Airspace restrictions due to conflicts increased global aviation’s carbon dioxide emissions in 2023

Abstract

As air traffic rebounds from its large drop during the Covid-19 crisis, civil aviation needs to continue addressing its climate impact. Knowledge of aircraft trajectories is essential for an accurate assessment of the CO2 (and non-CO2) climate impact of aviation. Here we combine an aircraft trajectory optimization algorithm and a global database of aircraft movements to quantify the impact of airspace restrictions due to conflict zones on CO2 emissions. Among current restrictions, we show that the Russian ban of its airspace to Western airlines following the invasion of Ukraine has the largest impact. Our analysis reveals an initial reduction of flights to and from East Asia that would have crossed the Russian territory. Routes then gradually reopened by making a detour, which led to an average increase in fuel consumption of 13% on the affected routes, with a greater impact for flights to and from Europe (14.8%) compared to flights to and from North America (9.8%). Although these flights represent only a small fraction of the daily flights, the large detours have increased global aviation CO2 emissions by 1% in 2023, equivalent to a quarter of the yet-to-be-achieved efficiency gain potential from improved air traffic management.

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communications earth & environment Article
https://doi.org/10.1038/s43247-024-01956-w
Airspace restrictions due to conflicts
increased global aviation’s carbon dioxide
emissions in 2023
Check for updates
Grégoire Dannet 1, Nicolas Bellouin1,2 & Olivier Boucher 1
As air traffic rebounds from its large drop during the Covid-19 crisis, civil aviation needs to continue
addressing its climate impact. Knowledge of aircraft trajectories is essential for an accurate
assessment of the CO
2
(and non-CO
2
) climate impact of aviation. Here we combine an aircraft
trajectory optimization algorithm and a global database of aircraft movements to quantify the impact of
airspace restrictions due to conflict zones on CO
2
emissions. Among current restrictions, we show that
the Russian ban of its airspace to Western airlines following the invasion of Ukraine has the largest
impact. Our analysis reveals an initial reduction of flights to and from East Asia that would have crossed
the Russian territory. Routes then gradually reopened by making a detour, which led to an average
increase in fuel consumption of 13% on the affected route s, with a greater impact for flights to and from
Europe (14.8%) compared to flights to and from North America (9.8%). Although these flights
represent only a small fraction of the daily flights, the large detours have increased global aviation CO
2
emissions by 1% in 2023, equivalent to a quarter of the yet-to-be-achieved efficiency gain potential
from improved air traffic management.
Airlines optimise their flight trajectories a few days to a few hours before
departure to minimise the operating cost of the flight. Fuel consumption is
one of the important factors considered and can be minimised by making
the best use of wind patterns. However airlines also have to take into account
a range of operational constraints such as weather conditions (e.g., to avoid
thunderstorms), safety regulations (e.g. keeping a minimum distance to
diversion airports), airspace crossing charges, staff costs and available air
routes, in particular in the case of partial or total airspace closures. Flight
optimisation thus seeks to balance fuel efficiency with other operational
costs and constraints.
Trajectory inefficiencies represent an important challenge but also an
opportunity to reduce CO
2
emissions1. Indeed, tackling trajectory ineffi-
ciencies is explicitly outlined in the strategic plans of the International Air
Transport Association2and the International Civil Aviation Organisation3.
They estimate that improving air traffic management operations has the
potential worldwide to achieve a substantial reduction of 3–5% in CO
2
emissions by the aviation industry. However, geopolitical considerations
often stand against that objective. Indeed airlines may be obliged by their
regulators or may decide unilaterally to avoid certain airspaces because of
safety concerns. Countries may also decide to close their airspace to all
aircraft from certain airlines or from certain countries. In this context,
armed conflicts and international sanctions are two main sources of airspace
restrictions. For instance, many airlines started to avoid Eastern Ukrainian
airspace after Malaysia Airlines Flight 17 was shot down by Russia-
controlled forces on 17 July 2014. Following the Russian invasion of Ukraine
in February 2022 and the ongoing war between Ukraine and Russia, Wes-
tern countries have banned Russian airlines from their airspace. Russian
authorities have reciprocated by banning Western airlines from their own
airspace, which resulted in longer flights4between Europe and Asia and
between North America and Asia.
Measuring and monitoring aviation emissions is complex. A growing
number of studies have investigated different methods to accurately esti-
mate CO
2
emissions from the aviation sector. Top-down estimates rely on
global kerosene fuel sales and usage, e.g. from the International Energy
Agency5. Such estimates have the advantage of being comprehensive but
they take several months to years to become available and include military as
well as some non-aviation usage. They also do not provide much infor-
mation on how fuel is used and on the geographical distribution of CO
2
emissions. Bottom-up estimates, based on actual flight movements, are
increasingly preferred6–8as they provide more accurate information on the
location of the emissions and non-CO
2
impacts than top-down estimates.
However bottom-up approaches require an accurate knowledge of the
global air traffic, which is a challenge because databases of flight movements
are incomplete in ways that are not well documented.
1Institut Pierre-Simon Laplace, Sorbonne Université / CNRS, Paris, France. 2Department of Meteorology, University of Reading, Reading, UK.
e-mail: gregoire.dannet@ipsl.fr
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The most common method to reconstruct trajectories, knowing the
departure and arrival airports of each flight, is to assume a geodesic tra-
jectory (also called great circle) between airport pairs. As there are, on
average, 90,000 flights per day, this method has the advantage of being
computationally efficient. Some studies use a correction factor to account
for the extra distance flown during the landing and takeoff phases and for
other air trafficinefficiencies9. However, this factor is based on distance
flown alone and does not account for the positive impact of tailwinds and
the negative impact of headwinds on flight time. Thus it can only be correct
on average as it does not take into account flight-specific adjustments made
by airlines to best exploit the wind patterns. The correction factor is also not
adjusted for the case of large airspace restrictions, which leaves CO
2
emis-
sions underestimated. Boucher et al.10 introduced a simple method to
compute time-optimised trajectories that proved to provide a reasonably
good estimate of flight times and trajectories when compared with actual
trajectories recorded from more than 1000 flights participating in the In-
service Aircraft for a Global Observing System (IAGOS) programme11.In
this study, we have extended the optimisation algorithm by Boucher et al.10
to take into account airspace restrictions and applied this algorithm to a
global database of flight movements in order to estimate the impact of major
airspace restrictions on flight trajectories and the associated increase in CO
2
emissions. We focus on major, country-wide airspace closures related to
international conflicts and sanctions because they are long-lasting and well-
documented. Specifically, we identify the flights that are potentially affected
by an airspace restriction. Then, we quantify the impact of the airspace
restriction by comparing the CO
2
emissions of the time-optimised trajec-
tories with and without the airspace restriction. Finally, we compute the
additional CO
2
emissions that are attributable to airspace restrictions and
present the results in the context of global air traffic.
Results
Table 1summarises the impacts of several airspace restrictions considered
in this study. The avoidance of the airspace of Libya, Syria, and Yemen
affectsoftheorderof60–100 flights per day each and leads to average
consumption increases of 2.7, 2.9, and 4.3%, respectively. As this represents
a relatively small fraction of daily flights, we focus the rest of this study on the
consequences of the Russo-Ukrainian war because the associated airspace
restrictions have been affecting a large number of flights for a long period of
time. In addition, the average distance of the affected flightsislargeand
consequently, the increase in fue l consumption isexpected to belarge as well
since fuel consumption is a quadratic function of the distance flown.
Approximately 1000 and 800 flights are affected daily by the avoidance
of the Ukrainian and Russian airspaces, respectively, on average during the
period March 2022 to December 2023. Over that period, we analysed
750,000 flights, representing a total of 1100 flights per day because a large
fraction of long-haul flights are affected by both airspace restrictions. Fig-
ure 1shows the time series from 2019 to 2023 of the number of Western
Airlines routes whose shortest trajectory crosses the Ukrainian or Russian
airspace, alongside the Russian Airlines routes whose shortest trajectory
crosses the European Union airspace. Western flights began to avoid Rus-
sian airspace shortly before the restriction was introduced. Air trafficthen
gradually recovered as airlines (and their passengers) adapted to the new
Table 1 | Statistics of the impact of the five airspace restrictions considered in this study, over the period March 2022 to
December 2023 on average, in terms of numbers of flights impacted per day, average flight distance without restriction, average
increase in flown distance and consumption per flight caused by the airspace restriction
Airspace Restriction Average number of flights impacted
per day
Average flight
distance (km)
Average distance
increase (%)
Average consumption increase (%)
Ukraine 984 7885 5.3 7.9
Russia 809 8336 5.5 8.0
Libya 103 6800 2.0 2.7
Syria 100 5000 2.5 2.9
Yemen 60 4970 5.5 4.3
The comparison was made between two optimised flights, one affected by the restriction and the other not affected by the restriction. The impact of airspace restrictions over Ukraine and Russia are shown
on two different lines but include a large number of flights affected by both.
Fig. 1 | Monthly average of total daily international flights and daily international
flights affected by airspace restrictions for Western and Russian airlines. Average
daily total international flights (red lines, right axis) of aWestern airlines and
bRussian airlines over the period 2019–2023. The black lines show the corre-
sponding average daily number of flights whose shortest trajectory crosses athe
Ukrainian and Russian airspaces and bthe European Union airspace.
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situation. This was not the case for the number of Russian international
flights, which plummeted as a result of the restrictions and never recovered
the following year. Figure 1also shows the number of all international flights
for Western and Russian airlines (red lines). A small decrease in interna-
tional flights is visible for Western airlines and can be attributed to the
airspace restriction, but this did not last, and overall, air traffic continues to
recover from the Covid-19 crisis in 2020. Russian international flights have
been more affected as the total number of international flights decreased and
never returned to pre-war levels. Most of the remaining Russian flights are to
destinations that do not have to fly through these airspace restrictions.
Russian airlines also swapped their European destinations for destinations
in the Middle East and Asia (see Supplementary Fig. S3).
Figure 2shows optimised and actual IAGOS trajectories for a European-
Japanese city pair in 2022, without the restriction (i.e., before March 2022)
and with the restriction (i.e., after March 2022). For both cases and directions,
the optimised flight trajectories and flight times are in reasonable agreement
with actual IAGOS data. In particular, the selected Lufthansa flight bypassed
Russia on its southern side for the outbound flight from Frankfurt-am-Main
to Tokyo and over the Arctic for the inbound flight. On average for the 294
IAGOS flights affected in 2022 and 2023, our optimised trajectories (for the
cruising phase) are 0.24% faster than actual flight times (see Supplementary
Fig. S5). It is conceivable that airlines have adjusted the airspeed, the altitude
or the payload of their aircraft for the longer routes, with possible impacts on
thefuelconsumption.Wehavecomparedtheaverageairspeedandaltitudeof
IAGOS flights from the years 2021 and 2022 before and after the Russo-
Ukrainian airspace restriction, but have observed only small differences for
these parameters (see the supplementary Section S5 for more details). This is
expected as aircraft are designed and optimised to flyatapredefined Mach
number and altitude range12. It is possible that the airlines have decreased the
aircraft payload to offset some of the additionalfuelconsumptionduetothe
longer routes, but we do not have the necessary data to confirm this
hypothesis. It should be noted, however, that the impact of the additional fuel
carried on the fuel consumption itself is already included in our calculation
through the quadratic equation from Seymour et al9. As the sub-optimality of
the IAGOS flights is similar in the absence of airspace restriction10,weare
confident that our method provides a very good estimate of the flight time
and, therefore, the fuel overconsumption. The additional flight time and fuel
consumption of the affected flights vary greatly depending on the extent to
which they would have crossed the restricted airspace. We illustrate this by
showing the spatial distribution of the emissions in Fig. 3. The restriction
forced all flights of Western airlines to follow similar trajectories on the
Europe-Asia and North America-Asia routes. The densest areas are in the
corridor south of Ukraine and north of Japan.
We used the K-means clustering method to categorise the affected
flights into different classes. The elbow method of this K-mean clustering
suggests that splitting the flights into four classes is optimal, highlighting
outbound and inbound routes between Europe and Asia and between Asia
and North America (see Supplementary Fig. S7). Over the period March
2022 and December 2023, on average, 67% of the affected flightswereonthe
Europe-Asia route, while the remaining 33% were on the Asia-North
America route. The histograms of the relative changes in flown distance,
flown time and fuel consumption with and without airspace restriction are
showninFig.4. Flights for which the difference in flown time with and
without the airspace restriction was lower than 1% were considered as non-
impacted and removed for our analysis (they accounted for around 11% of
the pre-selected flights as we made sure to select all flights that could be
impacted). The large majority of affected flights experience an increase in
flown distance ranging from 1% to 20%. However, a small subset of flights
shows a decrease indicating that certain flights had shorter distances due to
the imposed restriction. This is expected as our algorithm optimises the
flight duration and not the flight distance. For those flights, the trajectory
that crossed the restricted airspace had a longer distance but was better
optimised in terms of flight time than the trajectory that avoided the
restricted airspace. The histogram of the flight time fractional increase is
similar to that of the flight distance increase except for its lack of negative
values. In comparison, the histogram of the fuel consumption fractional
increase is shifted towards larger values, with most increases ranging from 0
to 30%. Even larger increases are possible, corresponding to flights having to
cope with both a large increase in flown distance and an unfavourable wind
pattern on their new route.
The distinction between the European and the North American routes
is worth noting (Fig. 4), with a smaller impact on the North American routes
Fig. 2 | Flights trajectories between Tokyo and Frankfurt-am-Main, before and
after the airspace restriction. Flight from Tokyo (HND) to Frankfurt-am-Main
(FRA) aon 7 January 2022 (i.e., before the airspace restriction) and bon 13 April
2022 (i.e., after the airspace restriction) and flight from Frankfurt-am-Main (FRA) to
Tokyo (HND) on c2 January 2022 and don 10 May 2022. The geodesic path (or
great circle) between the two airports is shown in black. The computed optimised
trajectory is in blue, and the actual trajectory from IAGOS in red. The wind pattern at
250 hPa is shown with the black arrows. The restricted airspace is shaded in grey. The
optimised and actual cruising times (in decimal hours) are also displayed in the
headers.
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compared to the European ones. The average increase in consumption is
calculated at 13% for all the flights but is 14.8% for the European flights and
9.8% for the North American ones on average. The direction of the route
also has a substantial impact on the fuel consumption. The Ukrainian and
Russian restrictions lead to an average increase of 11.8% of CO
2
emissions
for North American routes to Asia, in comparison to an increase of 7.5% for
routes from Asia to North America. The average increase reaches 16.8% for
flights from Asia to Europe compared with 12.7% in the reverse direction.
Flights from North America to Asia and flights from Asia to Europe are
being forced to take trajectories with strong headwinds more often,
increasing their flying time and, therefore, consumption.
Finally, we put the impacts of airspace restrictions into the context of
the broader framework of global aviation CO
2
emissions. For the sake of
computational efficiency, we follow the standard practice6,7,9,13 for trajec-
tories not affected by airspace restriction and estimate fuel consumption
based on the geodesic distance between airport pairs rather than considering
actual or optimised trajectories. We compute an increase in global aviation
CO
2
emissions of less than 0.2% for the Libyan, Syrian and Yemen
restrictions in Table 1. The Russo-Ukrainian restrictions led to an increase
of 0.5% in 2022, rising to 1% in 2023, which corresponds to additional
emissions of 8.2 MtCO
2
per year. The increase in 2023 can be attributed to
the fact that restrictions were in place throughout the entire year, and routes
had gradually reopened compared to 2022. Such an increase is remarkable
given that only 1100 flightsareimpacteddailyonaverage.Thisisbecause
these flights are among the longest flights worldwide, and even though they
account for a small percentage of the flights, they account for a dis-
proportionally large fraction of the emissions. On average, a deviated flight
emits 18 extra tons of CO
2
, roughly equivalent to the emissions of one single
short-haul flight. Non-CO
2
emissions have almost certainly increased
as well.
Fig. 4 | Distance, time and consumption variations
for flights affected by the Russo-Ukrainian air-
space restriction. Histograms of the fractional
increases in the flight distance, flight time, and fuel
consumption for trajectories with airspace restric-
tion compared to those without. Only flights affec-
ted (considered if a flight crosses the Ukrainian and
Russian airspace restrictions) are considered. The
histograms are shown separately for the four clusters
of routes: North America to Asia (NA →AS, grey),
Asia to North America (AS →NA, blue), Europe to
Asia (EU →AS, red) and Asia to Europe (AS →EU,
green). The bins range from −0.1 to 0.7 with a step of
0.05 (i.e., the [0,0.05] bin is located on the right-hand
side of label 0).
Fig. 3 | Change in-flight track density for flights
affected by the Russo-Ukrainian airspace restric-
tion. Change in-flight track density (km km−2) for
the flights affected by the Russo-Ukrainian airspace
restriction in April 2023, computed as the difference
between flight trajectories with restrictions minus
those without restrictions.
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Our approach has several limitations that are sources of uncertainties.
First, it should be noted that the fuel estimation model takes into account the
aircraft type but not the specific engines mounted on the aircraft, as this
information is not present in the database. As the model is a linear regression
of several flights, it cannot be considered as being accurate for a specific
flight. Seymour et al.9estimated the error in fuel consumption to be below
5%. Secondly, Boucher et al.10 acknowledge that some routes are better
optimised than others. Some flights may have operational constraints that
are not considered in the optimisation. Consequently, the optimised flight
timewillbesmallerthantheactualflight time in these cases, which in turn
will lead to a minimisation in fuel consumption and CO
2
emissions. Thirdly,
the flight database of FR24 is one of the most complete databases of aircraft
movements according to Quadros et al.7. However, the completeness of the
database cannot be ascertained, and lack of operator information in the
database can also lead to missing some flights in the study. Less than 2% of
the flights considered are missing operator data, which makes it impossible
to know the restriction that applies to these flights. Our study may be
missing affected flights by these restrictions. For all these reasons, we can
safely say that our study provides a lower bound of the impact of airspace
restrictions on CO
2
emissions. Lastly, air traffic in 2022 and 2023 was still
recovering from the COVID-19 pandemic. The longer the restriction
remainsinplace,themorethetraffic will rebound, and the greater the
impact will be on CO
2
emissions.
In conclusion, the Russo-Ukrainian war has undoubtedly affected
flight efficiency and contributed to an increase in CO
2
emissions by Western
airlines in a sizeable manner. However, this is not the only impact on global
aviation. There is also an apparent reduction in Russian international flights,
which may have led to some avoided emissions. There is also a likely impact
on the seat offer for direct flights between Europe and Asia and a transfer of
air traffic to other routes. In fact, non-stop flights gradually resumed after
the airspace restrictions but have not reached their pre-COVID-19 levels.
Since layover flights between Europe and Asia have become even more
economical compared to direct flights, it is likely that more passengers
choose to fly through one of the Middle East hubs. If more efficient air traffic
management can indeed contribute to the reduction of aviation CO
2
emissions, the current geopolitical situation presents a major obstacle to the
achievement of such a reduction.
Methods
Dataset
Aviation CO
2
emissions are calculated from a global reconstruction of air
trafficbasedontheFR24flight database. The dataset that we purchase from
FR24 consists of a list of flights characterised by their departure and arrival
airports, aircraft type, airline and flight number, and the latitude-longitude-
altitude coordinates of up to six datapoints of their trajectory: departure gate,
take-off, start of the cruise, end of the cruise, landing and arrival gate. The
data were pre-processed by FR24 using their proprietary code. This pre-
processing is required to assign the origin and destination airports of the
flights as the raw ADS-B data do not contain this information. We further
process a flight if the aircraft has been detected to be in flight at some point,
i.e. if at least one of the take-off, the start of the cruise, end of the cruise or
landingpointsisavailable.Thisisdone to avoid processing non-existent
flights for which an ADS-B signal could have been received at the airport,
but the aircraft did not actually fly. We have compared the FR24 database
with a sample of the EuroControl database for flights arriving and departing
from CDG and ORY airports in Paris for selected days and found a very
good agreement on the number of flights. However we cannot ascertain the
completeness of the FR24 database at the global scale.
Identification of restrictions
Since FlightRadar24 does not provide us with sufficient data points to
reconstruct the flight trajectories and because we also need to estimate the
trajectories that the aircraft would have taken in the absence of airspace
restrictions, we reconstruct the flight trajectories using the trajectory opti-
misation algorithm by Boucher et al.10 and the actual wind field from
ERA514. The Boucher et al. algorithm is too computationally expensive to be
run for all flights in our database. Instead, we first seek to identify the subset
of flights that are potentially affected by the different airspace restrictions in
the years 2022 and 2023. We focus on major country-wide airspace
restrictions around the world rather than small or partial restrictions (e.g.,
military space within a country or restrictions below a certain flight level).
Table 2provides a list of airspace restrictions considered in this study on the
basis of information from airspace safety websites15–17, news websites18–20,
and Wikipedia21, which we corroborated by analysing live air traffic
web sites22.
Boucher et al.10 showed that flights might deviate significantly from a
great circle to benefit from favourable winds, which increases the flown
distance relative to the ground but reduces fuel consumption. Thus it would
be incorrect to simply consider flights whose great circle between departure
and arrival crosses a restricted airspace. In this study, a flight was considered
to be potentially impacted if the geodesic trajectory between the departure
and arrival airports crosses either the restricted airspace itself or a 1° band
defined around it by a dilation morphological operation on the country
mask at 1° resolution. This identifies potential flights whose geodesic tra-
jectory does not cross the restricted airspace but whose time-optimised
trajectory might. A sensitivity test showed that increasing the size of the
restricted airspace further did not result in additional potentially affected
flights. Finally, the flight number was further used to identify the airline and
determine whether a particular airspace restriction applies or not to
that airline.
Aircraft classification
To focus on civil aviation, we screen out all non-commercial planes.
Aircraft technical data were extracted from the ICAO documentation23
using the aircraft type provided by the FR24 database. We renamed the
aircraft codes to their respective ICAO codes as described in Supple-
mentary Table S1. Supplementary tables are available in Supplementary
Data. Small aircraft (mono-seater, two-seater, gliders, etc.), helicopters
and some fighter aircraft were identified from the database. Specifically,
helicopters were identified based on a wingspan of 0, small leisure aircraft
based on a ceiling lower than 20,000 feet and a maximum take-off weight
(MTOW) lower than 5 tonnes, military aircraft based on a ceiling higher
Table 2 | Airspace restrictions considered in this study
Airspace restrictions Period Airlines affected Sources
Ukraine 24/02/2022-to date All airlines 15,17–19,21
Russia 01/03/2022-to date Western airlines 16,18–20,22
Western countries 01/03/2022-to date Russian airlines 15,19,22
Libya 2014-to date All airlines 15,21,22
Syria 2014-to date All airlines 15,21,22
Sudan 15/04/2023-to date All airlines 15,21,22
Yemen 10/07/2023-to date All airlines 15,21,22
The list of Western and Russian airlines affected by the restrictions is given in the supplementary Table S5 and Table S6, respectively.
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than 51,000 feet and a passenger capacity of 1 or 2. It would have been
useful to estimate CO
2
emissions from military aviation, but most mili-
tary flights are missing from the FR24 database so we prefer to ignore
them and focus on civil aviation only. A flowchart of the aircraft classi-
fication is available in Supplementary Fig. S1. Small aircraft and heli-
copters represent 12% of the flights in the database but correspond to less
than 2.5% of the distance flown. This category is later referred to as
General Aviation.
For the analysis, we differentiated business jets from commercial air-
craft. Business flights were separated from commercial flights based on their
number of passengers (lower than 25), their MTOW lower than 50 tons, and
their ceiling between 20,000 and 50,000 feet. Commercial aircraft were
divided into two categories, narrowbody and widebody, based on their
passenger capacity below or above 250, respectively.
Fuel consumption calculation
We compute the CO
2
emissions of each individual flight using the Fuel
Estimation in Air Transportation (FEAT) of Seymour et al.9for the flights
that are not affected by the airspace restrictions and a variant of that method
for the flights that are affected. The FEAT model consists of a reduced order
fuel consumption model, based on the Eurocontrol performance model, to
compute the fuel consumption of a flight with only the origin-to-destination
distance and the aircraft type as input. The fuel estimation model considers a
small deviation from the geodesic distance (also known as the great-circle
distance) to account for the take-off and landing phases at the departure and
destination airports, minor airspace restrictions and other air trafficman-
agement inefficiencies. The flight path distance d
fp
is approximated as:
dfp ¼1:0387 dgc þ40:5ð1Þ
where d
gc
is the great circle distance between the origin and destination
airports, and all variables are expressed in km. A detailed model is then used
to compute the fuel burned as a function of this corrected distance for a set of
different aircraft using the Base of Aircraft Data (BADA24)fortheclimb,
cruise and descent and the ICAO database25 for the landing and take-off
(LTO) cycle. These calculations are then fitted by a polynomial function that
expresses the fuel burned as a function of the distance d
gc
where the
coefficients α
i
,β
i
and γ
i
are estimated from least squares regression for each
aircraft type i:
Fi¼αid2
gc þβidgc þγið2Þ
It should be noted that Eq. (2)isafunctionofd
gc
and already includes the
effects of deviations. It does not consider how atmospheric winds may
decrease or increase fuel consumption; thus it has to be understood as valid
on average only and on the basis of a return flight, since inbound and
outbound flights are treated similarly although they may experience dif-
ferent average wind patterns. It does not describe either variations in fuel
consumption due to differences in payload.
Fuel burned can then be converted to CO
2
emissions using the usual
CO
2
emission factor for kerosene of 3.16 kg CO
2
/kg fuel. This method does
not estimate how the emissions are distributed along the flight route. While
the ADS-B technology makes it possible, in principle, to know accurately
each trajectory, computing the CO
2
emissions along the trajectory would
require a large amount of data that is not readily available given the
approximately 90,000–100,000 flights per day across the world. Therefore,
using a fuel estimation model with the geodesic trajectory and a scaling
factor is an acceptable and computationally efficient solution to perform a
bottom-up estimate of aviation emissions, provided that corresponding
uncertainties are accounted for.
We map the aircraft types onto the 133 aircraft types available in the
Seymour et al.9study. We have complemented the database by assigning an
equivalent aircraft (available in Seymour et al.) to a range ofaircraft based on
BADA. The list of equivalent aircraft assigned to aircraft missing from the
Seymour et al. database is available in the supplementary Table S2. For
aircraft with no equivalent in the Seymour et al. study, average coefficients
have been computed for categories of commercial aircraft and business jets,
knowing the different categories of each aircraft in the Seymour et al.
database (see supplementary Table S3 and Table S4). For flight data that do
not contain any indication of aircraft type, average coefficients from all
aircraft considered in the Seymour et al.studyhavebeenused.Thesedefault
values were applied to fewer than 0.6% of the flights. A flowchart of the
aircraft fuel consumption calculation is available in Supplementary Fig. S2.
For the consumption calculation of flights affected by restricted air-
space, the algorithm by Boucher et al. was modified to include a large penalty
for flight segments that would cross a restricted airspace, which pushes the
optimal trajectory outside the restricted airspace. Initial conditions for the
trajectory optimisations were also modified to exclude the restricted
airspace.
For each flight potentially affected by an airspace restriction, we compute
two time-optimised trajectories that both account for the wind patterns, one
that takes into account the airspace restriction and one that does not. Fuel
consumption and the associated CO
2
emissions are computed with the fuel
consumption model of Seymour et al. which we slightly modified to account
for detours and the wind pattern. The correction consists of feeding the
Seymour et al. model with a flight distance corrected in proportion to the ratio
of the optimised flight time to that of the geodesic trajectory:
dcorrected ¼dgeodesic toptimised
tgeodesic
ð3Þ
In this way the fuel consumption for the trajectory with airspace restriction
is always equal or greater than without restriction, which would not have
beenthecasehadwesimplyusedthegeodesicdistanceasacomparison
point. Emissions are then calculated as previously using the factor of 3.16 kg
of CO
2
emitted per kg of kerosene burnt26.
Data availability
The flight database cannot be openly shared due to the terms of the licence
agreement with FlightRadar24. The IAGOS data can be downloaded from
the IAGOS data portal (10.25326/20).
Code availability
The fuel estimation model is a straightforward implementation of https://
doi.org/10.1016/j.trd.2020.102528. The trajectory optimisation algorithm is
described in 10.3390/aerospace10090744 and available from https://github.
com/OB-IPSL/FlightTrajectories. The Python codes used to perform the
analysis are available on request from the corresponding author.
Received: 10 May 2024; Accepted: 6 December 2024;
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Acknowledgements
This research has been supported by the French Ministère de la Transition
Ecologique et Solidaire (grant No. DGAC N2021-39), with support from
France’s Plan National de Relance et de Résilience (PNRR) and the
European Union’sNextGenerationEU.
Author contributions
G.D: Computing, Investigating, Analysing, Writing. O.B: Investigating,
Writing. NB: Writing. All authors contributed to the paper.
Competing interests
O. Boucher receives consulting fees as a member of the Stakeholder
Committee of Groupe ADP. The remaining authors declare no competing
interests.
Additional information
Supplementary information The online version contains
supplementary material available at
https://doi.org/10.1038/s43247-024-01956-w.
Correspondence and requests for materials should be addressed to
Grégoire Dannet.
Peer review information Communications Earth & Environment thanks
Arturo Benito, LiudmylaMalytska and the other, anonymous, reviewer(s) for
their contribution to the peer review of this work. Primary Handling Editors:
Pallav Purohit and Martina Grecequet. A peer review file is available.
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