity tests performed with UCI CTM by Holmes et al.,3 with the difference that our short-term aviation O3 RF is not as responsive to surface CO emissions as those modelled with the UCI CTM. In addition, after accounting for the long-term negative RFs that were not given in their 2011 paper (long-term O3 and reductions in stratospheric water vapour, SWV), they also observe that the reduction in surface NOx emissions decreases the RF from aviation NOx, a 42% reduction in the aviation net NOx RF resulting from a halving of surface NOx emissions (C. D. Holmes, personal communication, October 19, 2018), which is in reasonable agreement with the sensitivity shown here. In general, to a great extent, the long-term CH4-mediated effects drive the response of aviation net NOx RF resulting from modified NOx emissions. Taking into account that these long-term RFs are fully parametrised as well as the fact that the CH4/O3 ratio is very model specific4 make the impact of surface NOx emissions on aircraft net NOx RF relatively more uncertain than the impact of other O3 precursor emissions. For example, if the new CH4 RF simplified expression that accounts for short-wave forcing is used23, reduction in surface NOx emissions not only decreases the aviation net NOx RF but also changes its sign from positive to negative. Table 2 gives the recalculated aviation RF numbers from Table 1 using a simplified expression for RF of CH4 as presented by Etminan et al.23 The improved understanding of CH4 RF has a significant impact on aviation estimates as it increases the negative CH4 RF from aviation NOx emissions by ~20%, which substantially reduces the aircraft net NOx RFs (Table 2). Moreover, the revision to the CH4 term provides a perspective that as aviation NOx emissions are reduced an increase in the global aviation net NOx RF is shown, and vice versa (Fig. 4 and Table 2). This revised formulation of the CH4 for RF does not contradict findings presented in this study, in terms of the sensitivity of responses, but turns out to be crucial for quantification of net NOx RFs and it provides a new perspective on the potential RF impact from future aviation NOx emissions. Other potential effects from NOx emissions include the direct enhancement of nitrate aerosol and indirect formation of sulfate aerosol (more efficient conversion of sulfur dioxide to sulfuric acid via increased OH). These aerosol effects are associated with large uncertainties and are addressed in only a few modelling studies24,25 and were not considered here. However, the effects of NOx on aerosol abundances are expected to result in negative forcings, such that inclusion of these processes would increase the negative NOx-associated forcings and be consistent with the findings of this work that emphasizes the role of the negative forcings.

Table 2 The recalculated aircraft NOx radiative forcing (RF) from Table 1 using a revised simplified expression for the RF of CH4 as presented by Etminan et al.23.
Fig. 4: Net NOx radiative forcing by emission rate, updated CH4 parameterisation.
figure 4

Aviation net NOx radiative forcing (RF) (the sum of the short-term positive O3 RF perturbation and the negative RF terms caused by a reduction in CH4 lifetime, see Methods), by aviation NOx emission rate according to a range of background emission scenarios, utilising the updated simplified expression for the calculation of CH4 forcing of Etminan et al.23 Aviation net NOx RF systematically decreases with increasing NOx emissions from aviation, showing a variation according to the background surface emissions, with high mitigation (RCP 2.6) having a smaller aviation net NOx RF than, lower mitigation scenarios (RCP 4.5, RCP 8.5) for the same aviation NOx emission. The pattern of behaviour is in contrast to Fig. 1 because the updated CH4 forcing expression accounts for the short-wave forcing of CH4, increasing CH4 RF estimates by approximately 25%, which in the case of aviation net NOx impacts greatly increases the negative terms from the reduction in CH4 lifetime from aviation NOx, tipping the net NOx term from being positive to negative with increasing aviation NOx emissions. Overall uncertainties are indicated by the grey shading, which is one standard deviation (68% confidence interval) from the ensemble of 20 NOx studies presented in Supplementary Fig. 1.

These new results (Table 2 and Fig. 4) show that as a generality, the net NOx RF from aviation decreases with air-traffic growth and corresponding increased aviation NOx emissions with reduced background emissions. The predicted cleaner background in the future acts with these reduced net NOx RFs. Therefore, it is worth highlighting that the ongoing efforts in cutting ground-level air pollution serve not only air quality improvements but are also beneficial for reducing the climate impact of aviation NOx emissions.

Climate change is considered to affect tropospheric chemistry. The modified oxidising capacity is expected to influence methane lifetime such that in a wetter and warmer climate it might either shorten or increase26,27 depending on the scenario. Also, on one hand, the increased water vapour might lead to increased O3 destruction in the tropics, whereas on the other, enhanced stratosphere–troposphere exchange could increase the net O3 flux to the troposphere14,28. The impact of the physical aspects of climate change on tropospheric composition is complex and is still highly uncertain. The inclusion of an interactive climate in the experiments might affect the results presented in this study. However, it is not expected that the current findings would become irrelevant, since it is the emission scenarios that to a great extent affect the future evolution of tropospheric chemistry29,30. The decreases in surface O3 precursor emissions over present-day values presented in RCP dataset are consistent with most other future emission scenarios that consider even more extensive air quality legislation, e.g. ECLIPSE (Evaluating the CLimate and Air Quality ImPacts of Short-livEd Pollutants) or SSPs (Shared Socioeconomic Pathways) databases. This is in stark contrast to aviation emissions, for which strong growth is predicted and the global civil fleet may more than double within the next 20 years, from ~21,000 aircraft in 2018 to ~48,000 aircraft in 203731. Whilst there is a possibility for the net NOx RF to be weakened due to a cleaner background, this is not as simple for an aviation CO2 RF. CO2 accumulates in the atmosphere due to its fractional millennial timescale which means that its climate effect is determined by the cumulative emissions over time. As a consequence, the RF in 2018 from aircraft CO2 emissions is around twice greater than that from aircraft NOx emissions32. However, what is even more important is the difference in the nature of their responses (Supplementary Fig. 3). At present, the temperature response from a unit emission of aircraft NOx is the strongest in the year of emission and it diminishes thereafter. Moreover, after around 15 years it changes the sign from positive (warming) to negative (cooling) to disappear after around 60 years. On the contrary, the emission of CO2 leads to a uniform positive (warming) temperature response from increased atmospheric levels of this gas and after a 100 years, the unit emission emitted in the year 1 still provides a significant positive signal (as modelled by the simple climate model, LinClim, see Methods).

There are various measures to reduce fuel demand (and therefore CO2 emissions) such as market-based measures or stricter aircraft CO2 emission standards; the latter, as it is associated with trade-off between aviation CO2 and NOx might raise some dilemmas. In view of the low impact of reducing aviation NOx any potential trade-offs with CO2 should not be risked and also any potential savings in CO2 should not be forsaken in the pursuit of lower NOx in terms of climate protection10. We acknowledge the necessity to reduce aircraft NOx emissions for local air quality benefits; the source apportionment in any given location is likely to be unique, depending on volume of air traffic and other local sources. However, the aircraft-related emissions of NOx are of clear importance for many locations. From a climate benefit point of view, we suggest that any vision of more stringent NOx regulations needs to be revisited, as it might be more worthwhile to concentrate more on CO2 reductions at the cost of NOx, not vice versa, especially in the light of necessary forthcoming decarbonisation to avoid an33 increase of 1.5°. Coherent comparative assessments that would consider both climate and air quality impacts are needed. There are just a few studies that try to tackle this issue34,35,36 and none that would consider these aspects under changing background conditions.

The CO2 emissions still provide the majority of the long-term warming (if not the instantaneous RF) from aviation, and a smaller change in its emission affects the total forcing much more than an equivalent change in NOx emission. The mitigation of non-CO2 effects is scientifically uncertain and trading against CO2 could produce perverse outcomes10, the climate benefits from any reduction of aviation CO2 emissions are indisputable.


Chemistry transport model and emission data

The model for ozone and related chemical tracers, version 3 (MOZART-3) was used for this study. This is a 3D CTM that has been evaluated by Kinnison et al.16 and used for an extensive range of different applications37,38, including studies dealing with the impact of aircraft NOx emissions on atmospheric composition39,40.

MOZART-3 accounts for advection based on the flux-form semi-Lagrangian scheme41, shallow and mid-level convection42, deep convective routine43, boundary layer exchanges44, or wet and dry deposition45,46. MOZART-3 reproduces detailed chemical and physical processes from the troposphere through the stratosphere, including gas-phase, photolytic and heterogeneous reactions. The kinetic and photochemical data are based on the NASA/JPL evaluation47.

The model configuration used in this study includes a horizontal resolution of T42 (~ 2.8° × 2.8°) and 60 hybrid layers, from the surface to 0.1 hPa. The transport of chemical compounds is driven by the meteorological fields from the European Centre for Medium Range Weather Forecast (ECMWF), 6-h reanalysis ERA-Interim data for the year 200648. This meteorological conditions were used for all runs, including the 2050 simulations.

The aviation NOx emissions for the years 2006 and 2050 were determined based on the REACT4C base case dataset (CAEP/8 movements)39 and ICAO-CAEP49 aviation emission projections, respectively. Emissions of aircraft NOx were calculated to be 0.71 Tg(N) year-1 in 2006 and 2.17 Tg(N) year-1 in the 2050 low air-traffic growth and optimistic technology-development scenario and 5.59 Tg(N) year-1 in the 2050 high air-traffic growth and low technology-development scenario. The 2050 aviation scenarios were chosen to represent the highest and lowest projected range of possible aircraft NOx emissions in 2050 from data derived from the ICAO-CAEP trends work49. First, three aviation traffic demand forecasts out to 2040 are produced (a low, central and high traffic-demand scenario) these demand scenarios are translated by ICAO-CAEP to fleet scenarios, fuel efficiency scenarios are then superimposed upon the fleet scenarios to produce a range of technology and operational improvement scenarios ranging from a technology freeze, through to low, moderate, advanced and optimistic improvement scenarios. Extrapolation of the fuel burn 2040 results out to 2050 is also undertaken and reported by the ICAO-CAEP. Further to the fuel efficiency and traffic demand assumptions, two separate NOx scenarios were developed by ICAO-CAEP resulting in the derivation of two future 2050 fleetwide NOx emission indices (EINOx in terms of grams of NOx per kilogram of fuel burned): a high and a low EINOx. In this study the high and low EINOx values for the future fleet are applied to the range of estimates of fuel burn in 2050 to calculate a corresponding range of NOx emission estimates in 2050. The range of NOx estimates in 2050 varies from the low NOx scenario of 2.17 Tg(N) year-1 (low EINOx, the low traffic demand with the more efficient optimistic fuel burn scenario, i.e. low fuel burn estimate) and the high NOx estimate of 5.59 Tg(N) year-1 (high EINOx, the high traffic demand forecast and the low fuel efficiency scenario, i.e. higher fuel estimate).

The present-day surface (non-aviation) emissions (base) represented year 2005. The anthropogenic and biomass burning emissions were taken from IPCC AR550 and the biogenic emissions were taken from POET51. Four different cases were investigated: global reduction of surface NOx emissions (−30% NOx), global reduction of surface CO emissions (−30% CO), global reduction of NMVOC emissions (−30% NMVOC) and global reduction of ALL these species simultaneously (−30% NOx, CO, NMVOC). All other sources of emissions, including aircraft NOx emissions were held constant for each experimental case. The 2050 gridded surface emissions (anthropogenic and biomass burning) were determined by Integrated Assessment Models (IAMs) for the three Representative Concentration Pathways52 (RCPs): a high mitigation scenario that forecast the smallest impact to climate (RCP 2.6), business-as-usual scenario (RCP 4.5) and high climate impact scenario (RCP 8.5). Concentrations of long-lived chemical species and greenhouse gases were based on the RCP emissions, converted to concentrations by Meinshausen et al.53 Natural emissions (e.g. isoprene, lightning and soil NOx or oceanic emissions of CO) were not specified in these future scenarios; thus, they were not modified here and were kept the same for all the simulations. The parametrisation of NOx emissions from lightning was defined as a function of the location of convective cloud top heights54,55 and their global source were calculated to be 4.7 Tg(N) year−1.

The series of sensitivity experiments were performed in order to have a broad perspective on how aircraft and background emissions might affect net NOx climate impact. The detailed list of simulations exploited in this study shows Supplementary Table 1.

Radiative forcing calculations

The Edwards-Slingo radiative transfer model56 (RTM) was used for the calculation of the forcing associated with aviation NOx-induced short-term O3. The monthly O3 fields from MOZART-3 were converted into mass mixing ratios and interpolated onto RTM vertical and horizontal resolution. The applied RTM is an offline version of the UK Met Office Unified Model and it calculates the radiative fluxes and heating rates based on the δ-Eddington of the two-stream equations in both, the long-wave (9 bands) and short-wave (6 bands) spectral regions. Cloud treatment is based on averaged International Satellite Cloud Climatology Project (ISCCP) D2 data.57 Climatological fields of temperature and specific humidity are based on ERA-Interim data48. In terms of the 2050 RF calculations, the concentrations of long-lived species were modified according to specific RCP scenarios53 and were consistent with MOZART-3 set up.

The CH4 concentrations change is assumed to be in equilibrium with the OH change due to the aircraft NOx perturbation from constant emissions58. Since CH4 mixing ratios were prescribed as a lower boundary condition and the simulations were not long enough, the steady-state CH4 concentration ([CH4]ss) was calculated from the change in its lifetime with respect to reaction with tropospheric OH derived from MOZART-3 simulations as shown in Eq. 1:

$$\left[ {{\mathrm{CH}}_4} \right]_{{\mathrm{ss}}} = \left[ {{\mathrm{CH}}_4} \right]_{{\mathrm{ref}}} \times (1 + 1.4 \times {\Delta} \tau _0/\tau _{{\mathrm{ref}}})$$
( 1)

A factor of 1.4 was used to reflect the CH4 feedback on its own lifetime3,58. Here τref denotes the lifetime of CH4 versus reaction with OH in the unperturbed simulation, Δτ0 the change in CH4 lifetime between the unperturbed simulation and the NOx-perturbed simulation and [CH4]ref the CH4 mixing ratio in the unperturbed simulation.

This steady-state CH4 aircraft response was further used for the CH4 RF calculations using, as in IPCC AR559, a simplified expression (Eqs. 2 and 3) originally defined in Myhre et al.60

$${\Delta} F = 0.036(\sqrt M -\sqrt {M_0} )-\left( {f\left({M,N_0} \right)-f\left( {M_0,N_0} \right)} \right)$$
( 2)
$$f\left( {M,N} \right) = 0.47{\mathrm{ln}}[1 + 2.01 \times 10^{ - 5}\left( {MN} \right)^{0.75} +\, 5.31 \times 10^{ - 15}M\left({MN} \right)^{1.52}]$$
( 3)

where N is N2O in ppbv, M is CH4 in ppbv and subscript 0 denotes unperturbed concentrations.

Long-term O3 caused by CH4 changes was calculated according to IPCC AR559, as 50% of the CH4 RF. Modified CH4 also affects SWV and give an additional RF of 15% of CH4 RF61.

The recalculated aviation RF estimates presented in Table 2 are based on the same methodology as original values shown in Table 1 and as described above. The only differences comes from the application of the new simplified expression for RF of CH423 as shown in Eq. 4 that replaces the old expression presented in Eqs. 2 and 3:

$${\Delta} F = {[a {\times} {\bar {M}} + b {\times} {\bar {N}} + 0.043]} {\times} ({\sqrt {M}} - {\sqrt {M_0}} )$$
( 4)

where a = −1.3 × 10−6 Wm−2 ppb−1, b = −8.2 × 10−6 Wm−2 ppb−1, M and N are concentrations of CH4 and N2O, respectively, and subscript 0 denotes unperturbed concentrations. For terms within the square brackets, the gas concentrations are the mean of the unperturbed and perturbed concentrations, e.g. \(\bar M\) = 0.5 × (M + M0).

The temperature responses from a unit aircraft CO2 vs NOx emissions

The time scales of the climate effects of CO2 and NOx are very different and these processes of the long-term accumulation vs short-term disappearing, respectively, were explored here. The responses presented on Supplementary Fig. 2 are based on a pulse emission of a 1 Tg(N) year-1 in year 1.

In order to observe the temperature response from a unit emissions of aircraft NOx the methodology presented by Aamas et al.62 have been applied and Absolute Global Temperature change Potentials (AGTP) have been calculated based on steady-state CTM/RTM results (base case). The forcing for NOx is assumed to be a result of a pulse that lasts for 1 year followed by an exponential decay of the resulting forcing from the end of the year 1 onwards. The NOx effect is the sum of the short-term O3 effect, CH4 (with SWV) effect and CH4-induced O3 effect, and there is a perturbation from the forcing for t  < 1 (this determines the temperature response of the emissions that occur in the first year) and from the forcing for t ≥ 1 (this determines the temperature response of atmospheric perturbation lasting past one year). Thus, the total AGTPNOx (provided that the time horizon (H) is >1) is the sum of \({\mathrm{AGTP}}_{{\mathrm{NO}}x}^{t < 1}\)(H) and \({\mathrm{AGTP}}_{{\mathrm{NO}}x}^{t \ge 1}\)(H):

  1. a.

    For perturbation from RF occurring t < 1

    $${\mathrm{AGTP}}_{{\mathrm{NO}}x}^{t < 1}( H ) = \; {\Delta} F_{{\mathrm{NOx}}}^{{\mathrm{SS}}}\mathop {\sum }\limits_{j = 1}^2 \left\{ c_j\left[ \exp \left( {\frac{{1 - H}}{{d_j}}} \right) - \exp {\left( { - \frac{H}{{d_j}}} \right)} \right] \right. \\ \left.+\; \frac{{c_j\tau }}{{\tau - d_j}}\left[ \exp \left( { - \frac{H}{{d_j}}} \right) - \exp \left( {\frac{{1 - H}}{{d_j}}} \right)\exp {\left( { - \frac{1}{\tau }} \right)} \right] \right\}$$
    ( 5)
  2. b.

    For perturbation from RF occurring t ≥ 1

$${\mathrm{AGTP}}_{{\mathrm{NO}}x}^{t \ge 1}\left( H \right) = {\Delta} F_{{\mathrm{NO}}x}^{{\mathrm{SS}}}\left[ {1 - \exp \left. {\left( { - \frac{1}{\tau }} \right)} \right]} \right.\mathop {\sum }\limits_{j = 1}^2 \frac{{c_j\tau }}{{\tau - d_j}}\left[ {\exp \left( {\frac{{1 - H}}{\tau }} \right) - \exp \left. {\left( {\frac{{1 - H}}{{d_j}}} \right)} \right]} \right.$$

The superscript SS indicates steady-state, τ is the lifetime and it is the short-lived lifetime (τs) for short-term O3 (here it is 0.267) whilst the primary-mode lifetime (τpm) characterises CH4 and CH4-induced O3 (for the MOZART-3’s base case it is 12.02 year). The cj are the components of climate sensitivity and dj are the corresponding time scales and these values are taken from Boucher and Reddy63.

In order to observe the temperature response from a unit emission of aircraft CO2 a simple climate model (SCM), LinClim was utilised. LinClim is a linear climate response model that has been customised specifically to aviation10,64,65. It uses a single impulse response function that is calibrated against more sophisticated parent model. Aviation fuel data are used to calculate CO2 emissions that is then applied in the linear response function from Hasselmann et al.66 in order to derive CO2 concentrations. The carbon cycle in LinClim is based on the Maier-Reimer and Hasselmann67 model and the CO2 RF is calculated using the function applied in IPCC AR468. The temperature response formulation is based on the method presented by Hasselmann et al.69 The calculated temperature response is also dependent on the climate sensitivity parameter and the lifetime of the temperature perturbation that are tuned to LinClim’s parent General Circulation Model (GCM), here it is ECHAM4.

Here the LinClim was used to calculate the temperature response from a pulse/unit emission of aviation CO2 over the long time period. The background scenario chosen was represented by RCP 8.553 as its global emissions are the closest to the current levels of CO2 in the atmosphere. The amount of aircraft NOx that is produced from the fuel burned is described by the emission index (EINOx). The current EINOx is 15.14 g(NO2)/kg(fuel)49 and it has been applied here. Knowing that for every 1 kg of fuel used, 3.16 kg of CO2 is emitted, the 1 Tg of emitted N is equivalent to 217 Tg fuel and therefore, 686 Tg of emitted CO2. This emission was released as a pulse in the year 1 and the consequent CO2 temperature response was observed for the following 100 years.

Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Data availability

All data discussed in the manuscript and Supplementary Information are presented in Source Data. All data generated for this study (2006 and 2050 CTM and RTM simulations) are available on request from the corresponding author. Source data are provided with this paper.

Code availability

The modelling data have been post-processed using IDL 8.5.1, and all the scripts are available on request from the corresponding author.


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This work was supported by the United Kingdom Department for Transport and the European Union’s Horizon 2020 Research and Innovation Action ACACIA under grant agreement No 875036.

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D.S.L. conceived of the research, A.S. led the study, R.R.L., L.L.L. and B.O. provided input data, A.S. performed the model simulations and generated all the figures and tables, A.S. and D.S.L. interpreted the results and drafted the manuscript with support from all authors.

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Skowron, A., Lee, D.S., De León, R.R. et al. Greater fuel efficiency is potentially preferable to reducing NOx emissions for aviation’s climate impacts. Nat Commun 12, 564 (2021).

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