Climate Impact of Optimizing ATM and ATC Procedures for Mitigating CO₂ and Non-CO₂ Emissions

Abstract

A comprehensive multidisciplinary review of recent advances in aviation emissions modeling methodologies and mitigation strategies through optimized in-flight operational procedures, and how they could be considered in evaluating their climatic impact is presented. With reference to the Terminal Maneuvering Area (TMA), the article critically examines current and emerging strategies, particularly those enabled by GNSS-based capabilities and Performance-Based Navigation (PBN), to enhance aircraft efficiency and reduce fuel consumption and associated chemical emissions. The study also explores the state-of-the-art methodologies for modeling both CO₂ and non-CO₂ emissions and addresses the problem of contrails formation, highlighting the main relevant aspects that can be useful for the definition of future mitigation strategies. Furthermore, it analyzes evolving optimization techniques aimed at real-time 4D trajectory planning able to consider the atmospheric conditions, with the overall objective of minimizing the aircraft environmental impact while in flight. Finally, the paper discusses suitable metrics for evaluating both short-term local air quality effects and long-term global climate implications, offering an integrated framework for sustainable aviation operations.

1. Introduction

Aviation has been linked to several negative environmental effects, with aircraft engines being one of the primary emitters of both gaseous and particle pollutants at the airport and throughout the flight [1,2,3]. The physical and chemical characteristics of particle and gaseous emissions in aircraft have been documented by a number of campaigns [4,5,6,7,8]. Pollutants generated by conventional aircraft engines include carbon dioxide (CO₂) and carbon monoxide (CO), nitrogen oxides (NO_x), sulphur oxides (SO_x), particulate matter (PM_2.5 and PM₁₀), aerosols, black carbon (BC), volatile organic compounds (VOCs) [9,10,11,12,13], and water vapor. The latter is also emitted in innovative propelling technologies employing hydrogen, along with nitrogen dioxide when a combustion process is exploited.

Each of these emitted species, including water vapor, can have its adverse effect on both the environment and human health through different interaction pathways. CO₂ as well as other pollutants, particularly sulphur oxides, determine a negative impact on planetary radiative forcing. Aviation-induced cloudiness, arising from water vapor emissions, can have the same effect, even if it does not always eventuate. In other cases, the emitted species can have an adverse impact only in given flight conditions, for instance in proximity of the ground, as the worsening of air quality is determined by carbon monoxide. Nitrogen oxides, highly toxic at elevated concentrations, can exert their harmful action when emitted at low altitudes (tropospheric NOx), as well as in the stratosphere, where they trigger a chain of chemical reactions, ultimately causing the depletion of the ozone layer, possibly determining a positive radiative forcing (stratospheric NOx).

Aviation industry is increasingly focusing on environmental sustainability, with a particular emphasis on reducing emissions, mainly those that contribute to climate change. This paper reviews the approaches applied in Air Traffic Management (ATM) and Air Traffic Control (ATC) to mitigate aviation environmental impact, with a discussion about the pivotal role of metrics. As it will be discussed, it is important and useful to show if and how a given measure reduces environmental impact, particularly when referring to climate. In recent years, both academia and industry have focused on reducing CO₂ and pollutant emissions to achieve immediate improvements in local air quality and long-term climate benefits. The main strategies to reach the target of CO₂ emissions and pollutants reduction rely, in the short-medium term, on propulsion system design updates, the usage of alternative fuels, and route optimization to reduce fuel consumption and related emissions and to allow avoiding already polluted airspace volumes. Over a long-term time horizon, then, the introduction has been envisaged and is actively in development of breakthrough aircraft propulsion configurations, such as the following: (1) intermediate solutions consisting in hybrid powertrains; (2) final target solutions based on full electric propulsion, using new batteries or fuel cells exploiting hydrogen as energy source. Nevertheless, such innovative propulsion technologies, even if able to provide clear and fundamental advantages in terms of strongly reducing (hybrid propulsion) or preventing (full electric) CO₂ and pollutants emissions, emphasized the need for also focusing on non-CO₂ emissions, which can have relevant negative impacts on the climate, because they still lead to the formation of undesired phenomena such as condensation trails (usually named as “contrails”).

In both the CO₂ and pollutants and non-CO₂ emission reduction strategies, a fundamental role is played by the operational aviation management level, i.e., by ATM/ATC operations. This is due to the fact that the planned and executed routes, in terms of their geographical, altitude, and speed-associated requirements, have an impact on the emissions of all kinds resulting from the flight execution. One of the aims of this paper is to analyze the existing and proposed optimization methodologies aimed at achieving aircraft route optimization, at the pre-tactical and tactical level, in order to reduce CO₂ and non-CO₂ emissions, in this way reducing the aviation environmental impact in turn. Such methodologies include the most recently introduced (e.g., Continuous Descent Approach) and emerging (e.g., contrail avoidance) ATM and ATC procedures for route optimization, which will be analyzed and summarized in the paper.

The focus of the paper will be on the air-side operations, while the optimization of ground operations (e.g., electric tug operations) is out of the scope of this work. The paper will provide a comprehensive framework that integrates various optimization models and algorithms to address the complex problem of routing aircraft in a way that minimizes environmental impact. The framework will include time-dependent vehicle routing considerations, as emissions are not only a function of distance but also of time and operational conditions.

The organization of the paper closely mirrors the stated objective of addressing air-side operations through an integrated, time-dependent routing perspective. Section 2 introduces the fundamental concepts related to aircraft emissions and climate impacts, with particular emphasis on the distinction between CO₂ and non-CO₂ effects and their dependence on flight phase, altitude, and atmospheric conditions, thereby establishing the physical basis for environmentally oriented air-side optimization. Section 3 reviews climate metrics and impact indicators used in aviation studies, clarifying how different metrics relate to temporal scales and operational decision levels, which is essential for embedding environmental considerations into routing and scheduling problems. Section 4 focuses on en-route operations and trajectory-based optimization approaches, discussing routing, altitude, speed, and timing strategies under varying meteorological conditions, and explicitly framing aircraft trajectories as time-dependent paths whose environmental impact is not solely a function of distance. Section 5 narrows the scope to Terminal Maneuvering Area operations, where sequencing, vertical profile optimization, and constrained routing are analyzed in the context of high traffic density and short decision horizons. Section 6 extends the discussion to network-level and ATM-oriented optimization, highlighting how multiple trajectories interact in time and space and how system-level routing and flow-management strategies can be leveraged to reduce environmental impact. Finally, Section 7 synthesizes the reviewed approaches and outlines future research directions, reinforcing how the proposed framework integrates diverse optimization models while remaining focused on air-side operations and explicitly excluding ground-side processes. Section 8 concludes the article reporting key messages and final remarks.

2. Efficient Operation of an Aircraft for Fuel Saving and Emission Reduction

The most efficient operation of an aircraft depends on many factors. For example, flight-plan and routing will be continuously modified and optimized, depending on the traffic situation and weather conditions (see Figure 1). Fuel planning for a commercial aircraft usually follows the same standard scheme as, for example, outlined by Airbus [14]. Below, the different flight phases are considered.

1)

Taxi on the airport: This is the fuel needed to start the engines and then taxi to the runway. This is the first opportunity to save fuel. Aircraft engines are designed to be efficient in flight, but not during idle time on the ground. Airports and air traffic providers are working on projects to optimize the movements and flow of aircraft on the ground to minimize the time from the gate to take-off.

2)

Take-off and climb to an optimum cruise level: Each and every flight is different. The climb performance of an aircraft depends on the actual weight, the weather conditions and air traffic situation. The crew can calculate the most efficient climb profile with the onboard systems. The cruise altitude or flight level is not primarily the decision of the flight crew. The air traffic controller assigns a certain level, climb rate, and speed based on the capacity of airspace and trajectory of the aircraft.

3)

Cruise flight: With regard to efficiency, the cruise altitude needs to change during the flight. This is the result of burning fuel and losing weight. Fuel is 15–40% of the take-off mass of an aircraft. By burning fuel during cruise, the aircraft becomes lighter and able to climb to higher altitudes, where flight is more efficient. This, in turn, offers the opportunity to burn less fuel. Today, an aircraft climbs in steps. By improving the data transmission between airplanes and air traffic control, the controller can assign the aircraft the most efficient flight level. In addition, the routing could be optimized during the flight. Depending on the air traffic situation, the controller could be looking for a direct routing being assigned to a certain flight; this avoids extra fuel burn.

4)

Descent: The so-called Continuous Descent is the most efficient way for the final phase of the flight. If the crew sets the thrust levers to idle and the aircraft then glides to the airport, fuel is saved, and emissions are reduced. But, in many cases, aircrafts today have to reduce the altitude through several steps (step-down descent) rather than in a continuous way (Continuous Descent Operations, CDO). This results in inefficient-level flying at lower altitudes. The flight management system of the aircraft offers the crew the possibility to calculate the most efficient descent and define a certain point of top of descent for the flight. The air traffic controller then has to check if the traffic situation permits this approach. Consequentially, by jointly optimizing the flightpath, the resulting actual descent profile could be as close as possible to the optimum descent one.

5)

Holdings: One of the most inefficient flight phases in commercial aviation operations are holdings, i.e., the waiting in near-circular flight until a landing slot is available. For example, an A320-family aircraft burns approximately 100 kg of fuel in a four-minute standard holding.

6)

Movement to the parking position and ground power: Similarly to the situation on departure, efficient surface movement guidance after landing helps save fuel. The power supply during the turnaround of the aircraft is another opportunity to save fuel. The aircraft could be powered on the ground either by a connector and electricity from the airport or by running the so-called APU, Auxiliary Power Unit onboard the aircraft, which burns kerosene.

3. Terminal Maneuvering Area (TMA) Approaches to Fuel Saving and Emissions Reduction

As is generally known, the goal of aviation’s ecological transition is to drastically lessen its negative effects on noise exposure and air quality. In fact, in order to restore the sustainable development of air travel after the tremendous decline in activity brought on by the global health crisis caused by the COVID-19 virus, environmental considerations have become a priority, just as safety has always been. Every stakeholder is fully involved in this shift because of cutting-edge technologies.

This environmental approach needs to be outlined through action plans and cooperative partnerships with stakeholders on both local and European levels. It should also align with the innovative governance started by IATA, the International Air Transport Association, to enhance the coordination of project implementation.

In this context, enhancing the environmental performance of flights requires special focus on the climb and descent phases. For aircrews, the approach phase is especially challenging: the pilot must control the speed, altitude, engine power, landing gear, flaps, and/or airbrakes while adhering to ATC directives. With an improved flight profile and proactive flight management, the pilot can operate as quietly and efficiently as possible. Managing the effects of noise is therefore a challenge that starts with regulating the flight path. This duty is shared by both the pilot and the air traffic controller.

The continuous descent approach reduces noise and fuel consumption in TMA by minimizing level-offs from the top of the descent to the runway, leading to fewer variations in engine speed. The airport layout is considered, and the descent profiles need to align with air traffic limitations related to safety (handling flight crossings, maintaining separation standards between planes) and capacity. Consequently, pilots and controllers are encouraged to apply optimized descent profiles whenever operationally feasible.

Operational units in the area examine the departure paths to establish, in collaboration with stakeholders, the altitude to achieve before departing from the initial trajectory. Constant thrust during continuous climb operations (CCOs) reduces traffic spread and minimizes noise effects. Whenever feasible, it is advisable to ascend to FL100 (approximately 3000 m) on the departure route prior to entering the cruising airways. A separate regulatory body overseeing airport noise typically scrutinizes departure protocols from major airports, as demonstrated to residents’ association representatives in an environmental consultative commission.

Additionally, extensive experience is needed in Performance-Based Navigation (PBN). Navigation based on GNSS (Global Navigation Satellite System) allows for the establishment of new routes for the areas surrounding an airport, eliminating the necessity for traditional ground infrastructure or radar guidance provided by the controller. As a result, PBN flight paths can serve as significant facilitators to prevent overflights of urban areas situated beneath the arrival paths and to streamline routes.

Nonetheless, a study on air traffic impacts is required to assess and evaluate the environmental effects that will arise from the establishment or alteration of new flight paths. Any alteration can, in fact, challenge intricate balances. Creating new PBN trajectories for arrivals and departures provides aircraft paths that are less dispersed over urban regions. Consequently, these studies emphasize the options between a nuisance concentration (similar to a PBN process) or nuisance dispersion. These so-called Required Navigation Performance—Authorization Required (RNP AR) satellite-based procedures offer optimal and safe access to an airport encircled by obstacles by integrating a precise sequence of lateral and vertical guided maneuvers.

The advantages of merging the PBN concept with the CDA implementation can be shown by suggesting a system for the automatic creation of Curved and Continuous Descent Approach (CCDA) paths. These flight paths decrease fuel usage and minimize noise effects around the airport. Additionally, the curvature of the path maintains the dispersion of tracks compared to the traditional ground-based step-down arrival pathway, in both lateral and vertical configurations. For instance, a potential system could execute the process outlined in the subsequent text [2].

Initially, detailed routes are developed, incorporating a calculated Top of Descent (ToD) point based on a set angle or a fixed initial altitude, in order to intercept the descent glide path at a constant or varying angle. This development incorporates geo-referenced mapping of obstacles to prevent potential issues with airport/external environmental limitations by automatically producing corrective maneuvers. Subsequently, the BADA aircraft performance metrics are thoroughly assessed and detailed to calculate the fuel consumption linked to each determined potential descent route. Ultimately, the CCDA route that reduces fuel usage is chosen. The performance of the resulting system is assessed based on fuel efficiency, noise effects, and lateral and vertical protected regions for tracking tolerance. Consequently, implementing curved and continuous descent approach trajectories would indeed be suitable for minimizing the impacts of aircraft noise, fuel consumption, and associated atmospheric emissions. Their implementation could enable the creation of well-optimized vertical profiles, by integrating adaptable lateral routes and ongoing descent activities, making level flight segments entirely unnecessary [15,16,17].

Additionally, one can consider the airport and external environmental limitations by supplying obstacle mapping from aeronautical charts, georeferencing processes, and appropriate Digital Surface Models (DSMs) and Digital Terrain Models (DTMs). This enables the automatic creation of an altered set of paths that improve the track distance within an acceptable range [18]. Here, all the factors affecting TMA have been identified for a specific airport and its corresponding Aerodrome Traffic Zone and Control Zones, detailing the simulation outcomes of the proposed method and highlighting the advantages gained from its implementation.

Certainly, the impacts of aircraft noise, fuel usage, and associated pollutant emissions can affect the living standards in residential areas close to airports and create environmental challenges that lead to limitations for air traffic operations, aircraft production, and the design of airport infrastructure. ICAO and EUROCONTROL [19,20,21,22,23] offer advice and suggestions on environmental assessments to address these challenges, aiding in the sustainable equilibrium between the increasing demand in aviation and the potential adverse effects on human activities.

In order to mitigate such negative consequences, the development of optimized arrival trajectories automatic generation algorithms has been studied in [24]. The basic and totally reasonable assumption is that a reduction in the fuel consumption in the arrival phase (i.e., the fuel efficiency improvement) will immediately lead, in turn, to a reduction in the associated chemical emissions deriving from the fuel combustion in the aircraft engine. Based on the fact that the proposed algorithms redesign or modify arrival procedures, thereby improving flight efficiency in the TMA and thereby improving environmental efficiency and capacity near airports. Indeed, the positive effect on capacity is related to the benefit here in terms of emissions deriving from the application of the proposed optimized trajectories, which may lead to an increase in admitted arrivals while still complying with the assigned environmental constraints for the airport. In other words, by reducing the emissions of each flight, an increased number of flights can be accepted without breaching the assigned environmental limits in terms of emissions of any kind. Of course, such possible positive impact on capacity is subject to the acceptability of the capacity increase from the ATC point of view, in terms of separation limits compliance as well as Air Traffic Controllers (ATCOs) acceptable workload limitations. Furthermore, in [24], the key ideas and mathematical frameworks required to establish a comprehensive system, inclusive of the algorithms mentioned earlier, capable of producing descent profiles effectively optimized for fuel efficiency compared to traditional step-down arrival routes, are presented and analyzed.

Finally, it is worth adding that the progressive intensification of noise emissions in highly populated areas in the proximity of major airport infrastructures has imposed significant operational limitations on ATM. These constraints are particularly evident during evening and nighttime periods, when stricter regulations are enforced to safeguard community well-being and maintain social acceptance of the airport operations. As a direct consequence, aircraft are frequently obliged to adopt complex and suboptimal ground trajectories, on purpose designed to circumvent densely inhabited zones. Such procedural adaptations represent a necessary compromise aimed at mitigating acoustic disturbance and reducing the exposure of local residents to excessive noise levels, but negatively affect the overall flight efficiency. For this reason, as previously stated, among the most significant strategies proposed to mitigate the environmental impact of aircraft operations is the implementation of a continuous descent profile, initiated at idle or near-idle thrust settings. This procedure typically starts upon entry into the TMA (or ideally at the Top of Descent (TOD)) and extends continuously from cruise altitude down to touchdown. This operational concept, well-known as Continuous Descent Operation (CDO) [24,25], aims to minimize the fuel consumption and the noise emissions by reducing level-off segments and maintaining a steady descent trajectory. On the other hand, this operational approach is constrained by the inherent unpredictability of the resulting flight trajectory and by the relevant challenges associated with maintaining relative spacing between aircraft. These limitations lead to further complexities in the operations aviation operations, as the dynamic nature of descent profiles reduces the ability to forecast positional accuracy and to ensure optimal separation standards. These aspects, nevertheless, are of capital importance in a busy traffic environment, such as the one of the high-density airports, which are indeed the ones where the noise impact issues are more relevant. However, in order to mitigate such drawbacks, it is feasible to implement arrival flow merging strategies [26,27,28] designed to complement and enhance CDO. These techniques aim to improve the efficiency and uniformity of terminal airspace management beyond the Initial Approach Fix (IAF) during the approach phase, thereby facilitating a more predictable and harmonized sequencing of arrival traffic.

4. CO₂ and Non-CO₂ Emission Modeling

4.1. CO₂ Emission Modeling

In general, the emission of a given species from an aircraft engine is specifically linked to its operative conditions, propulsive technology and consumption rate. The most established technologies for aircraft propulsion are the turbofan and turbo-propeller configurations—air-breathing internal combustion engines exploiting fuels containing hydrocarbons. A semi-empirical mathematical model of these engines has been developed by Eurocontrol through a collaboration with aircraft engines manufacturers and airlines companies, leading to the steady-state description contained into the well-known and widely adopted Base of Aircraft DAta (BADA) theoretical approach. The output of the model are the thrust $\mathit{T}$ and fuel flow $\mathit{F}\mathit{F}$, both depending on the control variable altitude ($\mathit{z}$), true airspeed ($\mathit{v}$), and ambient temperature/pressure [29].

In BADA modeling, the amount of emitted pollutant ${\mathit{Q}}_{{\mathit{p}}_{\mathit{i}}}$ can be derived from the calculated fuel flow through the general expression:

$${\mathit{Q}}_{{\mathit{p}}_{\mathit{i}}}={\int }_{{\mathit{t}}_{\mathbf{0}}}^{{\mathit{t}}_{\mathit{f}}}\mathit{E}{\mathit{I}}_{{\mathit{p}}_{\mathit{i}}}\left(\mathit{\tau }\right)·\mathit{F}\mathit{F}\left(\mathit{v},\mathit{z}\right)\mathit{d}\mathit{t},$$

(1)

with its differential counterpart:

$${\displaystyle \frac{\mathit{d}{\mathit{Q}}_{{\mathit{p}}_{\mathit{i}}}}{\mathit{d}\mathit{t}}}=\mathit{E}{\mathit{I}}_{{\mathit{p}}_{\mathit{i}}}\left(\mathit{\tau }\right)·\mathit{F}\mathit{F}\left(\mathit{v},\mathit{z}\right),$$

(2)

where Eurocontrol $\mathit{E}{\mathit{I}}_{{\mathit{p}}_{\mathit{i}}}$ stands for the Emission Index of pollutant ${\mathit{p}}_{\mathit{i}}$. BADA is considered one of the gold standards for evaluating pollutant emissions in aviation nowadays.

An alternative approach to BADA has been introduced by ICAO through an extensive data collection on engine emissions [30]. The ICAO emission indexes, which have the advantage of being fuel-specific, are measured in reference conditions, defined in [31], that for a subsonic engine prescribe 100% of rated engine thrust at take-off, 85% during climb, 30% in approach, and 7% in idle. ICAO has also established an efficient semiempirical model for CO₂ and NO_x emissions computation. It is based on the observation that the main source of CO and BC is the incomplete combustion of the hydrocarbon-based fuel at low-throttle settings [32]. Emitted CO₂ can be derived from CO and BC emissions by difference, since all the carbon in the fuel that does not go into CO or BC is transformed into CO₂. Experimentally, the mean emission index for both CO and BC can be derived from the following expression:

$$\mathit{E}{\mathit{I}}_{\mathit{C}\mathit{O}-\mathit{H}\mathit{C}}\left(\mathit{\tau }\right)={\mathit{c}}_{\mathbf{1}}+\mathbf{exp}\left(-{\mathit{c}}_{\mathbf{2}}\mathit{\tau }+{\mathit{c}}_{\mathbf{3}}\right),$$

(3)

where the nonlinear regression parameters, estimated using the ICAO database, are $\mathbf{c}=\{\mathbf{0.556},\mathbf{10.208},\mathbf{4.068}\}$ and $\mathbf{c}=\{\mathbf{0.083},\mathbf{13.202},\mathbf{1.967}\}$ for, respectively, CO and BC [33]. The resulting mean reference value for CO₂ emission index is 3.16-ton CO₂/ton fuel, under the ansatz of burning Jet-A1, a widely used hydrocarbon-based fuel for turbofan engines [34].

With similar arguments, it can be estimated the emission of nitrogen oxides, formed at high combustion temperatures, leading to reaction of atmospheric bi-atomic oxygen and nitrogen. Mean NO_x emissions from currently operated aircrafts can be estimated into the ICAO formal framework by using the following expression:

$$\mathit{E}{\mathit{I}}_{\mathit{N}{\mathit{O}}_{\mathit{x}}}=\mathbf{7.32}{\mathit{\tau }}^{\mathbf{2}}+\mathbf{17.07}\mathit{\tau }+\mathbf{3.53}.$$

(4)

An empirical correction to ICAO approach, usually dubbed Method 2, has been developed by Boeing since the mid-1990s [35,36]. Method 2 increases the accuracy of ICAO estimation, by introducing corrections to EI’s accounting for changes in ambient temperature, pressure, and relative humidity [37,38], leading to differences in the engine chemical reaction efficiency.

4.2. Non-CO₂ Emission Modeling

The approaches described so far can be employed for evaluating the emissions of CO₂ as well as some of the “Non-CO₂” compounds, like SO_x and NO_x. Condensation trails (usually contracted in “contrails”) originating in aviation [3,39,40] deserve a different discussion, given their peculiar nature. The environmental impact of contrails, particularly for their potential radiative forcing, is thought to be comparable to that ascribed to CO₂, although its quantitative evaluation is affected by large uncertainties due to the knowledge gaps concerning their formation, persistence, and variability with atmospheric variables.

Contrails form in the expansion of the engine plume, mixing with the atmosphere. The exhaust, warmer than air, bears a larger amount of water vapor. Contrails originating in aviation can be mainly observed in the upper troposphere when a turbo-fan engine is employed, as is the case for the currently operated medium- and long-haul flights. A global thermodynamic criterion for evaluating the probability of a contrail formation is the Schmidt–Appleman Criterion (SAC) [41], named after the scientists who pioneered studies in atmosphere thermodynamics and physical chemistry.

The Schmidt–Appleman Criterion assumes an adiabatic and vapor-conserving mixing process between the exhaust and the atmosphere. In fact, the hot and consequently humid engine plume attains local liquid saturation conditions, generating water droplets that can freeze. In order to observe the phenomenon, the slope of the exhaust mixing curve is evaluated, assuming the same diffusion rate for heat and vapor [42]. The point in a temperature–partial vapor pressure graph representing the plume-atmosphere mixture evolves along a straight line, whose slope $\mathit{G}$ can be expressed as follows:

$$G={\displaystyle \frac{P_v-P_{v\mathrm{\infty }}}{T-T_{\mathrm{\infty }}}},$$

(5)

with $P_v=X_{H_{2}O}P$ representing the water vapor partial pressure and $X_{H_{2}O}$ representing the water molar fraction; the underscript $\infty$ indicates the full mixed system and T indicates the temperature. For a turbo-fan engine, the slope parameter in Equation (5) has an analytical expression as a function of the air pressure and the engine efficiency [43]:

$$G={\displaystyle \frac{c_p{P}_{\infty }}{ϵ}}{\displaystyle \frac{E{I}_{H_{2}O}}{\left(1-\eta \right)Q}},$$

(6)

in which ${\mathit{c}}_{\mathit{p}}$ represents the isobaric specific heat capacity of air, measured at constant pressure, $\mathit{ϵ}=\mathbf{0.622}={\mathit{W}}_{{\mathit{H}}_{\mathbf{2}}\mathit{O}}/{\mathit{W}}_{\mathit{a}\mathit{i}\mathit{r}}$ the water/air molar masses ratio, $\mathit{E}{\mathit{I}}_{{\mathit{H}}_{\mathbf{2}}\mathit{O}}$ the water vapor emission index [30,44], $\mathit{Q}$ the total heat released per fuel mass, and $\mathit{\eta }$ = (thrust × distance per mass of fuel)/$\mathit{Q}$ the engine efficiency in cruise conditions, with the heat in the engine plume expressed as $\left(\mathbf{1}-\mathit{\eta }\right)\mathit{Q}$.

The threshold temperature for contrails is derived from ${\mathit{P}}_{\mathit{s}\mathit{a}{\mathit{t}}_{\mathit{v}}}^{\mathit{l}\mathit{i}\mathit{q}}$, the partial pressure of liquid water–steam phase transition described by the Clausius–Clapeyron equation [45,46]:

$${\displaystyle \frac{d{P}_{sa{t}_v}^{liq}}{dT}} = {\displaystyle \frac{1}{T}} {\displaystyle \frac{Q^{lat}\left(T\right)}{{\alpha }_v-{\alpha }_l}},$$

(7)

in which $Q^{lat}\left(T\right)$ is the latent heat of evaporation/condensation, and ${\alpha }_v$, ${\alpha }_l$ is the specific volume of the vapor and liquid phases, respectively. The threshold temperature, $T_{th}^{*}$, for condensation is given by the tangent point between the mixing line and the slope curve:

$${\left.{\displaystyle \frac{d{P}_{sa{t}_v}^{liq}}{dT}}\right|}_{T_{th}^{*}} = G.$$

(8)

How long a contrail persists in atmosphere determines its environmental impact, transforming in a cloud [47] undistinguishable from a natural cirrus [48] at sight. The condition to persist is to lay above the vapor–ice saturation curve. This condition can be relaxed if soot and sulfuric acid aerosols in the plume are available as condensation nuclei for the microscopical water drops. In fact, at the microscopical level, contrail cirri are distinguishable from natural clouds due to a difference in the water particle dimension spectrum [49,50]. The radiative forcing of a contrail depends on the radiative properties of its ice crystals [51], since aggregates of smaller ice particles scatter more shortwave radiation than an equivalent single ice crystal. Unfortunately, measurement campaigns performed so far do not provide a significant statistic, leaving a large range of uncertainty in evaluating contrail formation and evolution [42,52].

The interested reader is referred to [53,54,55,56,57,58,59] for further details on the formation, persistence, and radiative forcing modeling of condensation trails in aviation.

5. Emissions Reduction

Fifty years ago, first seminal studies appeared [60], considering the possibility to automatically optimize an aircraft trajectory according to a given objective, generating off-line a static optimal path for the aircraft. From the mid-1970s to the late 1990s, these studies were translated into several algorithmic approaches, mostly optimizing vertical guidance and standard turns, as the well-known direct great circle arcs and constant-bank turns for lateral path planning.

Significant savings were introduced with respect to manual operational paradigms, even if an effective real-time strategy was still missing. In fact, general routes found with static approaches can be largely suboptimal at ATM scale where weather, traffic congestions, and local phenomena (volcanic ash, NOTAM, etc.) are considered. Four-dimensional trajectories (4DT) represent a substantial evolution with respect to the limitations of flight plans submitted offline as static entities, whose optimality is progressively compromised by unforeseen weather and traffic circumstances.

The need for a holistic real-time approach in ATM and ATC has led, in the last two decades, to the development of several innovative approaches to the problem of 4D trajectories’ optimization. These algorithms aim to replan four-dimensional paths by incorporating updated weather conditions, traffic constraints, and environmental objectives, making them particularly suitable for reducing CO₂ and non-CO₂ emissions.

5.1. Multi-Objective Optimization

Multi-Objective Trajectory Optimization (MOTO) focuses on optimizing flight paths, accounting for both en-route and TMA operations, thus simultaneously addressing operational efficiency and environmental concerns. In fact, by recalculating and optimizing aircraft trajectories in real-time, MOTO balances multiple objectives, such as fuel efficiency, emissions reduction, and time minimization. This approach has been developed and refined over the last few years, thanks to research in optimal control theory, trajectory planning, and dynamic system optimization [60,61,62,63,64,65,66].

MOTO algorithms begin by rigorously modeling the diverse systems and processes that underpin the aviation sector, encompassing environmental conditions, operational dynamics, and aircraft performance. Among the key components represented in these models are local and global meteorology, operating expenses, emissions of atmospheric pollutants, airspace configuration, contrail formation, and aeroacoustic impacts. The optimization process, driven by several mutually competing objectives $J_k=Q_k\left(p\right),$ $k\in [ 1, n_J]$, typically yields an extensive ensemble of solutions that may be regarded as optimal in a broad sense. The solution ${\mathit{p}}^{*}\in P$ is a vector in the design space that can be regarded as optimal according to the Pareto criterion if there is not another point such that $\mathit{Q}\left(\mathit{p}\right) \le \mathit{Q}\left({\mathit{p}}^{*}\right)$ and $Q_i\left(p\right) \le Q_i\left(p^{*}\right)$ for at least one component i. The collection of such non-dominated points constitutes the Pareto front, or the Pareto frontier. These points are characterized by the absence of any solution that strictly dominates them with respect to all objectives. Conceptually, the Pareto front generalizes the notion of a single best solution in classical single-objective optimization to the multi-objective, multi-dimensional context. Since many real-world applications ultimately require the selection of a unique solution—even when the underlying optimization problem is highly complex—a multi-objective framework must still yield a single outcome that is necessarily Pareto-optimal and therefore lies on the Pareto front.

Consequently, a systematic trade-off mechanism is required to extract one preferred solution from the broader set of compromise ones, forming a central focus of multi-objective optimization theory. Following the growing social concerns on environmental impact, research in MOTO has increasingly addressed CO₂ and non-CO₂ emissions reduction, including contrail avoidance in both established and innovative propulsive solutions [67,68,69,70,71,72].

5.2. Simulation-Based Evolutionary Optimization

Another effective method for optimizing Air Traffic Management systems leverages computational intelligence techniques, specifically Agent-Based Modeling and Simulation (ABMS) combined with Evolutionary Computing (EC). These methodologies are applied to address the inherent complexities of ATM, a socio-technical system involving numerous physical and human actors working within highly dynamic environments.

As a recognized reference in the field, the study [55] focuses on enhancing ATM performance metrics, such as timeliness, fuel efficiency, safety, and workload distribution, through a simulation-based optimization framework capable of analyzing and fine-tuning operational parameters. The core of the approach lies in a distributed simulation architecture designed to perform offline “what-if” analyses during ATM’s strategic and pre-tactical phases. This framework incorporates real-world traffic data and simulates ATM scenarios to evaluate ATM-related performances under various conditions. The ABMS component models the human behavior, particularly the one of Air Traffic Controllers (ATCOs), whose decision-making processes are critical to system performances. The simulation framework accounts for human-related variables, such as workload and stress levels, in addition to technical constraints, such as airspace configuration and aircraft separation minima.

In [55], the optimization process is driven by a parallel implementation of the Non-Dominated Sorting Genetic Algorithm (NSGA)-II evolutionary algorithm, a Pareto-based multi-objective optimization method. This algorithm explores a vast search space of possible ATM configurations to identify Pareto-optimal solutions that balance conflicting objectives, such as minimizing delays while ensuring safety. The simulation evaluates each candidate solution against predefined performance metrics, including fuel consumption, sector occupancy, and the timeliness of flight trajectories. The study highlights the utility of evolutionary algorithms in finding trade-offs between competing objectives, enabling ATM improvements that consider both operational and environmental criteria.

Experimental validation is performed in [55] using real-world ATM scenarios, including high-density airspaces managed by Italian control centers. Case studies, such as transitions from direct to emerging free routing paradigm, are used to test the model’s ability to replicate complex traffic dynamics and emergent behaviors. Results demonstrate the effectiveness of the framework in optimizing critical parameters like horizontal separation minima and airspace sectorization. These optimizations yield improvements in timeliness and workload distribution while maintaining safety standards.

5.3. Air Traffic Flow Management with Emissions Considerations

Air Traffic Flow Management (ATFM) can also play a crucial role in reducing emissions. By formulating the ATFM problem as a bi-objective Mixed-Integer Linear Programming (MILP) model, it is possible to minimize both CO₂ emissions and total delay costs. This approach uses a Pareto-based scalarization technique to balance the trade-offs between emissions and delays. Reference [56] proposes an innovative methodology that incorporates ground delays, air delays, rerouting, and emissions minimization into ATFM decisions. The study addresses a gap in prior research, which has often focused on either operational delays or emissions without integrating the two into a unified optimization framework.

In [56], the model considers various operational constraints, such as airport and airspace capacities, aircraft turnaround times, and predefined flight paths. Objective functions minimize delay costs, factoring ground and air holding penalties and rerouting costs, and CO₂ emissions, which are demonstrated based on fuel consumption rates tied to aircraft type and passenger load. A scalarization method, the weighted comprehensive criterion, is employed to solve the bi-objective model, by transforming it into a single-objective optimization problem. The Pareto front generated from varying weights between delay and emission objectives provides insights into the trade-offs involved in achieving a balanced solution.

The authors of the study [56] also performed a numerical study on a 30-airspace sector network with 200 flights, which has demonstrated the practical applications of the model. Results show that the prioritization of the CO₂ reduction objective leads to increased ground delays and reduced air holding and rerouting. For example, minimizing CO₂ emissions by 0.34% results in a 6.18% increase in delay costs. The study highlights that ground holding is favored over air holding when focusing on emissions, as airborne delays incur higher CO₂ penalties. The model also reveals the impact of operational decisions, such as rerouting limitations, on overall system performances and environmental outcomes.

5.4. Uncertainties in the Optimization of Non-CO₂ Effects

Uncertainties in non-CO₂ effects fundamentally challenge deterministic flight planning optimization, because both the identification of sensitive regions and the aircraft’s response to the atmosphere depend on imperfect forecasts and incomplete. Weather induced-uncertainty in wind, temperature, humidity, and derived variables (e.g., potential vorticity) directly perturbs algorithmic approaches, so that regions flagged as high-impact in a deterministic optimization may not be critical in the realized atmosphere, degrading the expected mitigation and even producing inefficient or counterproductive re-routings if uncertainty is ignored.

As climate optimal planning typically relies on more meteorological inputs than cost optimal routing, its sensitivity to forecast error is higher, amplifying trajectory dispersion and cost–climate trade off variability. In parallel, structural uncertainties in climate impact modeling—i.e., choices of emissions inventories, contrail models, forcing efficacies, climate metrics, and even the scientific understanding of NO_x, contrails, and water vapor effects—mean that different models can assign markedly different impact to the same route, so a trajectory that is “optimal” under one estimate may offer little or no benefit under another.

These combined uncertainties limit the operational usefulness of purely deterministic ATM/ATC optimization in mitigating the occurrence, magnitude, and actual climatic impact of non-CO₂ as contrails and motivate stochastic and robust approaches that explicitly propagate ensembles of weather and climate impact estimates or seek solutions that deliver consistent mitigation across multiple climate metrics, as discussed in the following paragraph.

6. Metrics for Evaluating Impact

The alteration in the atmospheric composition disrupts the Earth’s radiative equilibrium. To restore the equilibrium, the near-surface temperature increases, prompting the Earth’s surface to emit additional energy back into space. As a result, the Earth eventually establishes a new equilibrium state, albeit at a higher surface temperature. The degree of temperature increase near the ground, in response to the initial radiative imbalance, is controlled by the climate sensitivity parameter, λ, which varies among different climate forcers.

The duration over which an emission influences near-surface temperatures is determined by two distinct timescales. First, the persistence of the radiative imbalance is governed by the lifetime of the atmospheric perturbation: for instance, while a fraction of emitted CO₂ can remain in the atmosphere for several centuries, contrails typically dissipate within a few hours. The second timescale is related to the physical response of the climate system to the radiative imbalance, a response modulated by the inertia of the coupled atmosphere-ocean system. This means that a one-year pulse emission of a short-lived species will initially produce a substantial near-surface temperature change that, then, gradually diminishes. Instead, a one-year pulse of CO₂ will induce a temperature increase that builds over several decades before it eventually declines.

Different climate forcers influence the climate in diverse ways, exhibiting variations in sign, lifetime, and spatial distribution. Therefore, it is crucial to employ a metric that takes these differences into account when assessing the climate impact of various technologies or scenarios. A climate metric provides a direct quantitative link between an emission and its climatic effect. The interpretation of climate impact depends on the specific question being addressed. As the analysis progresses from emissions to damage, the significance of the impact increases, but so does the associated uncertainty. Furthermore, because economic assumptions (such as depreciation or inflation rates) are integral to monetizing damage, such estimates are no longer regarded as strict physical climate metrics.

An illustrative example [73] underscores the importance of selecting an appropriate climate metric. When considering the radiative forcing of a newly constructed coal-fired power plant over time, initially the cooling effect from both direct and indirect sulphate aerosol processes dominates, leading to an overall cooling influence despite CO₂ emissions. However, owing to the long atmospheric lifetime of CO₂, its warming effect accumulates over time and eventually surpasses the initial cooling, with CO₂’s warming contribution becoming predominant after approximately 20 years. If one were to consider only the radiative forcing at the 20-year mark, the coal-fired power plant might be mistakenly classified as climate-friendly. Thus, the choice of a climate metric must be aligned with the specific research question and is typically composed of three interrelated aspects: the evolution of emissions over time, the selected climate indicator, and the chosen time horizon.

In summary, climate metrics provide a quantitative measure linking emissions (or a pulse of emissions) to their ultimate effect on Earth’s energy balance and near-surface temperature. They are essential for comparing different technologies and emission scenarios, by offering a common scale for impact assessment. Common metrics include:

-

Radiative Forcing (RF), which indicates the instantaneous change in the net (down minus up) radiative flux (W/m²) due to an atmospheric perturbation. The concept of radiative forcing is central to understanding how an emission perturbs the climate system. A common formulation for CO₂ is

$$\Delta F=\kappa ln\left({\displaystyle \frac{C_0}{C}}\right),$$

(9)

where ΔF is the change in radiative forcing (W/m²), κ is a constant (typically about 5.35 W/m² for CO₂), C is the current concentration, and C₀ is the pre-industrial baseline concentration. For non-CO₂ agents, adjustments are made to account for rapid atmospheric adjustments (e.g., stratospheric temperature, cloud effects), leading to definitions of adjusted and Effective Radiative Forcing (ERF).

-

Global Warming Potential (GWP), which is the integrated radiative forcing over a specified time horizon normalized to the forcing of CO₂. GWP is defined over a time horizon τ as

$${\mathrm{G}\mathrm{W}\mathrm{P}}_x(\mathsf{\tau })={\displaystyle \frac{{\int }_0^{\tau }{a}_x\left(t\right)dt}{{\int }_0^{\tau }{a}_{C{O}_2}\left(t\right)dt}},$$

(10)

where $a_x\left(t\right)$ is the radiative forcing at time t per unit emission of substance x, and $a_{C{O}_2}\left(t\right)$ is the corresponding radiative forcing for CO₂. Variations on this well-established metric have been developed, including Efficacy-weighted Global Warming Potential (EGWP), which is a modified GWP that incorporates the climate “efficacy” (i.e., the relative effectiveness of a given emission in causing temperature change), and GWP* and Extended GWP*, that aim to better represent the temperature impacts of short-lived climate pollutants.

-

Global Temperature change Potential (GTP), which is the change in near-surface temperature at a given future time due to an emission pulse, relative to CO₂.

-

Average Temperature Response (ATR), referring to the time-averaged temperature change over a defined period following an emission pulse. ATR links the integrated temperature response to a pulse emission. It is often calculated as

$${\mathrm{A}\mathrm{T}\mathrm{R}}_x\left(\mathrm{T}\right)={\displaystyle \frac{1}{T}}{\int }_0^T{\mathsf{\Delta }\mathrm{T}}_x\left(t\right)dt,$$

(11)

where ${\Delta T}_x\left(t\right)$ is the temperature change at time t following the emission pulse and T is the chosen time horizon (e.g., 100 years).

To facilitate comparisons between different technologies, the Climate Metric (CM) can be converted into equivalent CO₂ emissions (eqCO₂). If $C{M}_{tot}$ is the total climate impact (including all greenhouse and non-greenhouse effects) and $C{M}_{C{O}_2}$ is the impact per ton of CO₂, the conversion factor is given by

$$eqC{O}_2={\displaystyle \frac{C{M}_{tot}}{C{M}_{C{O}_2}}}\times C{O}_2,$$

(12)

where $C{O}_2$ indicates that resulting pure number represents tons of CO₂ emissions. This factor allows the total impact of a complex emission mix to be expressed in terms of a single and familiar unit: the tons of CO₂.

In the example of the coal-fired plant, the emissions development is a constant over time as the power plant is constantly used, the climate indicator is RF, and the time horizon is 20 years.

Thus, the introduction of a climate metric also allows us to concretely measure the impact of solutions designed to reduce or mitigate the effects of the considered emissions. The summary box provided in

Table 1. Suggested climate metrics depending on context, time horizon and operational objective.

Decision Level and Operational Purpose	Time Horizon	Suited Climate Metrics	Justification
Strategic planning, policy evaluation, technology assessment	Multi-decadal to centennial	CO2-equivalent, time-integrated metrics (e.g., GWP, ATR)	These metrics integrate radiative effects over long time horizons and express impacts relative to CO2, making them appropriate for assessing cumulative climate consequences, comparing mitigation strategies, and supporting regulatory or economic policy instruments. Short-lived variability is intentionally averaged out in favor of long-term climate relevance.
Pre-tactical ATM planning and scenario analysis	Seasonal to annual	Combined use of CO2-based metrics and simplified non-CO2 indicators	At this level, decisions rely on forecasted traffic and meteorological conditions and aim to balance cumulative emissions with expected non-CO2 effects, without requiring instantaneous resolution of atmospheric variability.
Tactical and real-time ATM/ATC operations (trajectory management, contrail mitigation)	Hours/days	Short-term or instantaneous metrics (e.g., RF, aCCF-based indicators)	These metrics explicitly capture the strong spatial and temporal variability of short-lived non-CO2 effects, particularly contrail-related forcing, and can be directly coupled with meteorological forecasts and real-time trajectory optimization. Their sensitivity to atmospheric conditions makes them unsuitable for long-term policy but essential for operational decision making.

highlights that the selection of a climate metric has to be consistent with the decision context, time horizon, and operational objective. Aligning the metrics with decision levels is essential to avoid misinterpretation of climate impacts and to ensure coherence between ATM operations, climate science, and policy-making.

For instance, current flight planning research [74,75,76,77] predominantly emphasizes micro-scale studies, independently optimizing aircraft trajectories. Nevertheless, the ATM system functions as an intricate network, necessitating the combination of micro-scale trajectory optimization with macro-scale ATM network oversight for environmentally sustainable operations. Balancing capacity and demand are essential at ATM network level, frequently necessitating measures such as postponing or rerouting aircraft. Conventional capacity-demand alignment is being updated via initiatives aimed at shifting from the usual sector-based to the recently introduced trajectory-based management paradigm. Nevertheless, current methods neglect climate influences and do not incorporate network interactions into strategic deconfliction techniques, missing out on collective behavior and uncertainties within the ATM network.

Consequently, it is necessary to address the void in existing studies regarding climate-optimized flight planning, which pertains to allowing flight planning to include diverse fuel types and aircraft technologies. Indeed, ongoing studies mainly concentrate on traditional kerosene fuel, and the planning of flights for various fuel types and aircraft categories remains unexamined. To explore how the integration of new technologies and fuel types affects traffic distribution patterns and ATM strategies in particular climate-sensitive regions, evaluating the capacity, efficiency, and environmental consequences of various operational scenarios necessitates flight planning that considers diverse fuel types and aircraft propulsion technologies. This also includes the consideration of Sustainable Aviation Fuels (SAF) [78,79,80] as well as liquid hydrogen and of new promising powerplants, such as the ones based on the exploitation of fuel cells to power the future aircraft electric propulsion systems [81,82].

For example, the climate response to emissions from fuels besides kerosene can differ, leading to alterations in climate-sensitive areas’ polygons, and, in some scenarios, it might remove the need for flight rerouting. To tackle this, alongside modifying climate change models, it is necessary to create aircraft dynamic models for these new fuel types and technologies and to adjust flight planning tools to account for these elements. Therefore, the subsequent limitations emerge concerning the ATM network scale:

Flight planning for climate optimization has yet to be conducted for fuel and aircraft types beyond conventional kerosene fuel, which is essential for grasping how emerging technologies affect traffic distribution patterns and ATM strategies.

Climate impacts are not consistently considered to restrict system capacity (as practiced in certain European cities to control road transport) and are typically not integrated into any network-level modeling and solution strategies. Pinpointing environmental hotspots in the airspace and integrating them into comprehensive aerial traffic management strategies constitutes a scientific gap that certainly requires addressing.

The development of self-evolving models based on AI techniques, particularly reinforcement learning, with fast execution times can be useful for addressing the challenges of optimizing trajectories at air transport network level, which involves all daily traffic in Europe, including approximately 30,000 flights. Therefore, the ability to solve large-scale simulations and develop network-wide climate indicators is crucial.

To manage international operations like aviation, market-driven tools (taxes, charges, marketable permits, etc.) are frequently favored as they theoretically attain climate objectives in an economical way. Nevertheless, due to the incomplete understanding of the non-CO₂ effects and their association with medium to high uncertainties, no environmental policy measures have been implemented in aviation regarding non-CO₂ effects.

Numerous studies have been proposed to reduce the climate impacts of non-CO₂ emissions by changing aircraft maneuvers to avoid climate-sensitive regions. These studies differ mainly in (1) how the climate-sensitive areas are defined and (2) how climate-friendly trajectories are determined [83]. The first attempts to consider climate hotspots were based on areas sensitive to the formation of persistent contrails [84]. Climate Change Functions (CCFs) were created to give information on the temporal and spatial dependence of non-CO₂ effects. These CCFs include five-dimensional datasets (longitude, latitude, altitude, time, kind of emission) that show the climatic impact of aviation emissions per flown kilometer and per emitted mass of the species [85].

CCFs were not appropriate for real-time operations because of their computational complexity. As a result, algorithmic CCFs (aCCFs) were created. Because the aCCFs are based on mathematical formulas that only require pertinent local meteorological input factors, they allow for a very quick computation of the individual non-CO2 climatic impact. (e.g., [86]). Because of their computational efficiency, the aCCFs are a good fit for trajectory optimization techniques [87]. A refined and uniform set (regarding emission scenario, metrics, etc.) of aCCFs has recently been established and presented within the EU initiative FlyATM4E [88].

Regarding climate-optimal trajectory planning techniques, a range of approaches has been utilized, including mathematical programming [89], meta-heuristic [90], indirect optimal control [68], and direct optimal control methods [91]. For example, the direct optimal control method has been utilized in [92] to reduce flight duration (or distance traveled) in regions prone to enduring contrail formation, in [91] to decrease the average temperature response over the upcoming 20 years (ATR20) linked to non-CO₂ emissions, and in [93] to lessen the global warming potential (GWP) of NO_x, H₂O, soot, SO₂, and contrails. Utilizing aCCFs to measure climate effects, ref. [90] applied a genetic algorithm to identify climate-optimal flight paths.

Concerning the optimization methodologies, the mathematical programming techniques are applicable solely to simplified problems of aircraft trajectory optimization (for instance, in the research performed in [89], the dynamic behavior of the aircraft is depicted using a linearized model). Meta-heuristic techniques (e.g., genetic algorithm) necessitate rapid aircraft trajectory forecasting to identify an optimal solution through numerous iterations; consequently, the flight planning challenge is often modeled with a simplified yet sufficiently representative problem (e.g., in [90], and optimization is framed with 11 decision variables to depict the lateral path and flight altitude, while the speed profile is assumed to be constant).

Ultimately, optimal control methods enable the modeling of more precise aircraft trajectory optimization challenges, as the issue is depicted as a dynamic optimization problem. However, there are certain disadvantages linked to tackling the identified issue. The dynamic programming technique (as an optimal control strategy) leads to the “curse of dimensionality” for intricate issues (e.g., a complete 4D aircraft trajectory optimization challenge). Concerning the indirect optimal control method, obtaining analytical solutions through Pontryagin’s maximum principle is challenging, particularly for issues involving singularities (for example, the literature has only dealt with a 2D trajectory optimization issue [68]).

The direct optimal control method, while highly adaptable in modeling aircraft trajectory optimization issues (such as utilizing a complete 4D dynamic model with nonlinear path and boundary limitations [91]), exhibits significant sensitivity to initial conditions; hence, local optimality is its primary limitation. Moreover, considering the airspace framework with both direct and indirect optimal control approaches is complex. Readers interested in this topic should consult [94] for a recent overview on climate-optimal aircraft trajectory planning, which examines both the modeling of climate-sensitive areas and methods for trajectory planning.

To measure the climate impacts beyond CO₂, particular meteorological variables are necessary. For aCCFs, it is essential to consider factors like temperature, potential vorticity, geopotential, relative humidity on ice, and outgoing longwave radiation. These variables are derived from conventional weather predictions. Various elements, such as insufficient comprehension of atmospheric conditions, computational intricacies, and nonlinear as well as occasionally chaotic dynamics, influence the reliability of weather predictions, indicating that the weather forecast is unavoidably uncertain [95]. If not considered in aircraft trajectory planning, the uncertainties related to weather forecasts in the aCCFs, and the dynamic behavior of aircraft (such as variations in wind and temperature) can result in inefficient flight paths.

Earlier studies in the area of climate-optimal aircraft trajectory planning have been carried out deterministically, overlooking the incorporation of any uncertainty sources [94]. An initial phase in handling and incorporating meteorological uncertainties into aircraft route planning involves acquiring dependable weather predictions that can anticipate likely changes in meteorological conditions. Probabilistic Weather Forecasting (PWF) is generally employed to define uncertainties in weather predictions [96]. Cutting-edge probabilistic weather forecasting is derived from the Ensemble Prediction System (EPS), which yields NEPS potential realizations of atmospheric conditions referred to as ensemble members [97].

From an operational perspective, reducing aviation’s climate impact is accomplished by adjusting aircraft operations to steer clear of regions where those non-CO₂ effects are markedly intensified, referred to as Climate-Sensitive Regions (CSRs). The maneuvers may include adjustments to departure time, cruising altitude, lateral trajectory, speed profile, and their combinations. To choose an appropriate climate-conscious flight path for aircraft, data concerning climate-sensitive areas must be accessible, enabling the assessment of trajectories in terms of their contribution to climate impact. Furthermore, the method for identifying an eco-efficient path based on the selected metric (i.e., indicative of CSR) significantly impacts the overall mitigation potential [94].

The strategies for mitigating aviation’s climate impact can be divided into two groups: Non-Trajectory Optimization (NTO) (or, in certain instances, simulation-based) approaches and Trajectory Optimization (TO) methods. In NTO methods, following an analysis of how non-CO₂ emissions impact the climate, slight modifications are made to the flight route, timing, or altitude, and the potential for mitigation is investigated (by simulating aircraft performance using trajectory predictors). Regarding TO methods, optimization techniques are used to establish the aircraft trajectory in a way that minimizes a cost function that includes certain user-defined objectives (namely, climate impact in this instance).

Based on the benchmark, there are different categories of trajectory optimization methods. The research presented in [98], primarily concentrating on reducing aviation’s climate effects, seeks to evaluate and categorize these methods into two groups: optimal control and non-optimal control strategies.

Optimal Control (OC) is recognized as one of the most trustworthy dynamic optimization methods because it operates in continuous time, takes into account the system’s dynamic behavior, can yield analytic solutions for certain problem types, and employs numerical techniques. In optimal flight planning, the goal is to identify viable paths for aircraft while accounting for real-world limitations and the aims outlined by the flight planner.

A key characteristic of optimal control compared to other mathematical optimization methods is its incorporation of the system’s movement over time as dynamic constraints in the optimization process, enabling a viable transition of the system. Typically regarded within the optimal control framework, the time derivative of the system’s state is represented using differential algebraic equations [99]. Alongside the system’s dynamical model treated as differential constraints, certain non-differential limitations may be enforced throughout the entire time horizon, referred to as path constraints. Typically, these kinds of constraints are expressed as equality and inequality constraints. Optimal control theory aims to find acceptable control strategies that enhance system performance while adhering to specific path and boundary limitations. Consequently, the optimization procedure requires an index to assess performance. In control engineering, specifically in optimal control, this type of cost functional is referred to as the performance index. The users’ goals need to be mathematically analyzed and incorporated into the performance index.

Numerous methods are present in the literature for addressing the optimal control problem. Nonetheless, certain factors must be considered to choose the appropriate one. The applicability of these methods varies based on the control policy structure (i.e., closed-loop or open-loop), whether the approach is online (e.g., receding horizon) or offline, the level of optimality (e.g., sub-optimal versus optimal or local versus global solutions), characteristics of the dynamical system (e.g., linear or nonlinear, quantity of state and control variables), the nature of the cost functional (e.g., linear, quadratic, or nonlinear), imposed constraints, the time horizon (i.e., finite or infinite), and the computational time.

One way to classify OC methods is by the approach they use to address the optimization problem, whether analytically or numerically. In theory, the Hamilton–Jacobi–Bellman (HJB) equation and Pontryagin’s Minimum Principle (PMP) are the two primary methods that define optimal solutions to the OC problem. The latter establishes the essential criteria for optimality, while the sufficient conditions are derived from HJB. Numerical methods employ indirect and dynamic programming techniques to numerically address the challenges derived from PMP and HJB, while the direct approach seeks to solve the OC problem by transforming the original infinite-dimensional issue into a finite-dimensional form.

Non-optimal control approaches attempt to address dynamical optimization issues in a more straightforward way. Certain simplifications typically assumed in these techniques involve neglecting aircraft dynamics and constraints or addressing them in a simplified manner, like through linearization. These techniques seek to deliver quick and, to a degree, dependable results, even if they do not produce the optimal paths. To address these optimization issues, different strategies, including geometric techniques, path-planning algorithms, combinatorial optimization, and meta-heuristics, are typically utilized [100]. In these approaches, the optimization issue is generally framed without accounting for aircraft dynamics or with partial consideration to estimate trajectory performance metrics like speed, fuel consumption, emission factors, and climate effects. Subsequently, optimization methods are applied to resolve the established problem.

For example, when the path of an aircraft is described using a series of discrete or continuous variables and its performance is easily forecasted, an appropriate option is a meta-heuristic method, utilizing iterative combinations of random heuristic techniques to improve the proposed solution. Simulated annealing, genetic algorithms, variable neighborhood search, and particle swarm optimization are algorithms employed as meta-heuristic solvers. Owing to exploration and exploitation characteristics, such algorithms can deliver approximate global solutions. Moreover, they do not depend on gradient information and are easy to implement. Additionally, for this type of issues, traditional NLP solvers are advantageous for delivering quick answers. The primary disadvantage of classical (or gradient-based) NLP solvers is their sensitivity to the initial estimate, often resulting in local solutions.

The cost function for these optimization issues can be similarly defined regarding objectives as those found in OC problem formulation. For example, the Lagrange component of the performance index can be estimated using a summation. These techniques are more advantageous when addressing the optimization of a large volume of flights while also accounting for the intricacies of air traffic (e.g., conflicts). Mathematical programming, meta-heuristics, gradient-driven NLP solvers like Successive Quadratic Programming (SQP), and interior-point techniques are suboptimal control approaches that have been utilized in research to address the climate optimal trajectory planning issue.

6.1. Optimal Approaches: A Summary

Across the reviewed literature, the selection of an optimization approach is consistently shown to depend on the specific operational context, with airspace density, meteorological uncertainty, and decision time horizon acting as the dominant discriminating factors. In low- to medium-density airspace and within strategic or pre-tactical planning horizons, where traffic interactions can be aggregated and system evolution can be assessed through scenario analysis, offline and simulation-based optimization methods are particularly appropriate. Approaches such as agent-based modeling combined with evolutionary multi-objective optimization or mixed-integer linear programming formulations for ATFM allow for the explicit representation of capacity constraints, controller workload, and delay propagation, while accommodating simplified aircraft performance and averaged meteorological inputs. In this context, the primary objective is not real-time optimality at the single-flight level, but rather the identification of Pareto-efficient policies that balance emissions, delays, and network resilience, making these methods well suited for policy assessment, airspace design, and demand–capacity balancing with environmental considerations.

As traffic density increases and operations move closer to the tactical horizon—especially in TMA—predictability, safety, and controller acceptability become overriding constraints. In such environments, optimization is necessarily restricted to a reduced set of decision variables, and methods focusing on vertical-profile and procedure-based optimization, such as Continuous Descent Operations, Continuous Climb Operations, and PBN-enabled curved approaches, are preferred. These techniques exploit deterministic guidance, predefined geometries, and limited flexibility to ensure compliance with separation minima and workload constraints, while still yielding substantial reductions in fuel burn, noise, and local emissions. Their suitability stems from the relatively low sensitivity to short-term meteorological uncertainty and from the need to maintain stable, repeatable trajectories in high-density traffic flows, where fully flexible 4D optimization would be operationally impractical.

At the tactical and near-real-time level, particularly in en-route airspace and under conditions where meteorological variability directly influences both fuel efficiency and non-CO₂ effects, more sophisticated trajectory optimization methods become necessary. When contrail formation, NO_x-induced climate effects, or climate-sensitive regions must be considered, the optimization problem inherently becomes high-dimensional and strongly coupled to atmospheric state variables. In these circumstances, direct and indirect optimal control methods, as well as fast meta-heuristic solvers coupled with reduced-order aircraft models and aCCF are most appropriate, as they enable the continuous adjustment of altitude, speed, lateral routing, and timing in response to updated weather forecasts. However, their applicability is conditioned by computational constraints and by the reliability of meteorological inputs; as forecast uncertainty increases, the benefit of fine-grained optimization diminishes, and robustness considerations may outweigh nominal optimality.

Finally, when decision horizons are extremely short and operational uncertainty is high—such as during arrival sequencing in congested TMAs or under rapidly changing weather—optimization strategies tend to converge toward hybrid or constrained approaches, combining limited tactical adjustments (e.g., minor altitude or speed changes, controlled time shifts) with flow-management techniques such as arrival merging. These methods sacrifice global optimality in favor of robustness, predictability, and safety, reflecting the fundamental trade-off identified throughout the literature: as airspace density increases and decision time shrinks, the preferred optimization paradigm progressively shifts from globally optimal, flexible trajectory planning toward locally constrained, procedure-oriented solutions that remain compatible with real-world ATM and ATC operations.

6.2. Future Research

6.2.1. Modeling of Emissions and Climate Effects for New Fuels and Propulsion Systems

The first major research direction concerns the extension of current emissions and climate-impact modeling frameworks beyond conventional kerosene-fueled turbofan aircraft. While existing methodologies, such as BADA-based fuel flow models and ICAO emission indices, are well-established for hydrocarbon combustion, they are not directly transferable to emerging propulsion concepts, including hybrid electric architectures, hydrogen combustion, and fuel-cell-powered electric propulsion. Future work must therefore focus on developing consistent aircraft performance and emissions models capable of representing these technologies across all flight phases, including climb, cruise, and descent. In parallel, the characterization of non-CO₂ effects for alternative fuels—particularly changes in water vapor emissions, soot particle number, and their implications for contrail formation and radiative forcing—remains an open scientific challenge. Addressing these gaps is a prerequisite for reliably assessing how new propulsion systems modify climate-sensitive regions and, consequently, the effectiveness of trajectory-based mitigation strategies.

6.2.2. Optimization Methodologies Across Scales and Under Uncertainty

The second research axis relates to the evolution of optimization techniques capable of bridging micro-scale trajectory planning and macro-scale ATM network management. While current studies largely focus on single-flight or limited-scope optimizations, future approaches must explicitly address large-scale, multi-flight problems involving thousands of daily trajectories, strong traffic interactions, and shared airspace constraints. This calls for scalable optimization frameworks that combine fast trajectory predictors, reduced-order climate metrics, and advanced solution strategies, including hybrid meta-heuristics, learning-based approaches, and receding-horizon control. Furthermore, the explicit treatment of uncertainty—particularly meteorological uncertainty affecting both aircraft performance and non-CO₂ climate effects—represents a critical research need. Integrating probabilistic weather forecasts and robust or stochastic optimization techniques into climate-aware trajectory planning is essential to ensure that optimized solutions remain effective and operationally acceptable under real-world variability.

6.2.3. Integration of Climate Metrics into ATM Decision-Making and Policy Frameworks

The third, cross-cutting research direction concerns the consistent integration of climate metrics into both operational ATM tools and higher-level policy instruments. While the literature clearly distinguishes between metrics suited for tactical decision-making (e.g., RF- or aCCF-based indicators) and those appropriate for strategic assessment (e.g., GWP or ATR), these metrics are rarely embedded within a unified decision–support framework spanning different time horizons and governance levels. Future research should therefore aim to develop multi-level architectures in which short-term, meteorology-dependent metrics inform tactical ATM/ATC actions, while aggregated CO₂-equivalent metrics support strategic planning, capacity management, and policy evaluation. Such integration would also enable the exploration of market-based measures, incentives, or constraints that account for non-CO₂ effects, an area that remains largely unexplored due to scientific uncertainty. Establishing transparent links between operational decisions, climate metrics, and policy objectives is essential to translate trajectory-level mitigation potential into system-wide climate benefits.

7. Relationship Between ATM/ATC Procedures and Climate Metrics

In this work, several optimization approaches have been addressed, with reference to different ATM/ATC decision levels. This, in turn, implied the consideration of different optimization variables and climate metrics, leading to the consideration of a very wide scope in terms of considered air traffic efficiency domains. In order to provide an outlook at a glance about the possible areas of application of the different approaches considered in the paper, this section reports a framework providing correspondence between the different aircraft traffic management levels and the applicable optimization approaches and climate metrics, as addressed in the paper. This framework is aimed to emphasize the most relevant optimization variables (route, altitude, speed, timing) and the most appropriate climate metrics (RF, GWP, GTP, ATR, eqCO₂) for the different typical ATM procedural and operational levels (strategic, pre-tactical, tactical).

To this aim, first of all, the following tables emphasize the typical ATM/ATC decision levels (

Table 2. An overview of the typical Air Traffic Management (ATM) and Air Traffic Control (ATC) decision levels.

Decision Level	Time Horizon	Description
Strategic	Before the flight (months/weeks/days)	Airlines and ANSPs (Air National Service Provides) develop network-wide flight plans, capacity assessments, and sustainability policies with broad environmental targets but limited operational precision.
Pre-tactical	Before the flight (hours)	The detailed flight planning is elaborated, integrating weather forecasts, confirmed traffic demand, and dynamic rerouting, in order to have confirmed flight plans before take-off that are deconflicted “a priori”. In this phase, trajectory optimization is carried out in order to achieve as many environmental benefits as possible.
Tactical	Real-time during the flight	ATC manages the traffic separation and ensure appropriate sector capacity and safety, allowing minimal trajectory flexibility, focusing on procedural efficiency (CDO/CCO) and immediate conflict resolution (to prevent loss of separation and collision risks). The safety of flights (i.e., maintaining traffic separation) is critical and of primary importance in this phase, whereas environmental optimization is still possible under limited flexibility but is not the main objective.

), the key optimization variables (

Table 3. An overview of the main aircraft path optimization variables.

Optimization Variable	Description
Route	The optimization variable is the track (lateral) reference of the aircraft. It is used for lateral path optimization, mainly via Performance Based Navigation (PBN) and direct routing. It can be used for contrail avoidance maneuvers and is applicable across all ATM/ATC levels. Even if it is most impactful strategically, it can also be considered in future contrail avoidance management at tactical level, provided that the real-time lateral contrail avoidance maneuver has been cleared in advance by ATC.
Altitude	The optimization variable is the altitude (longitudinal) reference of the aircraft. It is used for cruise altitude optimization and step-climbs. It can be used for contrail avoidance, both at pre-tactical and tactical (provided that the real-time longitudinal contrail avoidance maneuver has been cleared in advance by ATC) levels. It critically affects non-CO2 climate impacts, because of the modification of emissions release altitude.
Speed	The optimization variable is the speed (True Air Speed (TAS), Indicated Air Speed (IAS), Calibrated Air Speed (CAS)) reference of the aircraft. It is used for profile adjustments for arrival sequencing and fuel efficiency, with tactical flexibility in approach and landing phases. It mainly influences NOx emission indices, because of the modification of the throttle settings, leading to different emissions from the engine operation.
Timing	The optimization variable is the timing of the different flight phases (departure, arrival, sequencing, holding if any) for the aircraft. It can be used for slot allocation, holding minimization, climate-sensitive regions avoidance. It can be exploited at all ATM/ATC decision levels, and its primary benefits can encompass fuel burn reduction (CO2 emissions reduction) and contrail sensitive conditions/regions avoidance (non-CO2 climate impact).
Overall 4D trajectory optimization	Full 4D (3D + time) trajectory optimization combining all the above variables. It can be used to maximize the benefits above indicated, primarily at pre-tactical level, because of the required computational burden. However, research efforts are needed to enable the 4D trajectory optimization at tactical level (real-time during the flight), in order to implement future 4D-contract based trajectory management with wide trajectory negotiation possibilities during flight.

) and the main climate metrics (

Table 4. An overview of the main commonly considered climate metrics.

Climate Metrics	Description
Radiative Forcing (RF)	The metric refers to current climate impact in terms of perturbation [W/m2] and is relevant at tactical (and also pre-tactical) level for fuel burn assessments.
Global Warming Potential (GWP)	The metric refers to time-integrated forcing over 20 to 100 years’ time horizons and is relevant at strategic level (or even before, at policy decision making level) for comparisons of CO2 vs. non-CO2 impacts.
Global Temperature Potential (GTP)	The metric refers to the future temperature response and is relevant at strategic level for long-term strategic planning emphasizing final resulting climate impact outcomes.
Average Temperature Response (ATR)	The metric refers to the time-averaged temperature change and is relevant mainly at pre-tactical level, for non-CO2 optimization (contrail avoidance, thanks to the availability of reliable weather forecasts some hours before the flight).
Unified CO2-equivalent metric (eqCO2)	The metric refers to a conversion of the different impacts into a unified equivalent CO2 emissions level, in order to facilitate comparisons among different technologies. It can be used across all ATM/ATC decision levels to support decision making.

) considered in the paper. Finally, after that,

Table 5. Optimization approaches, related ATM/ATC decision levels, key optimization variables, climate metrics and applications.

Optimization Approach	ATM Level	Primary Variables	Climate Metrics	Key Applications
CDO/CCDA	Tactical Pre-tactical	Altitude Speed Route	RF eqCO2	Fuel consumption and noise reduction in TMA
CCO	Tactical Pre-tactical	Altitude Speed	RF eqCO2	Departure optimization
PBN/RNP-AR	Strategic Pre-tactical	Route	RF eqCO2	Terminal procedure design
Step-Climb	Pre-tactical Tactical	Altitude	RF eqCO2	Cruise efficiency
MOTO	Pre-tactical	4D (i.e., all variables)	GWP GTP ATR eqCO2	Multi-objective balancing
Contrail Avoidance	Pre-tactical Tactical	Altitude Route Timing	GWP20 ATR20 eqCO2	Climate-sensitive regions
ATFM emissions	Strategic Pre-tactical	Timing Route	eqCO2 GWP	Network flow Optimization
Arrival Merging	Tactical	Route Timing	RF eqCO2	TMA capacity Enhancement

indicates the relationship between the different optimization approaches considered in the paper and the related ATM/ATC decision levels, key optimization variables, main relevant climate metrics, and possible targets for the applicability of such optimization methodologies.

Finally, a flowchart is reported in Figure 2, providing the conceptual framework linking ATM/ATC decision levels with optimization variables, optimization approaches, aviation emissions, and climate metrics. In particular, the figure highlights how decisions taken at different ATM/ATC levels (strategic, pre-tactical, tactical) act on specific trajectory variables, are addressed through distinct optimization methodologies, affecting both CO₂ and non-CO₂ emissions, which in turn require different climate metrics, depending on the considered temporal and spatial scale.

8. Conclusions

This paper reported the outcomes of an extensive and articulated multidisciplinary literature analysis about the recent advancements in modeling the aviation emissions, quantifying them in terms of metrics and reducing them thanks to specific operational procedures implementation.

More specifically, the paper first provided an assessment of the state of the art, as emerging from an extensive critical analysis of the recent literature, about the main current as well as the more promising prospective operational procedures aimed at increasing the efficiency of the aircraft operations while in flight (the ground operations were out of the scope of the study), in particular with reference to the flight segments occurring in the TMA. After briefly introducing the main issues and solutions related to all the flight phases, the study addressed the critical analysis of the more relevant approaches aimed to optimize the flight profile in TMA, in order to reduce the fuel consumption and, in turn, the related chemical emissions. Particular attention has been devoted to the consideration of the recent ATM operational paradigms leveraging the exploitation of the GNSS-based capabilities, as enabler for the implementation of the Performance-Based Navigation (PBN) and of possible enhancements in the recent Continuous Descent Operations (CDO).

Following this first part of the study focused on the ATM operational aspects, the paper addressed the assessment of the methodological literature state of the art about the CO₂ and non-CO₂ emissions modeling. In this framework, the most important approaches have been critically analyzed and their advantages and drawbacks have been outlined. In particular, the study first considered the conventional standard approach based on the exploitation of the BADA database and then addressed the ICAO emission index. Particular attention, finally, has been devoted to the very relevant topic of the condensation trails (contrails) formation modeling, which is always gaining increasing attention in the aviation domain and which represents a fundamental base of knowledge as a prerequisite to inform and support the design of future effective solutions for contrail prevention and/or contrail avoidance.

Once the state of the art in terms of both operational and methodological domains in this way was assessed, the study reported the analysis of the most recent optimization procedures that are considered when addressing the emissions reduction problem. These methodologies are always evolving towards the target of enabling a real-time 4D trajectory optimization able to reduce the fuel consumption as well as the chemical emissions, while at the same time adapting the aircraft flight profile to the actual and near-future expected atmospheric conditions that may lead to the formation of contrails. The considered approaches addressed all the flight phases, both en-route and in TMA.

The last part of the paper, finally, outlined the results of an extensive study about the possible metrics that can be used in order to properly design the flight profile and trajectory optimization tools. These metrics can be beneficial in order to integrate not only the short-term consideration of the aviation operation effects—in terms of immediate pollutant emissions (whose main impact is typically on the local air quality)—in these optimization tools, but also the consideration of the longer-term effects of these emissions (whose impact is at climatic level) in terms of both geographical and time scales.

In summary, the paper aimed to provide an integrated multidisciplinary overview about the problem of CO₂ and non-CO₂ aviation emissions reduction and about its possible solutions. It addressed both the currently available know-how and operational procedures and the emerging evolutions in the methodological and procedural domains. In addition, the paper provided the reader with a detailed analysis of possible metrics that can be used when addressing the quantification of the impact of such emissions, not only over the short term and at a local scale but also over a long-term climatic scale and at a global level.

Future studies will be devoted to the coverage of the specific aspects that can also be related to the emerging use of Sustainable Aviation Fuels (SAF), as well as prospective exploitation of liquid hydrogen, and the consideration of future innovative hybrid and full electric propulsion powertrains in aviation.