Simulation and evaluation of sustainable climate trajectories for aviation
Thomas Planès, Scott Delbecq, Valérie Pommier-Budinger, Emmanuel Bénard
SSimulation and evaluation of sustainable climatetrajectories for aviation
T. Plan`es a, ∗ , S. Delbecq a , V. Pommier-Budinger a , E. B´enard a a ISAE-SUPAERO, Universit´e de Toulouse, 10 Avenue Edouard Belin, 31400 Toulouse,France
Abstract
In 2019, aviation was responsible for 2.6% of the world CO emissions as wellas additional climate impacts such as contrails. Like all industrial sectors,the aviation sector must implement measures to reduce its climate impact.This paper focuses on the simulation and the evaluation of climatic scenariosfor the aviation industry. For this purpose, a specific tool (CAST for ”Cli-mate and Aviation - Sustainable Trajectories”) has been developed. Thistool follows a methodology adapted to aviation using the concept of carbonbudget and models of the main levers of action such as the level of air traffic,reduction of aircraft energy consumption or energy decarbonisation. Thesemodels are based on trend projections from historical data or assumptionsfrom the literature. Several scenario analyses are performed in this paperusing CAST and allow several conclusions to be drawn. For instance, themodelling of the scenarios based on the ATAG (Air Transport Action Group)commitments shows that aviation would consume between 2.9% and 3.5% ofthe world carbon budget to limit global warming to 2 ° C and between 6.5%and 8.1% for 1.5 ° C. Also, some illustrative scenarios are proposed. By allo-cating 2.6% of the carbon budget to aviation, it is shown that air transport iscompatible with a +2 ° C trajectory when the annual growth rate of air trafficvaries between -1.8% and +2.6%, depending on the considered technologi-cal improvements. However, in the case of a +1.5 ° C trajectory, the growthrate would have to be reduced drastically. Finally, analyses including non- CO effects compel to emphasize the implementation of specific strategiesfor mitigating contrails. ∗ Corresponding author (+33 5 61 33 88 51)
Email address: [email protected] (T. Plan`es)
Preprint submitted to Elsevier February 3, 2021 a r X i v : . [ phy s i c s . s o c - ph ] F e b eywords: Sustainable aviation, Sustainable trajectories, Carbon budget,CAST
1. Introduction
Human activities generate GreenHouse Gas (GHG) emissions, in partic-ular of CO due to the combustion of fossil fuels. These various emissions,as well as other physical phenomena such as the modification of the terres-trial albedo, induce that the radiative forcing of the Earth, defined by thedifference between solar irradiance absorbed and energy radiated emitted, be-comes positive. This results in an increase in the global average temperatureof the Earth. The consequences of these rapid and significant temperaturevariations are many and varied [1]. Melting ice, rising sea levels, water stress,declining agricultural yields, heat waves or loss of biodiversity are examples,the extent of which will depend on the level of temperature anomalies. TheIntergovernmental Panel on Climate Change (IPCC) studies these differentquestions through numerous reports such as [2, 3]. Due to climate change,the states that have ratified the Paris Climate Agreements [4] have commit-ted to limit global warming well below +2 ° C above pre-industrial levels andto pursue efforts to limit the increase to 1.5 ° C.In order to comply with the Paris Climate Agreements, it is thereforenecessary to set up compatible trajectories, particularly in terms of GHGemissions. For example, at the global level, the IPCC defines trajectories tolimit global warming to 1.5 ° C or 2 ° C using the concept of carbon budgets [5].Several tools for exploring the impact of key levers of action on the reductionof GHG emissions have been proposed to simulate global trajectories easily.For instance, the En-ROADS simulator allows generating trajectories usingdifferent economic, technical and social parameters [6]. Similarly, the GlobalCalculator tool can be used to generate trajectories based on energy, land andfood scenarios [7]. These different prospective scenarios can also be applied tospecific sectors. The transportation sector is particularly interesting becauseof the rebound effect and the increase in travel speeds [8]. For instance,transportation-specific transition scenarios are considered as in France [9] orin a Chinese city [10]. More specifically, these analyses can also be appliedto the sector of aviation.Aviation has a significant impact on climate change through differentemissions and physical phenomena [11], like CO emissions, condensationtrails (contrails) or N O x emissions. It can be assessed using the notion of2ffective radiative forcing (ERF) [12]. This indicator can be estimated for CO emissions but also non- CO effects as shown in Figure 1. Overall, avi-ation has generated a positive ERF of 100 . mW/m in 2018 since 1940 andthus global warming [13]. The non- CO effects are dominated by contrails,which are complex phenomena that depend on local atmospheric conditions[14, 15]. From a quantitative point of view, aviation is responsible for about2 to 3% of world CO emissions (2.1% in 2019 according to [16]). In addition,by integrating the non- CO effects like contrails, the overall climate impactof aviation reached 3.5% of world ERF in 2011 [13]. In addition, accordingto the ¨Oko-Institut, due to the significant growth of the sector and the dif-ficulty of easily and rapidly implementing technological solutions to reducethe GHG emissions of aircraft, the aviation sector could represent up to 22%of global impacts on climate change by 2050 [17]. These values involve sig-nificant uncertainties, and a study is in progress to refine the results [18].However, these results show that the aviation sector is responsible for signif-icant effects on the climate and that the transition that has been initiatedmust be emphasized.An aircraft generates environmental impacts at different stages of its lifecycle. Figure 2 represents schematically the life cycle of an aircraft, includinguse, resource extraction or end-of-life phases. In order to better quantify theenvironmental impacts of aviation in the broadest sense, Life Cycle Assess-ment (LCA) type studies have been carried out. For example, a simplifiedLCA methodology for Airbus A320 aircraft has been developed [19]. A studyon other aircraft has been carried out and converges towards similar results[20]. Some studies focus more specifically on pollutant emissions close toairports [21]. All these studies show that climate impacts are one of themajor environmental issues for aviation, with however some discrepancies inthe evaluation of non- CO effects. In particular, these LCAs show that thecombustion and production of kerosene are the most impacting phases of thelife cycle. Thus, the reduction of aircraft fuel consumption and the use oflow-carbon fuels are the technological measures with the greatest impact tominimize CO emissions from aviation.Numerous studies have been conducted to evaluate new technologies toreduce aircraft fuel consumption. For example, hybrid-electric architecturesare being studied for aircraft with different operating ranges [22]. Thesearchitectures are envisaged for short-range aircraft. The use of new fuels isalso being studied. The main solutions being considered are biofuels [23] andhydrogen [24], but both face problems of energy availability.3 igure 1: Different components of aviation effective radiative forcing in 2019 [13] Knowing the climatic impacts of aviation and potential improvements,work has focused on the evaluation of prospective scenarios. For instance, a2005 study shows the need to stabilize the number of flights per inhabitantat levels slightly higher than those of the 2000s to limit the CO atmosphericconcentration to 450 ppm [25]. Then, the work of [26] indicates that aviationwould be responsible for 5.2% of the total anthropogenic warming under anIPCC scenario named RCP2.6, considering ICAO scenarios. Finally, otherstudies compare different mechanisms such as CORSIA (Carbon Offsettingand Reduction Scheme for International Aviation) or EU-ETS (EuropeanUnion - Emissions Trading System) [27] or show the difficulty of decarbonis-ing aviation [28].Although forward-looking scenarios for the aviation climate transitionexist, these different studies do not address the problem in its entirety andleave open questions. First of all, non- CO effects are often treated in an4 igure 2: Life cycle for an aircraft approximate way or not at all. Secondly, there are no reference models forsimply constructing and analysing aviation scenarios. Thirdly, the evaluationof these scenarios with regard to the Paris Climate Agreements is not alwayscarried out. Finally, a tool like the En-ROADS or Global Calculator tools,but dedicated to detailed simulations of the climatic trajectories specific toaviation, is missing.The aim of the work reported here is to present a tool which can analyzescenarios for air transport with regards to environmental criteria and generatesustainable aviation trajectories in terms of climate change. The contributionof the paper is to provide models for estimating different trajectories usingmain aviation levers of action. The results obtained make it possible toquantify and identify general trends for aviation’s climate transition and tointegrate them into a single freely accessible tool.The paper is organized as follows. In Section 2, the overall methodologychosen for the tool is presented. Then, the models developed for estimatingthe impacts of aviation and assessing the sustainability of trajectories are thesubject of Section 3. Subsequently, in Section 4, various scenarios are mod-5lled, evaluated and criticized and a global analysis is carried out. Finally,Section 5 offer concluding remarks and an outline of future work.
2. Methodology
In this section, the methodology used to develop the tool CAST is out-lined. First, the scope of the tool and the main data required for the im-plementation of the methodology followed in the tool are given. Then, thearchitecture of CAST is detailed as well as the main aspects of the softwaredevelopments.
The scope of this work is commercial aviation which includes freight andpassenger transport since freight is essentially carried out in a opportunemanner (i.e. by filling the cargo compartments). In this paper, military andgeneral aviation are not taken into account.To develop the software, input data on global air transport are required:number of passengers, Revenue Passenger Kilometer (RPK), total aircraftdistance or mean aircraft load factor. For this study, they are taken from theInternational Civil Aviation Organization (ICAO) [29]. The consumption ofkerosene is also needed. [30] indicates that commercial aviation is responsi-ble for the consumption of 88% of the world’s kerosene. The consumptionof other fuels such as biofuels is currently marginal and is not accountedfor. The world’s kerosene consumption data is taken from [31], it representsapproximately 348 Mtoe in 2019.In order to convert this kerosene consumption into CO emissions, Eu-ropean data from [32] are used to get the emission factor estimated to71 . gCO /M J if only emissions due to combustion are considered and86 . gCO /M J if both kerosene production and combustion are taken intoaccount. These values are close to the values used in American studies [33].To take into account the other phases of the life cycle to obtain the avia-tion global CO emissions, based on mean results from [20], these values areincreased by 2%.To correctly quantify the climate effects of aviation, it is necessary to alsoconsider the non- CO effects in addition to the CO emissions. First, Table1 gives the coefficients to obtain emissions from the consumed kerosene [13].To estimate the impact of these emissions in terms of ERF, coefficients aredefined using data from [13]. They are given in Table 2. The impact of the6ontrails is estimated in relation to the total distance flown by aircraft. Theimpact of CO is considered cumulative over time while the other phenomenaare calculated annually. Table 1: Emission factors for kerosene combustion
Emissions Value [unit] CO .
15 [ kgCO /kgF uel ] H O .
23 [ kgH O/kgF uel ] N O x . gN O x /kgF uel ]Aerosol (BC) 0 .
03 [ gBC/kgF uel ]Aerosol ( SO x ) 1 . gSO /kgF uel ] Table 2: ERF coefficients for aviation climate impacts
Climate impact Value [unit] CO .
88 [ mW/m /GtCO ] H O . mW/m /T gH O ] N O x .
55 [ mW/m /T gN ]Aerosol (BC) 100 . mW/m /T gBC ]Aerosol ( SO x ) − . mW/m /T gSO ]Contrails 1 . . − [ mW/m /km ]Using all these data, direct CO emissions from kerosene combustionfor commercial aviation are computed and amount to 921 M t in 2019, i.e.2.1% of the world CO emissions in 2019 [34]. For comparison, ATAG hasestimated these emissions at 915 M t in 2019, a difference of 0.7%. In termsof global emissions, the CO emissions due to the entire life cycle amountto 1134 M t , or 2.6% of the world CO emissions in 2019. Including alsonon- CO effects, while human activities generated 2290 mW/m until 2011[3], commercial aviation generated 80 . mW/m , i.e. 3.5%.7 .2. Architecture and development of the tool The objectives of CAST are to generate climate trajectories (or prospec-tive scenarios) for aviation and to evaluate their compatibility with temper-ature goals such as those defined in the Paris Climate Agreements [4].Figure 3 shows the schematic diagram which describes how CAST is built.CAST is based on models and scenarios, detailed in Section 3, whose inputdata can be divided into two categories: • the main aviation levers of action such as air traffic growth or fuelconsumption efficiency used in order to model the aviation sector; • the climate parameters used to define climate scenario targeted foraviation. CAST (
Models and scenarios ) Air traffic Efficiency Load factor Energy Non-CO Others
Aviation levers of action Climate parameters
Global parameters Allocated share
Aviation trajectories Climate analysis Other results
Consumption Emissions Radiative forcing Climate budget
Figure 3: CAST schematic diagram
To assess the complexity behind the CAST process, the number of inputsand outputs is given here. From its first beta-version, CAST uses 24 input8ariables to allow users to define their own scenarios and trajectories. Inaddition, it uses 69 input parameters present in the models developed toperform the analyzes proposed in CAST. These parameters are not meant tobe modified by the user but rather updated when more recent literature anddata are available. The CAST methodology can then compute and provide116 outputs along with 35 different graphs.With regard to the software development of the tool, CAST is developedusing the Python programming language. The tool is freely available. Pro-viding a free tool that scientists, organizations, authorities and companiescan interact with for defining together sustainable aviation trajectories is agreat motivation. The data and models are mainly manipulated and imple-mented using the
Pandas package [35] but also use other scientific computingpackage like
Scipy [36] for solving implicit models for instance. The user in-terface uses ipywidgets [37] for the widgets and ipympl [38] for the graphs.The CAST software is deployed as a web application thanks to
Voil`a [39].
3. Models
The purpose of this section is to present the main models used in CAST.First, the overall methodology for assessing climate trajectories is described.Subsequently, the models specific to aviation levers of action are detailed.Finally, the main climate models used are given.
To simulate different scenarios of air transport, the main levers of actionfor aviation must be defined and interrelated. The chosen approach is basedon the application of the Kaya equation to aviation. The Kaya equation(1) allows linking global CO emissions to demographics (population P OP ),economics (GDP per capita
GDP/P OP ) and technological parameters (en-ergy intensity
E/GDP which can be related to efficiency and energy contentin CO CO /E ) [40]. The interest of this equation is that it simply showsthe main levers for acting on CO emissions [41]. However, some factors inthe equation are interdependent and the analysis can therefore be complex[42]. CO = P OP × GDPP OP × EGDP × CO E (1)9quation (2) is a proposal for aviation. The first factor is the RevenuePassenger Kilometer (RPK) and it represents the level of air traffic, couplingthe number of passengers and the distance flown. The increase in air traf-fic leads to an increase in CO emissions. The second factor ASK/RP K is the ratio between the Available Seat Kilometer
ASK and the RevenuePassenger Kilometer
RP K . It therefore represents the inverse of the meanaircraft load factor. For a fixed RPK, the CO emissions decrease if the loadfactor increases. Next, the third factor E/ASK is the ratio between theenergy E consumed by aviation and the Available Seat Kilometer ASK . Ittherefore represents the energy consumption per aircraft seat per kilometerand its improvement reduces CO emissions. Finally, the last factor CO /E is the CO content of the energy used by the aircraft. An improvement inthis factor, for example through the use of biofuels or hydrogen producedwith low-carbon energy, reduces CO emissions. These different parametersrepresent the main levers of action to decarbonize aviation. CO = RP K × ASKRP K × EASK × CO E (2)Kaya equation for aviation being only a proposal, it can be simplified,modified or detailed. For example, additional coefficients can be added totake into account indirect emissions or non- CO effects. Similarly, somecoefficients can be refined. For instance, the factor of energy consumptionper seat can be split between a factor that represents the improvements inefficiency per kilometer and another factor for improvements in flight andground operations. Finally, it is important to note that some factors are nottotally independent. For example, the fuel change may lead to an increasein energy consumption per seat or the level of air traffic may affect the meanaircraft load factor. Nevertheless, these different levers of action enable initialanalyses to be carried out.Figure 4 represents the evolution of the different parameters from equa-tion (2). Despite the improvement in the mean aircraft load factor and energyconsumption per seat (divided by 2 in 30 years), aviation’s CO emissionshave doubled in 30 years due to the strong increase in air traffic. It is in-teresting to note that due to the almost exclusive use of kerosene, the CO energy content of aviation has remained constant.If the historical study of the Kaya equation makes it possible to justify theimportance of the different levers of action, a projection analysis is interestingto establish transition scenarios. As a consequence, modelling the future10
990 1995 2000 2005 2010 2015 2020Year100200300400 E v o l u t i o n o f t h e d i ff e r e n t p a r a m e t e r s ( b a s e i n ) Kaya equation for aviation
RPKASK/RPKE/ASKCO2/ECO2
Figure 4: Evolution of Kaya equation parameters for aviation since 1991 evolution of the different parameters can allow the development of transitionscenarios for aviation’s CO emissions, and more globally for the climateimpact of aviation. The objective of this section is to present the models for the various leversof action specific to aviation. The action levers chosen are those of the equa-tion (2), with a distinction for operations and non- CO effects. Two casesarise for establishing the models. Either historical data are available and de-terministic historical models can be computed from these data. These modelscan be used to project the data into the future years to determine trend mod-els. Or historical data is lacking and simple models are then computed onthe basis of assumptions from the scientific literature. The parameter corresponding to the lever of action on air traffic is
RP K .To establish evolution scenarios, the approach consists in studying the his-11orical evolution of this parameter. Figure 5 represents the historical valuessince 1991 [29] as well as the historical trend model. The latter was obtainedusing a simple exponential base function with a fixed growth rate as pre-sented in the equation (3) with
RP K the initial value in 1991, x the yearand τ the smoothed growth rate over the period 1991-2019. RP K ( x ) = RP K (1 + τ ) x − (3)To determine the parameter τ , an optimization was performed using theSLSQP method to minimize the Root Mean Square (RMS) error betweenthe historical data and the model. This has the advantage of smoothing thevalues due to different crises (2001 September 11 attacks or financial crisisin 2008). The optimal rate obtained is then 5.5% for the period 1991-2019,with an RMS error of 0.032. By restricting the study to the evolution of thelast 10 years, this rate reaches 6.5%, which shows an acceleration of the airtraffic growth trend as depicted in Figure 5. R e v e nu e P a ss e n g e r K il o m e t e r [ R P K ] Evolution of world air traffic
HistoricalModel
Figure 5: Model of historical world air traffic
Nevertheless, due to the saturation of certain markets such as Europe,12anufacturers anticipate a decline in this rate in the coming years. Forexample, with regard to the evolution of the total distance flown by aircraft,Boeing was counting on annual growth of 4.7% from 2017, compared with4.4% for Airbus [43]. Moreover, ICAO has announced an average forecastfor RPK of 4.1% per year between 2015 and 2045 [44]. Finally, this growthrate could in the future decrease or even become negative due to the currentcrisis and economic, political or health measures.To model the air traffic in the coming years, the exponential model with τ as tuning parameter is kept for its simplicity and its good representation ofthe evolution of this lever of action. The equation (4) is used in CAST. Thepre-Covid forecast growth rate is 4.5% and the post-Covid forecast growthrate is 3.0% [45]. RP K ( x ) = RP K (1 + τ ) x − (4) The second lever of action concerns the improvement of the energy ef-ficiency per seat, excluding the integration of flight and ground operationsimprovements. Contrary to air traffic trends, simple models do not ade-quately model historical trends. Indeed, technological limitations lead toreduced gains in recent years. For example, according to [46], energy con-sumption per kilometer and per passenger (including the aircraft load factor)decreased by about 1.5% per year on average between 1975 and 2000, butless significantly afterwards. Similar results can be seen in Figure 4.To establish trend models of the energy efficiency per seat and scenarios, athree-step specific methodology has been developed based on historical dataof energy consumption per seat from [31, 29].1. Synthesis of a past trend model from historical data.2. Projection of the past trend model up to 2050 and modelling of thisprojection to obtain a trend model for future evolution.3. Definition of different scenarios using the simplified projection modelThe interest of this method is to separate the modelling of historicaldata from that of the projection. It allows obtaining an accurate model torepresent the trend evolution and a simple model to simulate the projectionand to define transition breaks. 13he difficulty is to select a type of regression model that can representthe evolution of the historical data and that allows the projection of the datain the future. Consequently, polynomial models are not considered becauseof their limits outside the field of study [47] and exponential models arepreferred.To perform the first step, three basic exponential models, more or lesscomplex, given in the equations (5), (6) and (7), are here considered andcompared over the period 2002-2019 due to the anomaly following 2001September 11 attacks. For each model, an optimization using the SLSQPmethod is performed on the coefficients in order to minimize the RMS errorbetween the historical data and the model. Figure 6 summarizes the modelsobtained. Model 3 provides the minimum RMS error, by a factor of 4 withrespect to model 2 and by a factor of 7 with respect to model 1, which is afixed decay rate model. Model 3 is therefore selected as the past trend modelbased on historical data. f ( x ) = f (1 − τ ) x − (5) f ( x ) = f f − e − (cid:15) ( x − x ) (6) f ( x ) = γβ ln [ α ( x − x )] (7)with f , τ, f f , (cid:15), x , α, β, γ different coefficients. For the selected model 3: γ = 2 . , β = 0 . , α = 0 . , x = 1990.The second step consists in projecting the past trend model to obtaina trend model for future evolution. The projection of the historical modelis represented by dotted lines on Figure 7. In order to generate differentscenarios on the evolution of this lever of action from 2020 to 2050, the mod-elling of this projection is carried out by considering three different modelsin the same way as before. Figure 7 shows that the optimizations of theselast models give close approximations. Therefore, the simplest model of thetrend efficiency by seat Ef , given by equation (8), is selected. It allows sim-ple modelling of the trend up to 2050 with only one coefficient τ . If the trendis computed using data projected between 2020 to 2050, τ equals to 1.0%. Ef ( x ) = 1 .
22 (1 − τ ) x − [ M J/ASK ] (8)14
002 2004 2006 2008 2010 2012 2014 2016 2018Year1.21.41.61.82.0 E n e r g y c o n s u m p t i o n p e r A S K [ M J / A S K ] Modeling the historical energy consumptionof aircraft per ASK
HistoricalModel 1Model 2Model 3
Figure 6: Models of historical aircraft energy efficiency by ASK
Finally, the last step consists in defining different scenarios for the futureby playing on the parameter τ . τ equals to 0 corresponds to the ”Absence”scenario in which the energy efficiency remains at the 2019 level. The valueof τ = 1 .
0% corresponds to the ”Trend” scenario of Figure 8. Other scenariocan be studied using the model developed in step 2 and different values of τ which reflect more or less ambitious changes. The ”Unambitious” scenariocorresponds to a rate of 1.5%, which corresponds to the average annual im-provements over the last 5 years calculated from historical data. Similarly,the ”Ambitious” and ”Very ambitious” scenarios correspond respectively toa rate of 2.0% and 2.5%, which corresponds to the average annual improve-ments over the last 10 and 15 years. Figure 8 summarizes the differentscenarios considered. Energy efficiency per seat can also be improved by reducing the travelleddistance, optimizing flight paths and designing better infrastructure for air-craft on the ground. All these improvements, known as flight and ground15
000 2010 2020 2030 2040 2050Year1.01.21.41.61.82.0 E n e r g y c o n s u m p t i o n p e r A S K [ M J / A S K ] Modeling the projected energy consumption of aircraft per ASK
HistoricalModel HistoricalModel 1Model 2Model 3
Figure 7: Models of projected aircraft energy efficiency by ASK operations, represent another lever of action. These operations have beenlittle modelled in recent decades and there is no available historical data tomodel their evolution.To overcome the lack of data and model the evolution of operations, itis proposed to use sigmoid functions which can represent an evolution ofimplementation until a maximum level is reached. These model are presentin many technological, sociological or economic fields [48, 49]. The equation(9) represents the models used in this paper. s ( x ) = V f e − α ( x − x ) (9)where s is the sigmoid model, x the year, V f the final value of the model, α a coefficient to set the speed of change and x the reference year for theinflection.In the case of operations modelling, sigmoid functions allow modelling forexample the effect of specific measures to reduce consumption. The choiceof the coefficients of the model allows introducing several scenarios. These16
000 2010 2020 2030 2040 2050Year0.60.81.01.21.41.61.82.0 E n e r g y c o n s u m p t i o n p e r A S K [ M J / A S K ] Scenarios for improving aircraft energy efficiency
HistoricalModel HistoricalAbsenceTrendUnambitiousAmbitiousVery ambitious
Figure 8: Scenarios for aircraft energy efficiency by ASK scenarios, particularly the realistic one, have been established from the in-dustrial data [16, 50]. For each scenario, it is assumed that α = 0 . x = 2030. • Absence : no new operations are considered; • Pessimistic : operational improvements are only marginally imple-mented and allow a reduction of consumption of 4% compared to valuesin 2019, which means that V f = 0 . • Realistic : operational improvements are developing and allow a reduc-tion of consumption of 8%; • Optimistic : operational improvements are widespread and allow a re-duction of consumption of 12%; • Idealistic : improvements in operations are generalized and optimizedand allow a reduction of consumption of 15%.17 .2.4. Load Factor
To model the evolution of the aircraft load factor, an approach similar tothat of efficiency is used. Indeed, historical data are available from 1991 [29]and enable trend models to be produced for describing the behaviour of theobserved data. The model of the aircraft load factor, based on a sigmoid andgiven in equation (10) as a function of the year x , is obtained by minimizingthe RMS error between the historical data and the model. It is interestingto note that this model converges to an aircraft load factor of about 90%. g ( x ) = 51 . .
71 + e − . x − [%] (10)Then, to model the projections, sigmoid functions are also used. Theaircraft load factor is then modelled using the equation (11) with α, β, x coefficients. The trend model of projected data is described with coefficients α = 0 . β = 0 .
15 and x = 2030. Different settings for these coefficientslead to the different scenarios presented in Figure 10. The sigmoid modelallows modifying the rate of change of the aircraft load factor but one of thelimits is the jump in value observed in 2020. LF ( x ) = 82 . (cid:18) α e − β ( x − x ) (cid:19) [%] (11) One lever of action concerns the decarbonisation of energy, i.e. the reduc-tion of the CO content of the energy used. In the same way as for operations,this action lever is currently used marginally and modelling using sigmoidfunctions can be used.To estimate the maximum decarbonisation rate of alternative fuels, anaverage value of about 25 gCO /M J is considered for biofuel emissions [23].The results are comparable for hydrogen even if major challenges remain [51].Therefore, it is considered that the decarbonisation rate of alternative fuelscompared to kerosene is 70%. The scenarios therefore focus on the proportionof the aircraft fleet that will operate on alternative fuels in the future.For these scenarios, only the overall decarbonisation rate is modified. Thelatter can take values between 0% (no aircraft has access to low-carbon fuels)and 70% (the entire fleet has access to low-carbon fuels). The coefficientsof the equation (9) are set to α = 0 . x = 2040 to obtain trajectoriesconsistent with the industrial data [16, 50].18
990 2000 2010 2020 2030 2040 2050Year65707580859095 A i r c r a f t l o a d f a c t o r [ % ] Scenarios for improving aircraft load factor
HistoricalModel HistoricalAbsenceTrendUnambitiousAmbitiousVery ambitious
Figure 9: Scenarios for aircraft mean load factor
However, these scenarios will have to be refined in the future taking intoaccount the constraints on the availability of global energy resources. CO effects The last major lever of action to reduce the climate impacts of aviationconcerns the mitigation of non- CO effects. In this article, only specificstrategies against contrails are considered.Many strategies to prevent the formation of contrails are being consid-ered, both from a technological and operational point of view [52, 53]. Thetechnological measures mainly considered are the reduction of the quantityand size of emitted particles [52]. From an operational point of view, mod-ifying the flight altitude for certain atmospheric conditions is studied [53].Quantitative studies have been performed to estimate the potential gains ofthese strategies. For example, different scenarios are studied in [54] and leadto contrails reductions between 20% and 91.8%. Similar analyses are alsoachieved in [55]. These different studies, valid for kerosene, must however beadapted for the use of alternative fuels. For instance, the use of hydrogen19lso leads to the formation of contrails, but the comparison with conventionalfuels remains uncertain [56, 52].As with previous models, the modelling of this lever of action is based onthe use of sigmoids. The scenarios considered here are extracted from [54]and are given below. They are based on changes in flight altitude and theuse of more efficient combustion chambers, called Dual Annular Combustor(DAC). • Absence : no strategies on contrails; • Pessimistic : slight changes in altitude, which do not lead to over-consumption, are implemented on conventional engines; • Realistic : more significant altitude changes, which result in slight over-consumption, are implemented on conventional engines; • Optimistic : slight changes in altitude, which do not lead to over-consumption, are implemented on improved DAC engines; • Idealist : more significant altitude changes, which result in slight over-consumption, are implemented on improved DAC engines.
In addition to the various levers of action presented, more specific optionshave been included in CAST. They allow in particular studying the specificeffects due to the Covid-19 epidemic as well as the impact of different eco-nomic, logistical or political measures.To model the impact of the Covid-19 epidemic, the tool is based on pro-jections made by IATA [57]. IATA has forecast a 66% drop in air traffic in2020 compared to 2019 and a return of air traffic to the 2019 level by 2024.Finally, the aircraft load factor has been affected by the epidemic and IATAhas forecast a load factor value of 58.5% in 2020 against 82.4% in 2019.Specific measures are also implemented in CAST. For instance, economicmeasures to represent CORSIA agreements are also considered [27]. Theseare marked-based measures that compensate for emissions of CO abovethe 2019 level to allow carbon-neutral growth from 2020. Secondly, anotheroption is to model social measures concerning air transport. Indeed, 1%of the people in the world are responsible for 50% of CO emissions fromaviation [30]. The implemented option allows dividing by 2 the number offlights for this part of the population.20 .3. Climate analysis To evaluate scenarios for aviation obtained from the models defined above,the concept of carbon budget is introduced and generalized in a simplifiedway to non- CO effects in this section. The assumptions for allocating carbonbudgets are also given and the analyses are carried out until 2050.The carbon budget is an interesting concept for estimating the impact ofgreenhouse gases on the global average temperature [58] and allows studyingthe ability of trajectories to reach climate targets [59]. The latter makes itpossible to relate the increase in average temperature to the cumulative quan-tity of CO emissions [3]. As a consequence, it is possible to determine theremaining quota of CO emissions to respect a maximum temperature rise.These carbon budgets yield different estimates, with significant uncertaintyexpressed in percentiles of Transient Climate Response to cumulative carbonEmissions (TCRE) [60]. Table 3 summarizes the different world carbon bud-gets estimated by IPCC [5]. To take into account Earth system feedback,100 Gt must be subtracted from these budgets. Table 3: Remaining carbon budgets from 01.01.2018 (without Earth system feedback)
Percentiles of TCRE 1.5 ° C carbon budget 2 ° C carbon budget33% 840
GtCO GtCO
50% 580
GtCO GtCO
67% 420
GtCO GtCO One method to calculate the carbon budgets is to use equation (12) ex-tracted from [61]. CB represents the carbon budget, T lim the limit temper-ature rise, T hist = 0 . ◦ C the temperature rise already achieved until 2015, T non − CO the impact of non- CO effects (equals to 0.1 ° C for 1.5 ° C and to0.2 ° C for 2 ° C),
T CRE = 0 . ◦ C (for median value) and ESF = 100 Gt Earth system feedback. CB = T lim − T hist − T non − CO T CRE − ESF (12)IPCC has also taken into account the possible deployment of carbon cap-ture and storage strategies, known as BECCS (Bio-Energy with Carbon Cap-ture and Storage). Four scenarios have been defined in [5]. P1 does not21onsider BECCS when P2 considers a storage capacity of 151
GtCO , P3 of414 GtCO and P4 of 1191 GtCO , all by 2100.A corrected carbon budget CB c, is defined, especially to take intoaccount BECCS. It can be estimated with equation (13) using the IPCCcarbon budget CB , the correction due to Earth system feedback ESF , thecarbon storage
BECCS and the CO emissions in 2018 and 2019 E CO ,old . CB c, = CB + BECCS − E CO ,old (13)Considering an analysis up to 2100, this budget is equal to the worldcumulative CO emissions between now and 2100, which gives equation (14)with E CO ,k the annual world CO emissions. CB c, = (cid:88) k =2020 E CO ,k (14)A model with a fixed annual rate of decrease x is selected to compute areference trajectory for CB c, . Equation (15) is a reformulation of equation(14) with this assumption. This equation can then be solved implicitly inorder to determine the annual rate of decrease x . CB c, = (cid:88) k =2020 E CO , (1 − x ) k − = E CO , (1 − x ) − (1 − x ) x (15)To limit the analysis to 2050, x being known, CAST uses equation (16)to compute the world corrected carbon budget until 2050 CB c, . CB c, = E CO , (1 − x ) − (1 − x ) x (16)To compute the carbon budget allocated to aviation until 2050 for a targetof 1.5 ° C or 2 ° C, a share of the world carbon budget must be performed. If F is the rate of the carbon budget allocated to aviation, then the correctedcarbon budget given to aviation until 2050 is F.CB c, . F is set by defaultin CAST to aviation’s share of world CO emissions in 2019, i.e. 2.6%, butcan be modified. Indeed, the choice of this share results from a politicalchoice. For instance, increasing this share gives more flexibility to aviationto the detriment of other sectors, and conversely.22he approach described above is extended to non- CO effects to com-pute ERF budgets. Adapting the equations for carbon budgets, a correctedequivalent carbon budget for 2100 ECB c, is estimated with equation (17),with E GHG,old the GHG emissions in 2018 and 2019 given in [62].
ECB c, = T lim − T hist T CRE − ESF + BECCS − E GHG,old (17)The approach to compute the corrected equivalent carbon budget for2050
ECB c, is then the same as before, this time considering annualGHG emissions E GHG,k . Equation (18) gives
ECB c, , to which a share F must be allocated for aviation. In this case, F is set by default in CAST toaviation’s share of world ERF in 2011, i.e. 3.5%. ECB c, = E GHG, (1 − x ) − (1 − x ) x (18)Finally, this equivalent carbon budget for aviation is multiplied by theERF coefficient for CO in order to obtain an equivalent in ERF. This climatebudget in ERF can then be compared with the adjusted ERF of aviation in2050, which is the ERF of aviation in 2050 from which the cumulative CO effect until 2019 is subtracted (38 . mW/m ).
4. Results and discussions
In this part, CAST is used on some scenarios in order to check theircompatibility with the objectives of the Paris Climate Agreements in terms of CO emissions or ERF. First, the ATAG commitments proposed by aviationstakeholders are analysed using CAST. Then, various illustrative scenariosare developed by selecting a set of levers of action and assessed with respectto 2019 situation to highlight the potential for decreasing the climate impactof aviation. In order to detail the methodology for analyzing a scenario using CAST,a study is carried out on ATAG commitments. For the analysis, BECCSare not considered and the IPCC carbon budgets with a 50% probability ofremaining below the targeted temperature increase (1.5 ° C or 2 ° C) are takeninto account. 23 modelling of 2009 ATAG commitments is shown in Figure 10 whichrepresents the trajectory of global CO emissions for aviation. In this sce-nario, a 4.5% annual growth in RPK air traffic is considered as well as a1.5% annual improvement in fuel efficiency (yellow part) and an optimisticimprovement in operations (orange part). The evolution of the load factoris not considered and its value is therefore that of 2019. Concerning thedecarbonisation of energy, using the models developed in the article, a fi-nal decarbonisation rate of 93% for alternative fuels is necessary to obtainthe trajectory defined by ATAG (green part). It is interesting to note thatthis value is much higher than the 70% decarbonisation rate estimated to beachievable for biofuels or hydrogen. Lastly, to cushion the transition, eco-nomic carbon offsetting measures are being put in place to compensate for CO emissions above the 2019 level (blue part). Figure 10: Modelling of 2009 ATAG commitments
The analysis of this scenario shows that the cumulative global emissionsof CO for aviation until 2050 are equal to 30.5 Gt. In comparison, the worldcarbon budgets until 2050 for 1.5 ° C and for 2 ° C are respectively equal to 378Gt and 865 Gt. Therefore, considering this scenario, aviation would consume8.1% of the world carbon budget for 1.5 ° C and 3.5% of the world carbonbudget for 2 ° C until 2050. Since aviation accounts for 2.6% of global CO emissions in 2019, it would consume more than this share in this scenario.Due to Covid-19, air traffic was severely disrupted in 2020 and will be24mpacted for years to come. ATAG has updated its commitments to takeinto account the impacts of Covid-19 (Figure 11). The return of air trafficto the 2019 level is only envisaged for 2024 and the annual growth rate forthe following years is estimated at 3.0%. To model this update in CAST, theforecasts for improvements in energy efficiency and operations are kept tothe 2009 commitments. The final decarbonisation rate obtained is decreasedto 78%, which is still higher than the possible expected value of 70%. Figure 11: Modelling of 2020 ATAG commitments including Covid-19
Using the same type of analysis as for the 2009 ATAG commitments,the cumulative global emissions of CO until 2050 are about 24.7 Gt, whichcorresponds to 6.5% of the world carbon budget for 1.5 ° C and 2.9% of theworld carbon budget for 2 ° C until 2050. In the same way as for the previousscenario, aviation would consume more than the 2.6% share in this scenario.In terms of global ERF, 2020 ATAG commitments result in an ERF foraviation of 201 . mW/m in 2050, i.e. an adjusted ERF of 163 . mW/m .In this scenario, aviation would consume 51.6% and 18.9% of the world ERFbudgets in 2050 for respectively 1.5 ° C and for 2 ° C. Since aviation accountsfor 3.5% of global ERF in 2011, this scenario would consume more than thisshare. This large budget overshoot is due to the fact that the impact of con-trails, which represents more than half of the climatic impacts of aviation, isnot mitigated in the ATAG commitments. This result shows the importanceof integrating measures against contrails in the future.25 .2. Simulation and analysis of three illustrative scenarios
The objective of this part is to use CAST to simulate and analyse someillustrative scenarios. For all these case studies, BECCS are not consideredand the IPCC carbon budgets with a 50% probability of remaining below thetemperature target are taken into account. The studies carried out for thesescenarios are limited to fixed allocated shares for aviation that correspondto current impacts, i.e. 2.6% for global CO emissions and 3.5% for globalERF. Three illustrative scenarios are defined according to different levels oftechnological development. The settings for these scenarios are based on themodels for the levers of action in Section 3.1.
Trend scenario for aircraft efficiency and load factor considering akerosene-fuelled fleet without new operation : Trend scenarios are con-sidered for the evolution of the aircraft energy consumption (1% an-nual improvement) and load factor. Improvements in operations arenot considered. Moreover, it is assumed that only kerosene continuesto be used as aircraft fuel. Using these assumptions, the global CO emissions per RPK would be 89 gCO /RP K in 2050.2. Trend scenario for aircraft efficiency and load factor including low-carbon fuels and new operations : Trend scenarios are considered forthe evolution of the aircraft energy consumption (1% annual improve-ment) and load factor. For operations, a realistic improvement is takeninto account, in accordance with the models in the previous section.Moreover, a transition to low-carbon fuels (70% reduction compared tokerosene) for half of the fleet by 2050 is considered. This corresponds inthe models to a total energy decarbonisation for the entire fleet of 35%.Using these assumptions, the global CO emissions per RPK would be54 gCO /RP K in 2050.3. Technology-based scenario : Technologies are pushed forward with op-timistic assumptions. First, the annual rate of improvement in aircraftfuel efficiency is 1.5%, which corresponds to the average value for thelast 5 years. In comparison, ATAG also considers annual improve-ments of 1.5%. Next, it is assumed that the entire fleet will be able to26e fuelled by alternative low-carbon fuels (70% reduction compared tokerosene) by 2050. Using these assumptions, the global CO emissionsper RPK would be 20 gCO /RP K in 2050.The level of air traffic, modelled with the annual growth rate of RPK,is considered variable in these scenarios. Four distinct cases are studied:estimated trend of traffic growth before Covid-19 (4.5%), estimated trend oftraffic growth after Covid-19 (3%), stagnation of traffic at the 2019 level andtraffic necessary to equal the carbon budget for 2 ° C. The effects of Covid-19are included in the last three cases for the level of traffic. CO emissions In this section, illustrative scenarios are analysed in terms of CO emis-sions and carbon budgets.Firstly, the analysis of the trend scenario excluding low-carbon energywith the estimated growth of air traffic before Covid-19 shows cumulative CO emissions of 60.0 Gt. It largely exceeds the carbon budgets for 1.5 ° Cand 2 ° C allocated to aviation, which are respectively 10.0 Gt and 22.8 Gt.These cumulative CO emissions corresponds to 6.9% of the 2 ° C world carbonbudget for 2050. Similarly, considering the projections after the Covid-19crisis, the cumulative CO emissions are equal to 38.8 Gt, which also exceedsthe carbon budgets allocated to aviation. The results are similar for thetwo other scenarios. Indeed, the trend scenario including low-carbon energyleads to cumulative CO emissions of 47.9 Gt for a RPK growth of 4.5%and to 31.5 Gt for a RPK growth of 3%, and the technology-based scenarioleads to cumulative CO emissions of 27.0 Gt for a RPK growth of 4.5%and to 23.4 Gt for a RPK growth of 3%. Therefore, in order to respect atrajectory compatible with the Paris Climate Agreements for these scenariosconsidering these allocated carbon budgets, air traffic growth projectionsmust be reduced.The analysis is then performed for air traffic that remains at the 2019level. In this case, the cumulative CO emissions amount to 27.2 Gt forthe trend scenario excluding low-carbon energy and to 23.0 Gt for the trendscenario including low-carbon energy. The carbon budgets are therefore ex-ceeded for a stagnation of air traffic. Thus, to comply with the Paris ClimateAgreements with these assumptions, it is therefore necessary to reduce airtraffic compared to 2019. In order to respect the carbon budget for 2 ° C,air traffic must be reduced by 1.8% per year in the trend scenario excluding27ow-carbon energy and by 0.2% in the trend scenario including low-carbonenergy. For instance, Figure 12 represents the aviation carbon trajectory inthe case of the trend scenario including low-carbon energy.Finally, for the technology-based scenario, a reduction in air traffic is notnecessary. Indeed, the cumulative CO emissions of this scenario amount to18.2 Gt when considering the air traffic at the level of 2019. As a consequence,aviation would only consume 2.1% of the global 2 ° C carbon budget, whichrespects the carbon budget allocated to aviation for 2 ° C. A traffic growthof 2.6% compared to 2019 is even possible while respecting the 2 ° C carbonbudget. However, if the assessment of this scenario is performed comparedto the carbon budget allocated for 1.5 ° C, a decrease in air traffic is necessaryas for trend scenarios.
Figure 12: Trend scenario including low-carbon energy which respects 2 ° C carbon budget
Table 4 summarises the main results. Illustrative scenarios with trendRPK growth are not compatible with carbon trajectories corresponding tothe Paris climate agreements with an allocated share of 2.6%. For 2 ° C, adecrease in air traffic is necessary considering the trend scenarios whereasa RPK growth is possible in the technology-based scenario. For 1.5 ° C, allillustrative scenarios lead to a drastic air traffic decrease.Another analysis can be conducted using CAST. Indeed, given the highuncertainty on the availability of energy resources, different studies can becarried out with the global decarbonisation rate of the fleet in 2050 as a28 able 4: Results for the analysis of illustrative scenarios in terms of carbon budgets
Illustrativescenario 1 Illustrativescenario 2 Illustrativescenario 3Scenariocharacteristics Trend scenariofor the energyefficiency (-1%per year)excludinglow-carbonenergy Trend scenariofor the energyefficiency (-1%per year)includinglow-carbonenergy for halfof the fleet(-35% in 2050) Technology-based scenariofor energyefficiency(-1.5% peryear) includinglow-carbonenergy for allthe fleet (-70%in 2050)Share of the2 ° C worldcarbon budgetconsumed for a3% growthrate 10.3% 8.3% 6.2%Air trafficgrowth rate torespect a 2.6%share foraviation for2 ° C -1.8% -0.2% 2.6%variable. Figure 13 represents for example the possible RPK growth rate as afunction of the decarbonisation rate of the fleet for carbon budgets at 2 ° C andan allocated share of 2.6% on illustrative scenario 2 (trend scenario includinglow-carbon energy). The area in the figure that requires alternative fuelwith a decarbonisation rate of more than 70% compared to kerosene, whichcorresponds to the hypothesis of maximum achievable decarbonisation rate,is highlighted in grey. 29
20 40 60 80 100Decabonisation rate of the fleet using low-carbon energy [%]10123 R P K a nnu a l g r o w t h r a t e [ % ] Air traffic growth according to the decarbonisation of thefleet to respect carbon budget 2°C 2050 (share of 2.6%)
Illustrative scenario 2Hard-to-reach area
Figure 13: Influence of the decarbonisation rate on trend scenario including operations
In this part, illustrative scenarios are analysed in terms of ERF.Analyses with CAST show that no illustrative scenario is compatible withclimate budgets in ERF without a strong decrease in air traffic. To limit thedecrease, strategies against contrails can be put in place. To mitigate con-trails, widespread altitude changes with more efficient combustion chambers,described in Section 3, are considered.First, the technology-based scenario including strategies against contrailsis analysed in terms of climate budget in ERF. To limit the temperatureincrease to 2 ° C for a 3.5% share of the climate budget allocated to aviation,the climate budget is respected with an annual growth rate of 0.8%, whichresults in an adjusted ERF from aviation of 30 . mW/m in 2050, i.e. aglobal ERF from aviation of 68 . mW/m in 2050. Figure 14 representsthe trajectory in ERF for this scenario. Equivalent analyses for the otherillustrative scenarios are performed and lead to an RPK annual decreaseof 1.3% for the trend scenario excluding low-carbon energy and an annualdecrease of 0.5% for the trend scenario including low-carbon energy. However,when it comes to limiting the temperature increase to 1.5 ° C, whatever theillustrative scenario, a strong decrease in air traffic is necessary as for carbon30udget analyses.
Figure 14: Technology-based scenario which respects 2 ° C ERF budget
The analysis shows that ERF trajectories give different traffic levels thanfor carbon trajectories for 2 ° C. However, because of uncertainties and method-ology, the use of carbon trajectories is recommended.
5. Conclusions and future work
In this paper, the methodology and models to develop the tool CASTfor simulating and assessing climatic scenarios for the aviation industry arepresented. This tool is used to simulate scenarios concerning the futureclimate impacts of aviation, and to assess their compatibility with the Parisclimate agreements.Regarding the methodology and the models, two main themes are ad-dressed. Firstly, the evolution of aviation is modelled via different levers ofaction, like the level of air traffic, the fuel consumption efficiency or the useof low-carbon fuel, that are linked via an adapted Kaya type equation. Tomodel these different levers of action, several strategies are used. For thosewith historical data, deterministic models are developed to define trend sce-narios. For the others, hypotheses from the scientific literature are taken intoaccount and projections are made. Secondly, climate models are used both toestimate the climatic impact of aviation, but also to assess the compatibility31f the trajectories with the Paris climate agreements. In addition to CO emissions, non- CO effects are considered using aggregated models from thescientific literature to estimate the impacts in terms of ERF. The evaluationof the scenarios is based on the notion of carbon budgets.As examples, several scenarios are assessed with CAST. First of all, ATAGcommitments are modelled and compared with trajectories compatible withthe Paris Climate Agreements. The most recent ATAG commitments wouldresult in a consumption of 3.0% (respectively 6.8%) of the world carbonbudget for limiting the temperature increase to 2 ° C (respectively 1.5 ° C). Thisrepresents more than the 2.6% share of global CO emissions from aviationin 2019. Note that, in these commitments, the non- CO effects are not takeninto account, even though they currently account for about 2/3 of the globalERF of aviation. Then, different scenarios are simulated to take into accountdifferent levels of technological improvements. Regarding the compatibility ofthese scenarios with the Paris climate agreements for 2 ° C for CO emissionsand considering a 2.6% share for the allocated carbon budget, the evolution ofworld air traffic is expected to be between an annual traffic decrease of 1.8%(trend scenario without new fuels) and an annual growth of 2.6% (ambitiousscenario including low carbon fuels). However, air traffic should decreasedrastically to be compatible with a +1.5 ° C trajectory. Lastly, additionalstudies on the non- CO effects show the importance of implementing specificstrategies to refine the possible scenarios for aviation.Although CAST is already a mature tool for simulating and assessingclimate scenarios, some limitations remain to fully analyse scenarios. First,regarding the decarbonisation of alternative fuels, constraints on the avail-ability of energy resources (land available for biofuels, low-carbon electricityavailable for hydrogen production) are not addressed. These aspects willbe taken into account in a future version of CAST. Second, some modelsrepresent the future evolution in a simplified way. For instance, the differ-ent scenarios considered for the evolution of the different levers of actionare projected models taking into account current trends and knowledge. Abetter link between these projections and the envisaged future technologieswill be implemented in a future version of CAST using a bottom-up ap-proach. This would allow more accurate modelling of technologies and fleetrenewal impacts. Subsequently, to improve approaches for non- CO effects,methodologies using Global Warming Potential (GWP) indicators are envis-aged, such as the modelling of other strategies to mitigate non- CO effects.Finally, for most of the studied scenarios, climate constraints are based on32n allocated share corresponding to the current impacts of aviation. Thisshare could be determined by coupling these studies with social-economicparameters in order to make trade-offs regarding the distribution of carbonbudgets. Supplementary material
CAST is available at: http://cast.isae-supaero.fr/
Acknowledgements
The authors would like to thank all the people who took part in CASTbeta testing for their relevant feedback. This study is supported by ISAE-SUPAERO, within the framework of the research chair CEDAR (Chair forEco-Design of AiRcraft).
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