1. Introduction
In recent decades, with the exception of a huge decrease during the COVID-19 crisis, demand for air travel has been growing every year, raising environmental concerns since it contributes to the increase in greenhouse gas emissions and thus to anthropogenic radiative forcing, with both
and non-
emissions. While other industries, including those within the transport sector, have been better able to partially decarbonise, aviation faces serious challenges. The pledge to achieve net-zero emissions by 2050 is based on technological solutions [
1,
2], which are not currently available, sustainable aviation fuels [
3], whose production is still too low for the demand, and carbon compensation mechanisms or offsets [
4,
5], which have received increasing criticism [
6]. The goal thus appears unrealistic without curbing, or at least stopping, the continued rise in air traffic.
This concern has become more evident recently, even at a political level. For example, in 2023, during the negotiations for the appointment of the Prime Minister of Spain, Pedro Sánchez, it was agreed to include the provision to eliminate short flights if a train alternative of no more than 2.5 h is available in an attempt to reduce aviation-related greenhouse gas emissions [
7]. There was no mention of how this 2.5 h threshold was determined, but it corresponds to that applied in France since 2023 [
8]. Even within the industry, major airlines are now offering integrated tickets to circumvent short-haul flights, replacing them with rail when stopovers are required [
9].
Over the past decades, research and industry efforts have mainly concentrated on quantifying aviation’s carbon footprint, while non-
emissions have received comparatively little attention despite their substantial environmental impact. The climate effects of aviation’s non-
emissions, particularly contrails, regarded as the most significant non-
contributor, are at least as relevant as those of
itself and may even triple the overall climate impact of a single flight [
10]. These pollutants are released at cruising altitudes of up to 13 km, where they directly influence the atmosphere, with their effects being highly dependent on dynamic meteorological conditions [
11]. In addition to their climate implications, non-
emissions also have serious consequences for air quality and human health. While decarbonization strategies in aviation have largely targeted
reduction, addressing non-
pollutants should also be prioritized, particularly to protect the health of the population living close to airports [
10].
In 2020, the European Commission requested the European Union Aviation Safety Agency (EASA) to deliver an updated assessment of aviation’s non-
impacts on climate change, in line with the requirements of the EU’s Emissions Trading System (ETS) directive [
12]. The report examined potential financial measures, such as imposing monetary charges on aircraft NO
x emissions and/or including these emissions within the EU ETS. A key finding was the urgent need for a reliable, internationally harmonised methodology to estimate cruise NO
x emissions. By the end of 2027, the European Commission is expected to publish the results of its monitoring, reporting, and verification system for non-
aviation impacts, and if deemed appropriate, to introduce a legislative proposal addressing these effects [
12]. Nevertheless, practical tools for assessing non-
emissions remain scarce or highly complex. For example, Lee et al. employed an extensive multi-sheet spreadsheet, covering contrail cirrus,
, NO
x, water vapour, sulfate and soot aerosols, and corresponding
-equivalent metrics, to estimate the contribution of global aviation to anthropogenic climate forcing [
13].
Some available models to assess aviation emissions were reviewed in [
14]. Most of these models use constant average seat numbers, depending on the flight distance, or only a few aircraft types to build their models, such as the International Civil Aviation Organisation (ICAO) Carbon Emissions Calculator [
15].
Many alternatives can be found in the literature for the estimation, with high precision, of fuel consumption (and hence emissions) for individual flights. These estimators, based on a set of operational parameters, rely on complex and often closed models. For example, many employ simulators that use EUROCONTROL Base of Aircraft Data (BADA) models, which require licensing and limit their use in terms of potential comparison of aircraft models [
16]; others are based on actual fuel consumption recorded by the flights, stored in their Quick Access Recorder (QAR) [
17], and reported by the Aircraft Communications Addressing and Reporting System (ACARS) [
18]. The models usually need, among other things, information on aircraft performance (aircraft type) and path profiles [
19], real track data [
20,
21], or detailed trajectories, incorporating weather conditions [
22,
23]. Due to their complexity, they might even only focus on a part of the flight, such as the climbing phase, as in [
17]. In general, high accuracy can be obtained, even considering uncertainties, but with the need for many parameters that might not be available at the strategic level when details on the operations are limited (e.g., only the distance between airports considered, and not the actual route (or 4D trajectory), is available). Very importantly, these are models that are closed and therefore not readily available to the community.
EUROCONTROL released a web-based modelling platform, IMPACT [
24], for the calculation of detailed 4D trajectories for user-defined aircraft operations, providing information on engine thrust and fuel flow estimated using BADA [
25]. This system enables the estimation of the environmental impact of aviation (in terms of emissions) but still requires a small set of operational details, such as distance flown and aircraft type. IMPACT has many advantages: it requires a limited set of parameters, circumventing some of the limitations of the previously described models and enabling the evaluation of use cases even for planning and strategic analysis; it relies on state-of-the-art BADA performance models; and it is backed up by an internationally recognised institution (EUROCONTROL). These considerations mean that the obtained estimations can be broadly considered as acceptable by relevant stakeholders. However, being a web-based platform, it cannot be integrated into external modelling tools, and as it relies on BADA, some of their licensing limitations still apply. IMPACT was used in previous research to generate generic models for the estimation of emissions as a function of distance and seats in the aircraft for short- and medium-haul flights, as reported in [
14].
In recent years, other models have been presented, such as the Fuel Estimation in Air Transportation (FEAT), a reduced-order fuel consumption approximation with the origin-destination airport pair and aircraft type as inputs, enabling the estimation of fuel consumption for global scheduled aircraft movements described in [
26]. This is a simplified model that enables quick computation of fuel usage per route, in a similar manner to how it is developed in this article, but it still requires the consideration of actual individual aircraft types. As shown in this article, we generalise the emissions by implicitly considering the aircraft type using the number of seats available as a proxy, bringing some significant benefits.
Finally, it is worth noticing how other alternatives for the estimation of emissions are also available, such as airline emission calculators. These might, however, present some limitations on their integration with other models and on the analysis of their underlying assumptions. In any case, a recent study shows the importance of uncertainty estimation among existing models, since they use different degrees of approximation and assumption [
27].
The consideration of the number of seats and the type of flight, based on its distance, is essential to comprehensively evaluate the environmental impact of different modes of transportation. This can be used for the estimation of the emissions associated with providing an amount of supply between a given origin and destination [
28]. This enables the evaluation of policies and multimodal networks [
29].
With all these considerations, this article provides a set of analytical models to estimate emissions (
and non-
) for the total trip (gate-to-gate) using as input only the
flight distance(great circle distance) and
number of seats. This allows for the estimation of fuel consumption even when the aircraft type is unknown, for example, in applications of the substitution of air travel by rail. The models also support sensitivity studies concerning the number of seats and can be used for analysing different transportation modes, considering carbon emissions costs, as studied in [
30]. Other applications include the strategic consideration of new operations, such as the splitting of flights with an intermediate stop for refuelling to increase fuel efficiency by shortening the stage length of a mission, as shorter stage lengths allow for a reduction in the amount of fuel and therefore the weight of the aircraft and the kerosene burnt [
31]. The small number of inputs supports the analysis of these aspects even when limited information is available. To consider uncertainties associated with the operations, corrections are applied, e.g., considering flown distances longer than the great circle distance, or the actual aircraft performance considered to fit the model. The selection of modern aircraft models, as reported by their historic usage, means that the emissions models reported in this article can be considered valid for current and future operations.
This article does not aim to create a new set of models to estimate fuel consumption based on detailed trajectories or to validate the model with reported fuel usage. Instead, it relies on the community-accepted estimations from IMPACT. It develops a metamodel that generalises the results from IMPACT to require only two variables: the great circle distance between origin and destination and the number of seats in the aircraft. The fitted models are therefore validated against the goodness of fit with respect to IMPACT. These models are parsimonious in that they rely on few variables [
32] and effective because they are analytically tractable, physically realistic, and conceptually insightful [
33]. As such, they are particularly well suited for strategic analysis in air transportation, providing system-level insights that might be obscured by details while requiring only limited input information.
A first model estimates the total fuel consumption from which greenhouse gases (GHG) proportional to this fuel can be computed (namely carbon dioxide (), sulphur oxide (SOx), and water vapour). Then, additional models are generated fitting the results from IMPACT on other non- emissions that are not proportional to fuel (nitrogen oxide (NOx), carbon monoxide (CO), and non-volatile particulate matter (nvPM)).
Note that the models provide an estimate of the
and non-
emissions but do not provide an estimate of the impact of aviation on climate (for example, as equivalent radiating force), as that is beyond the scope of these models. For that, the consideration of dynamic weather conditions should be included [
11].
In this work, we thus propose indicators that can easily be used to evaluate the totality of flight emissions. Specifically, we develop the theoretical framework for the models and showcase their applicability. The article is structured as follows. First, the data and methodology used to estimate the fuel and emissions from IMPACT are described in
Section 2. This section includes all assumptions and correction factors used to generate full trip fuel and emission estimations from only the great circle distance. Then, the fitting of the analytical models for fuel (and emissions proportional to fuel) and for other non-fuel proportional emissions is described in
Section 3. This section also includes a comparison of the results obtained with the goodness of fit with respect to IMPACT and the comparison with other models. Finally, the article presents a case study demonstrating the capabilities of the produced models to analyse all scheduled commercial flights departing or arriving in Spain on a given day (in
Section 4) and closes with conclusions in
Section 5.
4. Case Study
All analytical models described in
Section 3 can be found for direct use in a GitHub repository [
58]. They are coded both in Python 3.10 and in MATLAB R2024b, with the inclusion of the models’ ranges of application.
To show the applicability of these models, we analyse a case study considering all scheduled commercial flights departing from or arriving in Spain on 6 September 2019, based on data from the Official Airline Guide (OAG). The objective is to estimate total , NOx, and CO emissions. This approach allows for the evaluation of emissions in relation to commercial variables that influence airlines’ strategic decisions on aircraft acquisition and network design, particularly regarding aircraft size, flight frequency, and route distance.
On the selected date, 5038 flights were operated from or to Spain between 278 airports, consuming 34,160 tonnes of fuel and emitting, considering only tank-to-wheel emissions, a total of 107,945 tonnes of , 528 tonnes of NOx, and 68 tonnes of CO.
Figure 7 presents the Cumulative Distribution Function (CDF) of
, NO
x, and CO, and compares then with the CDF of flights and ASK. The analysis shows that 82% of flights to or from Spain occur on routes shorter than 2000 km. These account for 45% of total ASK and 43% of
emissions. When the threshold is extended to 4000 km, the cumulative shares rise to 95% of flights, 66% of ASK, and 60% of
emissions. These figures indicate that only 5% of flights realised long-haul routes that day (i.e., longer than 4000 km), yet they generated 34% of total ASK and 40% of
emissions. This value is slightly lower than what was observed in [
59], considering passenger flights from 31 European countries, but still implies a relatively concentrated share of emissions from a small fraction of flights, despite their limited frequency.
For other pollutants, the distribution patterns are somewhat different. NOx emissions closely mirror emissions for flights under 2000 km (40% vs. 43%, respectively). However, they diverge at longer distances. Between 2000 and 4000 km, NOx accounts for 14% of emissions (compared to 17% for ), while flights over 4000 km contribute a larger share of NOx (46%) than (40%). This reflects the fact that cruise phases, longer in long-haul operations, are key contributors to NOx formation. CO emissions are even more concentrated in short-haul segments: % occur on flights under 2000 km and % under 4000 km. This underlines the strong impact from take-off and climb phases on CO formation and the inefficiency of short sectors in terms of local air quality.
Although flights between 2000 and 4000 km exhibit relatively higher emission efficiency, short-haul flights remain a major contributor to overall emissions due to their high volume. In this range, operational efficiency has led to a more competitive service and an increased demand, as Jevons’ paradox states. In the range above 4000 km, we can observe that a small share of long-haul operations contributes disproportionately to total emissions, which is a structural feature of the air transport system with implications for policy and network design. It is definite that the cumulative evolution of emissions aligns more closely with ASK than with the number of flights, across all pollutants and fuel consumption.
The same case study is represented by an origin–destination (OD) matrix of flight frequencies, associated distances, and aircraft sizes. Fuel consumption is estimated as a function of aircraft size and distance, and shows the pattern in which fuel per ASK decreases up to approximately 100–120 seats and increases thereafter, as already seen in
Section 3. Ignoring airline identity, the analysis now focuses exclusively on the aircraft mix per route to evaluate the potential for emission reductions through fleet reshaping.
Using a continuous approximation model to optimise seat allocations across routes, we propose a new aircraft assignment under ideal regulatory conditions that allows for cross-carrier coordination and the hypothetical adoption of optimal aircraft sizes. Although this scenario is not operationally realistic, as it is implemented across all airlines, it provides a useful upper bound on the potential emission reductions achievable through aircraft resizing. This policy-oriented analysis is facilitated by the use of the continuous models proposed in this article, which avoid the time-consuming task of matching specific aircraft types, often constrained by limited or proprietary data, while allowing for capturing systemic trends and boundary conditions.
For each OD pair, a more efficient aircraft assignment is identified following these rules:
- 1.
For aircraft with fewer than 100 seats, we explore up-gauging opportunities, replacing multiple small aircraft with a smaller number of larger ones to consolidate capacity and reduce fuel consumption. The algorithm sums the total number of seats from the subset of aircraft with fewer than 100 seats (considering only subsets with more than one aircraft) and searches for a minimum fleet of 100-seat (or smaller) aircraft such that the resulting average size is less than or equal to 100 seats.
- 2.
For aircraft with more than 350 seats, typically long-haul wide-bodies or jumbos, we explore down-gauging, splitting high-capacity flights into multiple smaller ones, in line with industry trends favouring fuel-efficient mid-size jets. In this case, the algorithm scans a subset of aircraft with more than 350 seats and explores how to split them into the minimum number of flights with aircraft seating of at most 350 passengers, such that the resulting average seat capacity remains below 350.
Figure 8 shows the distribution of flights on the day of study as a function of their seats and distance. Note that here each dot can represent one or several flights; the flight density is thus further studied with the lateral histograms, showing the number of flights as a function of their distance and of their seats.
Figure 8a shows the original scenario, while
Figure 8b reflects the new scenario after applying the fleet reshaping.
To properly interpret
Figure 8, it is essential to consider the structure of Spanish air mobility, which can be understood by examining the distribution of flights across domestic and international routes. Spain’s national airport network is categorised into four groups: (i) airports on the Spanish Peninsula, (ii) airports serving the Balearic and Canary Islands, (iii) European airports, and (iv) intercontinental airports. The extensive Spanish coastline and the significance of tourism, accounting for
% of national GDP in 2023 [
60], underscore the strategic relevance of air services to and from island regions. It is also relevant to note that most of Spanish flights (67%) are intra-European. These routes are primarily served by aircraft with seating capacities between 100 and 250 seats (average: 180 seats) and with typical stage lengths exceeding 1000 km (average: 1528 km). A small number of these flights are operated with wide-body aircraft, likely reflecting airline-level resource optimisation and fleet utilisation strategies.
On the reference day,
% of flights were operated by aircraft with fewer than 100 seats. These were predominantly deployed on intra-island routes in the Balearic and Canary Islands (51%), followed by short-haul flights within the Peninsula (18%). This operating pattern results in a distinct cluster of flights below 500 km and 100 seats in the seat-distance scatter plot, clearly observable in
Figure 8a. After applying the reshaping strategy, this cluster is substantially reduced in
Figure 8b, as also reflected in the marginal histograms for aircraft under 100 seats.
Intercontinental services accounted for only 9% of total flights, and aircraft with more than 350 seats represented just 1% of operations. These large-capacity flights form a sparse upper band in the scatter plot of
Figure 8a, which disappears after fleet reassignment. Most wide-body aircraft with 250–350 seats operate on routes exceeding 4000 km, contributing to the long right tail observed in both the seat and distance distributions. Despite representing a small fraction of flights, this segment accounts for approximately 11% of total fuel consumption.
Following the proposed aircraft reassignment, the total number of flights is reduced from 5038 to 4986 (−
), using aircraft with larger seat capacities, as observed on the seat histogram of
Figure 8b, which is shifted up with respect to
Figure 8a. This leads to a decrease in the total fuel consumption from 34,160 tonnes to 33,008 tonnes (
), with equivalent reductions in
emissions. NO
x emissions fall by
, and CO by
, reflecting the increased benefit of optimised aircraft sizing for these pollutants.
5. Conclusions
We develop analytical models to estimate fuel consumption and emissions in the aviation sector. These analytical models are a fit to EUROCONTROL’s IMPACT model with a set of operational assumptions. This set of parsimonious models, which rely on very few variables (distance and seats), provide a simplified but accurate estimation of fuel, and key non- emissions. This approach is particularly effective for strategic assessments involving large datasets, as it enables researchers and policymakers to understand the fundamental structure of emissions without requiring detailed flight-level performance data. By focusing on key variables, namely aircraft size and flight distance, the model isolates the core mechanisms of fuel and pollutant output in a scalable and tractable manner. However, it necessarily simplifies the technological heterogeneity of the fleet. Moreover, our analysis focuses on fuel per seat-kilometre and does not capture the role of cargo, a limitation that should be kept in mind when interpreting the results.
While fuel consumption and emissions remain central concerns due to their contribution to global warming, non- pollutants such as NOx and CO are also highly relevant, particularly in relation to public health and local air quality. Applying the same modelling framework to non- pollutants allows comparative assessments across aircraft types and operational profiles and highlights the need for pollutant-specific strategies within broader decarbonization initiatives.
When validating against other aircraft-dependent models, the proposed models show a good level of accuracy, with a slight underestimation since the newest generation of aircraft has been considered to develop these analytical models. The accuracy will thus increase over the years, as the share of these aircraft increases, corresponding to the usual trend of decreasing fuel intensity (emissions per seat-km).
The models are suitable for current and future operations (as new models are assumed when several alternatives are possible) and consider corrections for operational aspects, e.g., horizontal and vertical inefficiencies with respect to great circle distance, which are particularly suited for the European context. The models, however, assume current fuel usage, as the relationship between fuel consumption and emissions is based on conventional jet fuel. If new engines and fuel mix are used (e.g., sustainable aviation fuels or hydrogen aircraft), the model would need to be adjusted to reflect the new relationship between fuel usage and emissions. Other factors, such as corrections due to average winds, could be included in future versions of the model.
We apply the models to a one-day snapshot of Spanish air traffic and identify several significant patterns. Although long-haul flights represent a small share of total operations, they account for a disproportionately large share of fuel consumption and especially NOx emissions. Conversely, short-haul flights operated by small regional aircraft tend to produce higher CO emissions per unit of output. These distinct profiles underscore the importance of size-aware and pollutant-specific analysis.
To explore mitigation potential, we implement a reshaping strategy under idealised conditions, reallocating inefficient aircraft types. The strategy involves consolidating short-haul flights operated by small aircraft into fewer, larger flights (up-gauging), and replacing oversized aircraft on long-haul routes with smaller, more efficient models (down-gauging). This reassignment yields a reduction in total fuel consumption, primarily due to the removal of large wide-bodies, with only a reduction in total flights. NOx and CO reductions are even more pronounced, demonstrating the disproportionate emissions impact of aircraft size.
Finally, while this study emphasises emission intensity, total emissions must also be considered. This can be easily achieved using the analytical models presented here, since they provide system-level insights from both perspectives. The results reveal a persistent structural challenge in aviation: traffic growth continues to outpace efficiency gains, leading to rising aggregate emissions. This highlights the necessity of systemic interventions in addition to technological improvements.