Aviation plays a critical role in the modern world, contributing to an estimated USD 2.7 trillion and employing 65 million people in 2016 [1]. Aviation’s emissions mass are comparatively low for the transport sector as a whole [2]. However, the unique location in the atmosphere where aviation is active is in the upper troposphere lower stratosphere (referred to as the UTLS hereafter) during cruise altitudes, where emissions have an outsized impact on the climate. Perturbations to the climate associated with the emissions of aviation at cruise altitude are understood to include, in descending order, radiative forcing, contrail (condensation-trail) cirrus, CO₂, NO_X, aerosols, hydrocarbons, and water vapour, amongst others [3]. In this study, the influence of the emissions of nitrogen oxides (NO, nitric oxide, and NO₂, nitrogen dioxide, collectively referred to as NO_X) and background and unburnt emissions of volatile organic compounds (VOCs) from aircraft at cruise altitude is investigated using a combination of a global Lagrangian chemistry-transport model and a box model which is a further development of previous work by Derwent et al. [4]. Derwent et al. (2024) [4] investigated the consequences of aircraft NO_X emissions on ozone formation in the UTLS using a global chemistry transport model followed by a box model. Ozone impacts were quantified at hourly intervals along 21 real intercontinental flight paths which followed air traffic corridors. The study found NO_X impacts to be greatest nearer to the tropics and least significant when involving trans-polar routes. NO_X impacts were also found to be significantly smaller than identified from global models used in aviation NO_X assessments. The research objective was to analyse how the NO_X–O₃ relationship for aircraft emissions varies on a global scale with a focus on an expanded spatial-temporal output, and then, to bring to light the significance and relevance of such information in mitigating the impact of aviation on the atmosphere, by elucidating how much the formation of ozone can be reduced in hypothetical flights at a cruise altitude. This was achieved by comparing various path trajectories.

Numerous studies [5,6,7,8,9] have developed different models to estimate the spatial and temporal distribution of ground-level ozone; however, this focuses on aircraft emissions in the UTLS. Reportedly, 90% of aviation’s emissions by mass are emitted in the UTLS [10]; therefore, it is prudent to focus on the perturbations in the chemical and physical interactions in this region of the atmosphere. The UTLS describes the region ±5 km from the tropopause (~8–18 km above sea level [11]). The UTLS region is also particularly climatically and radiatively sensitive to perturbations in gases such as greenhouse gases, as well as aerosols. This is due to greater radiative efficiencies compared to ground level, increased residence times of pollutants, and lower background concentrations and temperatures of chemical species [12,13].

Aviation typically utilises paraffinic kerosene as a fuel, which under clean combustion would lead to emissions of a stoichiometrically set ratio of CO₂ and H₂O. However, Jet-Fuel A-1 is the standard fuel used for commercial aircraft, which is composed predominantly of kerosene, with impurities and additives [14]. However, any propulsion involving the intake of atmospheric air into engines inherently involves NO_X emissions due to the intake of atmospheric nitrogen (N₂). The amount of NO_X emissions is coupled with the temperature of the intake air in the engines. Aviation’s NO_X emissions have been recognised since the 1990s to enhance ozone production and to reduce methane concentrations [15,16]. NO_X emissions lead to a non-linear NO_X–O₃ relationship, whereby, at low NO_X concentrations, hydroperoxyl (HO₂) radicals increasingly react with NO (Equation (1)), as opposed to its self-reaction radical loss (Equation (2)), leading to hydroxyl radicals (OH). M represents background air molecules.

To the point where photochemical ozone formation is inhibited, at very low NO_X, by hydroxyl radical loss via its conversion to HNO₃ in Equation (3):

From Equation (1), NO₂ photolysis produces ground-state atmospheric oxygen, O(³P), and subsequently O₃ via the reaction of O(³P) with O₂.

The ozone production rate is dependent on the availability of O₃ in the polluted atmosphere, and described as NO_X sensitive (NO_X-limited) when increases in NO_X leads to promoted levels of photochemical O₃, with changes in VOCs having little effect [4,17]. Thus, VOC is limited (VOC-sensitive/NO_X saturated) when photochemical ozone formation becomes increasingly sensitive to NO_X mixing ratios, to a point where it decreases with increasing NO_X.

The hydroperoxy and NO are provided in a generalised scheme for Equations (1) and (2) for VOCs, where RH represents a VOC:

Alkoxy radicals, RO, are formed by the oxidation of VOCs (RH) by hydroxyl radicals and NO₂:

Net reaction:

The ozone production from NO_X and VOCs is simplified and summarised in Figure 1.

Incentives, policies, and an industry-wide pledge to reach net-zero carbon emissions by 2050 [19] from the aviation industry have led to developments toward alternative aviation fuels, such as so-called Synthetic/Sustainable Aviation Fuels, hydrogen, and to a lesser extent ammonia [20,21,22,23,24,25,26,27]. Implicit in the combustion of fuels in the air are NO_X emissions. Therefore, it is still prudent to have an understanding of the consequences of fuels on the chemistry of NO_X. Ozone plays an important role in maintaining the influence of the Earth’s radiation budget [28]; however, perturbations in its mixing ratio are known to alter this radiation budget, thus contributing toward global warming, as well as potentially meteorological effects which may lead to changes in cloud formation and tropospheric stability. The net result of the ozone production, due to direct NO_X emissions, constitutes to approximately 16% of aviation’s global warming (of a total radiative forcing of 100.9 mWm⁻²) for the years 1940 to 2018. This makes NO_X-induced effects the third most significant aviation contributor toward climate change after the effects of contrails and CO₂ emissions. The comparisons of radiative forcing effects are valid for current aviation fuels; however, as mentioned, ozone formation due to NO_X emissions will still contribute with an uptake of alternative fuels. Niklaß et al. [29] showed the potential to re-route aircraft with virtually no additional fuel burn, resulting in a 12% reduction in climate impact associated with aircraft emissions, with other studies suggesting a 10–20% reduction with only a few percent increase in fuel burn. In terms of ozone formation due to aviation emissions in the UTLS, three main sources are understood to exist: NO_X photochemical reactions, heterogenous reactions of aerosols, and contrail effects. Heterogenous reactions on aerosol particles have a reported negligible impact on ozone production, but contrail ice can affect the ozone response from aircraft emissions by ±0.5% on a macroscopic scale depending on the time of year and day [30].

Previously, we have reported on the ozone production along flight trajectories on 21 intercontinental routes between major aviation hubs [4]. NO_X emissions have two distinct components acting on different time-scales. Only the initial rapid ozone production occurring over a period of hours to days is analysed here. The hydroxyl radical–methane–ozone (OH-CH₄-O₃)-driven chemistry, which acts over timescales of months and years resulting in the decay of net ozone, is not analysed in this study. In this study, our previous work has been expanded on to cover the whole globe. Ozone formation along a variety of trajectories have then been investigated. Mitigating climate effects of emissions through the optimisation of flight trajectories to reduce the impact on climate sensitive regions has been gaining interest over recent decades [29]. Such trajectory optimisation has primarily focussed on mitigating the formation of persistent contrails and is a significant logistical task requiring cooperation with stakeholders including air traffic management. Trajectory optimisation to reduce ozone formation can also be applicable given the strong spatial and chemical variability in NO_X–O₃.

The following section analyses the NO_X–O₃ relationship for aircraft emission variations on a global scale with a focus on an expanded spatial-temporal output. The following section brings to light the significance and relevance of such information in mitigating the impact of aviation on the atmosphere, by elucidating how much the formation of ozone can be reduced in hypothetical flights at a cruise altitude. This is achieved by comparing various path trajectories.

Figure 2 presents the sensitivity to NO_X and VOC on the STOCHEM gridded globe, with red representing NO_X-sensitive regions, blue represents VOC sensitive regions, and green equally sensitive regions. NO_X-sensitive regions clearly dominate the globe throughout the year. There is significant variation between NO_X-sensitive to VOC-sensitive areas in regions within 30∘ latitude of the poles on the change from summer to winter seasons, predominantly in the Antarctic region. The fact that NO_X regions are dominant aids in focussing on how to reduce ozone formation in the UTLS. For example, recent work on formation flight and its associated NO_X saturation is valid.

Outputs for the O₃ formation (ppb) per NO_X (ppb) per 5∘×5∘ STOCHEM grid were averaged per latitude and per longitude and plotted in Figure 3. Figure 3 shows that average O₃ formation (ppb) per NO_X (ppb) varies little with longitude bar; though a slight increase can be seen around the Pacific Ocean longitudes, there is a consistency throughout the months. However, the latitude appears to play a significant role in explaining variations in the O₃ formation (ppb) per NO_X (ppb). This could be due to the inherent link between latitude and solar irradiance with the month of the year. This is further supported by a narrow range across the months for O₃ formation (ppb) per NO_X (ppb) at the equatorial regions and then toward the poles significant divergence in the range of O₃ formation (ppb) per NO_X (ppb) values with the month. November to January appears to show the largest O₃ formation (ppb) per NO_X (ppb) and March to July the lowest O₃ formation (ppb) per NO_X (ppb). The general decrease in O₃ formation (ppb) per NO_X (ppb) poleward and minima O₃ formation (ppb) per NO_X (ppb) during the boreal spring months is consistent with our previous study, as are the magnitudes of O₃ formation (ppb) per NO_X (ppb).

Modelled outputs of O₃ formation (ppb) per NO_X (ppb) based on STOCHEM and PTM models for the globe in a 5∘×5∘ degree grid are presented in Figure 4. It should be stressed that these plots show the ozone formation per NO_X ppb, and thereby, they are not necessarily the regions with the highest ozone mixing ratios when including aviation plume effects; it is the influence of additional emissions that is of interest here. As evident from the plots in Figure 4, regions over the mid-southern latitudes of the Eastern Pacific Ocean through to the Northern Indian Ocean are susceptible to the greatest ozone formation for a unit of NO_X. These marine-based regions align with regions known to exhibit monsoons and El Niño and La Niña, where vertical transport between atmospheric layers may be influencing convection patterns. There are also more local hotspots over the continental land masses, in particular over the regions of Africa and South America, which align with regions with regions of known lightning hotspots which may be enhancing NO_X levels. Local hotspots also exist over Europe, North America, and Asia, most prominently in the boreal winter months. Temperate and polar regions show a correlation with the season, with ozone formation peaking in northern latitudes in the boreal winter and in the austral winter for the southern hemisphere. There appears to be a coupling between the season and ozone formation in regions, potentially due to the inherent dependence of many reactions on the photolysis, and hence, solar irradiance, thereby being coupled to the season. The Antarctic continent also displays significant fluctuations and abnormal responses, likely due to the strong coupling to seasonality, and the fact that it receives significantly less solar irradiance due to its geographical position. This may warrant more investigation into this region. However, very few flights are known to traverse the Antarctic continent. The range plot, defined to be the difference in the minimum from the maximum P(O₃) per cell, shows the variation in P(O₃) across the year, with the majority of regions varying by 5–15 O₃ (ppb) per NO_X (ppb). Variation occurs mostly over the marine hotspots described, but with little variation over the South Atlantic Ocean. Minimum and maximum plots show the minimum and maximum P(O₃) per gridded cell, respectively. Minimum values are fairly consistent and of the order of 5–15 O₃ (ppb) per NO_X (ppb). Maximum values are broadly over three marine hotspots and over land masses to a lesser degree, with significantly more variation from 10 to 35 O₃ (ppb) per NO_X (ppb)]. This geospatial variation follows closely with that of the literature [51,52].

An understanding of the geo-spatial sensitivity to ozone provides important information allows trajectories to be planned that avoid regions that are most sensitive to perturbation by plumes of emissions from aviation. Therefore, route optimisation based solely on O₃ formation along flight trajectories was tested.

Optimal routing was computed to find the routes and weights of least ozone formation per NO_X. Table 1 shows 10 example routes, 3 short-haul and 7 long-haul routes, with typical flight lengths, great circle distances, as well as the weight of ozone (ppb) formation per NO_X (ppb) for unoptimised routes (via the Haverine path), an optimised path, and a real-world flight. Routes were selected to cover a global range and regions indicated to be most sensitive to NO_X. Optimal routing can be seen to reduce the O₃ formation (ppb) per NO_X (ppb) of the order of approximately ~40%, which is not insignificant. Trajectories, in Table 1, traversing through tropical regions have significantly larger atmospheric responses from ozone formation than those in boreal or austral regions. Optimal routing would also be more beneficial for long-haul missions, as deviations in flight may be less significant proportionally. The variation in ozone formation along different flight trajectories illustrates the potential to reduce the impact of NO_X emissions on the atmospheric response. This highlights the potential and increasingly important balancing of route optimisation to reduce persistent contrail effects, NO_X emissions, fuel burn, turbulence, and phenomena.

Based on the O₃ ppb per NO_X ppb, ozone formation can be estimated for entire flight trajectories, for any aircraft type, and any engine configuration and type based on fuel burn and meteorological conditions, because NO_X emissions are a function of the temperature and pressure of the air at intake and fuel burn.

It is not always practical nor feasible for aircraft to fly the optimal in terms of climate impact trajectory due to weather and safety issues. Air Traffic Control, responsible for flight trajectory decision making, takes into account many factors, including weather, payload, and air traffic constraints [53]. Therefore, alternative metrics can be conceived, giving valid weighting to the ozone production and its climate impact together with the increased fuel burn for alternative routes, etc. The programme created has the option to add waypoints along the trajectory, for situations where an aircraft may want to avoid particular geographical areas in flight or to follow pre-determined airway flight plans as closely as possible, to account for such scenarios.

It is important to acknowledge the limitations of this work. Dijkstra’s algorithm uses pre-defined and static weights for the graph at the time of computation. Although in this case, MetOffice data from the Unified Model was used in the STOCHEM process, the graph can be updated with forecast data or alternatives. The setup was designed to represent the physical–chemical behaviour. Tensorflow was applied with a non-linear method to generate a finer scale grid. This is, thus, a predicted graph. Alternative approaches such as various forms of Generative Adversarial Networks. In terms of the algorithms, the great circle trajectory was chosen to represent the shortest possible path and follow what would be typically regarded as the most straightforward path. Alternatively, the A* or Bellman–Ford approach could be applied towards the use of dynamic programming algorithms. The heuristic A* approach, which priorities nodes nearest to the destination, may reduce the runtime, but will not elucidate the degree to which ozone formation could be reduced along flight trajectories. The Bellman–Ford approach allows for graphs with negative weights unlike Dijkstra’s algorithm; however, this was not found to be needed for this application. Dijkstra’s algorithm is a greedy algorithm, that is to say it finds the locally optimal choices to find the global solution as opposed to considering the consequences, and can therefore have long runtimes. However, for the purposes of this work, runtimes were not found to be an issue and not in the timescales for route planning. Real-world operations would not have to follow the path of least weight, but follow the intended trajectories, and in cases where regions are sensitive to ozone formation, avoid such regions with either vertical or horizontal deviations where it is feasible. One could conceive a multi-objective approach, such as a weighted sum method, for optimising the path for contrail, Ozone, fuel burn, flight time, and turbulence factors.

Should such a route optimisation procedure be adopted, the process could be conceptually similar to that of contrail avoidance, minimisation, or mitigation planning. As an example, flight planning analyses weather, air traffic, and operational constraints to determine an ensemble of possible trajectories for a route along with the trajectory, posed here, which avoids regions most prone to forming ozone. Pilots approve the trajectory to be followed and submits the flight plan to air traffic management. The flight then follows the planned route with adjustments for turbulence and or air traffic congestion following air traffic control procedures.

To develop this model further, the timing of departure of an aircraft could be include to further improve the current understanding of diurnal variations. Additionally, focusing on all pressure levels of the STOCHEM-CRI model would allow for the inclusion of the ascent, descent, and taxiing phases of flight to be taken into account in route optimisation, thereby developing a three-dimensional model and flight trajectory. However, this may not be as useful given the lack of flexibility in re-routing in these stages of flight. This model has been developed on offline data and has not yet been used such that it can generate predictions based on forecasts of meteorological and chemical conditions, which is due to the model using chemical and meteorological data from the MetOffice Unified model (UK Met Office, Exeter, UK).

Aviation is a significant sector and plays a non-negligible impact on anthropogenic perturbations to the radiation balance of Earth’s atmosphere, with ozone formation being the third most potent contribution from aircraft emissions. A combination of global Lagrangian chemistry-transport model and a box model has been utilised to examine the background NO_X and VOC sensitivity of the UTLS. Seasonal and geospatial variations in the sensitivity of the atmosphere have been commented on, finding anomalous behaviour around the Antarctic continent which needs further investigation, hotspots around the Indian and Pacific Oceans, local hotspots, increased O₃ ppb per NO_X toward equatorial regions, and maxima in O₃ ppb per NO_X during the local autumn and winter months and minima during boreal spring months. This has then been used to suggest the potential for route optimisation, which has been approached via two algorithms to show optimal routing can reduce ozone formation due to NO_X emissions by of the order of 1–40%. Developments have been suggested to make the model more useful in terms of flight planning to reduce it is climate impact as well as improvements to the chemical accuracy.