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Impact modeling and sustainability assessment

This part of the documentation is deprecated. It describes AeroMAPS in late 2023

It will be updated soon!

After defining the evolution of air transport via dedicated models, specific models evaluate the associated impacts, and then compare them with limits via a sustainability assessment.

Impact modeling

In the following, the models used for estimating the impacts induced by air transport are described. Currently, the majority of impact modeling concern environmental impacts.

Emissions and climate impacts

CO2 emissions

Based on the modeling of the air transport system through a Kaya decomposition, the estimation of the evolution of CO2 emissions is simple by multiplying the different factors. In addition, a coefficient corresponding to other life cycle emissions (excluding combustion and fuel production) can also be applied, but it only represents a few percent of the aviation environmental impacts 1.

Decomposition of the levers of action into sub-levers

The reduction of CO2 emissions with respect to a trajectory at the technological level of the last historical year is represented as a cascade of levers of action: demand, aircraft efficiency, fleet operations, load factor and aircraft energy, each lever being the difference between two successive emission levels. Some of these levers can be further decomposed into sub-levers. Each decomposition is exact by construction: the sub-levers, including an explicit residual term, sum to the lever they split.

The notations below are common to all decompositions. The reference year \(t_0\) is the last historical year. For passenger traffic, \(e(t)\) is the fleet mean energy per ASK and \(e^{*}(t)\) the same quantity before the operational gain, \(LF_0\) the load factor and \(EF_0\) the mean CO2 emission factor of the energy used, both at \(t_0\). Index \(0\) denotes values at \(t_0\). Unit conversion factors are omitted.

Aircraft efficiency per aircraft

This decomposition requires the bottom-up fleet model. The fleet model measures the contribution \(C_a(t)\) of each aircraft \(a\) as the shift it causes in the mean energy per ASK of its fleet category, with respect to the recent reference aircraft of that category. The evolution of this contribution since \(t_0\) is converted into avoided emissions with the reference-year factors of the cascade, and weighted by the share of ASK of the market \(m\) served by the category:

\[ \Delta CO_2^{a}(t) = \frac{RPK(t)}{LF_0} \, \frac{e_0}{e^{*}_0} \, EF_0 \, \frac{ASK_m(t)}{ASK(t)} \, \big[ C_a(t) - C_a(t_0) \big] \]

The same expression gives the other passenger sub-levers:

  • fleet renewal, with the contribution of the old reference aircraft, which measures the replacement of the old reference aircraft by the recent one; each new aircraft is then only credited for its additional gain beyond fleet renewal;
  • continuous improvement, with the opposite of the contribution of the recent reference aircraft baseline, which drifts over time when a continuous improvement factor is set and would otherwise belong to none of the aircraft.

The freight sub-lever is computed from the freight energy per RTK before operations \(e^{*}_{f}(t)\):

\[ \Delta CO_2^{freight}(t) = RTK(t) \, \big[ e^{*}_{f,0} - e^{*}_{f}(t) \big] \, \frac{e_{f,0}}{e^{*}_{f,0}} \, EF_0 \]

The residual is the aircraft efficiency lever minus all the terms above. It carries the traffic mix between markets of different energy intensity, and the gain of any aircraft added to the fleet after the process was set up (as the graphical interface does), since the list of output variables is fixed at setup.

Fleet operations per operational concept

This decomposition requires the generic operations module (see the air transport documentation). The gains \(g_i\) of the operational concepts compose multiplicatively into the aggregate operational gain \(G\), each concept acting on the consumption left by the others:

\[ 1 - G(t) = \prod_i \big( 1 - g_i(t) \big) \]

The aggregate gain is shared between the concepts in proportion to the logarithm of their individual factors:

\[ c_i(t) = G(t) \, \frac{\ln \big( 1 - g_i(t) \big)}{\ln \big( 1 - G(t) \big)} \]

The contributions \(c_i\) sum exactly to \(G\) and do not depend on the order in which the concepts are declared, which a sequential attribution would. Since the operations lever \(L_{ops}\) is proportional to \(G\) for passenger and freight traffic alike, each concept receives the share \(c_i / G\) of the lever. The sub-levers are also summed per category of concepts. The residual is zero unless the operational gain is applied differently to some traffic.

Aircraft energy per pathway

This decomposition requires the generic energy models. Each pathway \(p\) is credited with its energy consumption \(E_p(t)\) multiplied by the difference between the reference emission factor and its own mean emission factor \(EF_p(t)\):

\[ \Delta CO_2^{p}(t) = E_p(t) \, \big[ EF_0 - EF_p(t) \big] \]

The reference is the mean emission factor of the reference year rather than that of fossil kerosene, so that the sub-levers sum exactly to the energy lever. When low-carbon fuels are already used in the reference year, fossil kerosene therefore carries a small negative sub-lever. The residual collects what the pathway terms do not cover.

Carbon offset per scheme

This decomposition requires the generic offsets module, activated by the models.offsets block of the configuration file, which then replaces the simple offset models and their single price. The emissions left after the levers of action are offset by schemes (an emissions trading system, CORSIA, a removals obligation...), each with its own quantity rule and its own price \(p_s(t)\). Three rules are available:

  • level: the emissions above a baseline set at a fraction \(b_s(t)\) of the emissions of a reference year \(t_{ref}\), times the fraction \(k_s(t)\) of emissions in the scope of the scheme, as in CORSIA:
\[ Q_s(t) = \max \big( CO_2(t) - b_s(t) \, CO_2(t_{ref}), \, 0 \big) \, k_s(t) \]
  • share of residual: a fraction \(\sigma_s(t)\) of the emissions left once the level-based schemes are applied:
\[ Q_s(t) = \sigma_s(t) \Big[ CO_2(t) - \sum_{s' \in \text{level}} Q_{s'}(t) \Big] \]
  • quantity: a prescribed annual quantity \(Q_s(t)\).

The carbon offset is the sum of the scheme quantities, so the sub-levers carry no residual, and its price is the quantity-weighted mean of the scheme prices:

\[ Q(t) = \sum_s Q_s(t), \qquad p(t) = \frac{\sum_s Q_s(t) \, p_s(t)}{Q(t)} \]

The single-price cost chain of offsetting is therefore reproduced exactly, while the expense is also available per scheme and per category of schemes. The rules reproduce those of the simple offset models, including one of their limits: prescribed quantities are not deducted from the residual that the share-based schemes apply to. A warning is issued when the schemes offset more than the emissions, or when the shares of residual exceed 100 %.

Every lever per market

The cascade is recomputed for each passenger and freight market with its own traffic (and baseline traffic for the demand lever), its own energy intensities per energy type, and its own emission factors for the energy lever. Freight markets have no load factor lever. The global cascade uses fleet-wide mean intensities, so the sum over markets differs from the global lever by a cross-market mix term, reported as a residual for each lever. This term is the effect of traffic shifting between markets of different intensity; it is not a numerical error.

Using the decompositions

The decomposition models are part of the standard model bundles and need no configuration:

Decomposition Model Registered with
Aircraft efficiency per aircraft DetailedCo2EmissionsPerAircraft models_efficiency_bottom_up
Fleet operations per concept DetailedCo2EmissionsPerOperationalConcept the generic operations module, when models.operations is declared
Aircraft energy per pathway DetailedCo2EmissionsPerPathway models_energy_without_fuel_effect, models_energy_with_fuel_effect
Carbon offset per scheme OffsetsUseChoice the generic offsets module, when models.offsets is declared
Every lever per market DetailedCo2EmissionsPerMarket the top-down, push and bottom-up efficiency bundles

The sub-levers are output columns in MtCO2 avoided, named co2_emissions_lever_<lever>_<kind>_<name>, for instance co2_emissions_lever_efficiency_aircraft_<category>_<aircraft>, co2_emissions_lever_operations_concept_<concept>, co2_emissions_lever_energy_pathway_<pathway>, co2_emissions_lever_offset_scheme_<scheme> or co2_emissions_lever_energy_market_<market>; residuals end with _other or _market_cross_mix. Values below 10-9 MtCO2 are set to zero so that the outputs are deterministic. The helper functions of aeromaps/models/impacts/emissions/co2_emissions.py (aircraft_efficiency_sub_lever_columns, pathway_energy_sub_lever_columns, operations_concept_column, market_lever_dataframe) list the columns, so that no name has to be typed by hand.

Four plots show the sub-levers:

  • air_transport_co2_emissions_detailed replaces each decomposable wedge by its sub-wedges, with the keywords efficiency_granularity ("aircraft" or "category"), energy_granularity ("pathway" or "family") and offset_granularity ("scheme" or "category"); a lever whose decomposition is not available is drawn as a single band. The keyword lever_order sets the stacking: "aeromaps" (default) follows the cascade (efficiency, operations, load factor, energy, offsets), and "atag" follows the ATAG roadmap, with the alternative aircraft (hydrogen and electric pathways) stacked with the aircraft technology ahead of operations and load factor, then the drop-in fuels, then the offsets. Only the stacking changes, not the value of any sub-lever;
  • air_transport_co2_emissions_grouped is the same plot per fleet category, per fuel family and per category of offsetting schemes;
  • air_transport_co2_emissions_per_market draws each lever per market in one panel per lever, since some market contributions become negative and a stacked chart would depend on the stacking order;
  • operations_gain_by_concept, operations_gain_by_category and operations_contrails_gain_by_concept show the operational gains themselves;
  • carbon_offset_by_scheme, carbon_offset_by_category and carbon_offset_expense_by_scheme show the offset quantities and expenses.

The tutorial Decompose the CO2 levers of action into sub-levers goes through all of them and checks that each decomposition is exact.

Non-CO2 emissions

For estimating non-CO2 emissions, the concept of Emission Index (EI) is used. They make it possible to obtain different emissions (NOx, SOx...) depending on fuel consumption (or CO2 emissions). Values for fossil kerosene from 2 have been used and are provided in Tab.1. The values can be adapted for alternative energy carriers.

Emission Value Unit
CO2 3.15 kgCO2/kgfuel
H2O 1.23 kgH2O/kgfuel
NOx 15.1 gNOx/kgfuel
Aerosols (soot) 0.03 gBC/kgfuel
Aerosols (sulfur) 1.2 gSOx/kgfuel

Tab.1 Emission Index for fossil kerosene combustion.

Based on these data, the estimation of the climate impact of aviation is achieved by the calculation of the ERF (Effective Radiative Forcing), which is based on the use of coefficients for the different impacts. These are obtained through an analysis of the data from 2 and are summarized in Tab.2. CO2 emissions are cumulative: therefore, at first order, the coefficient to estimate the ERF must be applied on the cumulative CO2 emissions. The impact of the other emissions is estimated from the annual emissions. Finally, the impact of contrails is assumed to be correlated with the total annual distance flown.

Climate impact Value Unit
CO2 (cumulative) 0.88 mW/m2/GtCO2
H2O 0.0052 mW/m2/TgH2O
NOx 11.55 mW/m2/TgN
Aerosols (soot) 100.7 mW/m2/TgBC
Aerosols (sulfur) -19.9 mW/m2/TgSO2
Condensation trails 1.058.10-9 mW/m2/km

Tab.2 Coefficients for estimating the ERF of aviation climate impacts.

Using the data and taking into account CO2 and non-CO2 effects, aviation (including private and military) generated 3.8% of the effective radiative forcing between 1750 and 2018 and commercial aviation is responsible for 5.1% of the increase in effective radiative forcing over a more recent period (2000--2018), compared to global ERF estimated in the IPCC AR6.

Lastly, equivalent emissions can be estimated to simplify the comparison with CO2 emissions, but also to estimate the impacts on the temperature evolution in a second step. Multiple metrics are available in the scientific literature to estimate them 34: GWP, AGWP, GTP, AGTP, etc. GWP is the most known and used metric, often used with a 100-year time horizon. However, this metric is limited for representing the evolution in terms of temperature for Short-Lived Climate Pollutants (SLCPs) 5, which is the case for aviation non-CO2 effects. As a consequence, an alternative metric is used here. GWP* is an improved climate metric developed recently 678, one of the major interests of which is to better evaluate the effect of SLCPs. It allows to estimate the equivalent emissions in CO2-we for a better match with the evolution in temperature (warming equivalent). In this sense, it thus represents a simplified climate model compared to other more complex climate models that may require long computation times 9. Compared to GWP, it does not only take into account the absolute value of the emissions but also the variation of the emission rate. The following equation allows estimating the equivalent emissions, noted \(E_{CO_2\text{-we}}\), of a gas \(G\) for a time horizon \(H\), as a function of the absolute emissions \(E_G\) and the variation of emissions \(\Delta E_G\) over a period \(\Delta t\). The parameters \(r\) and \(s\) depend on the gas and represent the influence of cumulative or short-term effects.

\(E_{CO_2\text{-we}} = \text{GWP}_H ~ \left(r ~\frac{\Delta E_G}{\Delta t}~H + s~E_G \right)\)

This equation can be modified to be used for aviation non-CO2 effects, based on assumptions from 62, with in particular \(r=1\) and \(s=0\). As a consequence, the following equation is used with \(E_{CO_2\text{-}we}\) the equivalent emissions of a non-CO2 effect for a given year, \(\Delta F\) the corresponding variation of the ERF over a period \(\Delta t\) of 20 years (smoothed over 5 years to better represent global trends), a time horizon \(H\) of 100 years and the absolute global warming potential of CO2 over 100 years \(AGWP_H\) of 88 yr.mW/m2/GtCO2.

\(E_{CO_2\text{-}we} = \frac{\Delta F}{\Delta t} \frac{H}{AGWP_H}\)

Temperature estimation

Based on the knowledge of the CO2 emissions and non-CO2 effects via equivalent emissions, it is possible to estimate the temperature increase due to air transport \(T_{k}\) for the year \(k\). For this purpose, the following equation is used with \(T_{2019}\) the temperature increase from air transport in 2019 (from 10), \(E_{CO_2, k}\) the annual CO2 emissions and \(E_{CO_2\text{-}we, k}\) the annual equivalent emissions for non-CO2 effects using GWP*. The value of the TCRE (Transient Climate Response to cumulative carbon Emissions) depends on climate model settings, with median estimates on the order of 0.45°C/1000GtCO2. However, it is also possible to estimate the temperature increase from air transport using dedicated climate models for more accurate results.

\(T_{k} = T_{2019} + TCRE ~ \sum_{i=2020}^{k} (E_{CO_2, k} + E_{CO_2\text{-}we, k})\)

Energy resources

The description of the energy carriers envisaged for air transport makes it possible to estimate the quantities of fuels to be used (embarked energy), but also the quantities of energy required to produce them using conversion efficiencies. The quantities of biomass and electricity consumed are then directly calculated. The selectivity of the pathways producing these energy carriers, defined as the proportion of kerosene in the fuel output (usually measured by energy), can also be taken into account. It allows to estimate the amount of energy that has to be used to produce kerosene and other outputs. However, in general, an allocation of consumption is made to other outputs for estimating the "real consumption" due to kerosene (which means that selectivity is not taken into account).

Economic

The current cost models implemented in AeroMAPS are described in this section. A recap of the energy cost models is first provided. Alternative energy cost models were presented in detail in 11, with a model taking as an input each fuel pathway annual energy consumption to derive annual energy expenses and the required investments chronology for the energy sector. A direct operating cost model adapted to AeroMAPS was recalibrated in 12 and adapted to AeroMAPS in 13.

Alternative energy cost model

As mentioned in the air transport modelling section, three biofuel production pathways are modelled within AeroMAPS: Hydroprocessed Esters and Fatty Acids (HEFA), Fischer-Tropsch (FT), and Alcohol-To-Jet (AtJ). Regarding their production costs, three main drivers are identified by the literature 1415: the capital required to build a conversion plant (Capital Expenditures  CapEx), and the operational expenditures, in which we can distinguish between the supply of energy to be converted, referred to as feedstock in the following, and other expenses (personnel, various inputs, maintenance, etc.), referred to as OpEx. Despite large new scale-up plans for theses fuels like ReFuelEU, these are still niche markets, meaning that no mature price exists for the trade of these biofuels. A proxy metric used is the Minimal Fuel Selling Price (MFSP). It is the fuel selling price at which the fuel production project has a null Net Present Value (NPV). This value is the difference between the expenses and the revenues from a project during all its lifespan and considering the time value of money: a large investment immobilized in a project whose revenues occurs much latter represents an opportunity cost. It is considered by the discount rate r, which discounts future cash flows. Overall, the MFSP can be determined using the following equation, where \(CAPEX_t\) are the capital expenditures at year \(t\), \(OPEX_t\) the operational expenditure on the same year, feedstock expenditures \(FEED_t\) excluded. \(P_t\) is the quantity of fuel produced. One can see that MFSP is indeed the minimal constant price at which the fuel should be sold to ensure the project profitability.

\(MFSP = \frac{\sum_{t=0}^{N-1}\frac{CAPEX_t}{(1+r)^t}+\frac{OPEX_t}{(1+r)^t}+\frac{FEED_t}{(1+r)^t}}{\sum_{t=0}^{N-1}\frac{P_t}{(1+r)^t}}\)

In AeroMAPS, the biofuel MFSP were directly taken from a literature review 161415, and the CapEx values were also taken or estimated by reversing the previous equation under standard financial assumptions. It allows to estimate the annual investment required in each production pathway besides computing the MFSP of the fuel used. Once this MFSP is known, computing the extra cost for the airlines is straightforward by subtracting the cost incurred by purchasing a similar amount of fossil kerosene, assuming both fuels are perfect substitutes. A last metric is used: the carbon abatement cost \(CAC\). It combines the MFSP of a fuel with its environmental benefit, which is modeled in the environmental impact module of the tool. For the biofuel \(i\), it is the ratio between the cost difference \(\Delta_C\) to the fossil reference and the emission factor difference \(\Delta_{EF}\) with the same fossil reference, as shown below. It is used with /tCO2 as a unit and allows to evaluate the economic efficiency of various alternative fuels. The concept can be generalized to any decarbonization measure.

\(CA_i =\frac{\Delta C}{\Delta EF}= \frac{C_i-C_{fossil}}{EF_{fossil} -EF_{i}}\)

Both electrofuels and hydrogen are modelled in an equivalent way as biofuels. Schematically, hydrogen can be either used directly, burned in a gas turbine or as a fuel of a redox reaction in a fuel cell, or indirectly through the production of a synthetic kerosene. In the latter case, it is combined with CO2 in a Fischer-Tropsch (amongst others) pathway to produce a drop-in fuel. The cost modelling follows a similar process as before, but the MFSP equation is this time directly used as an explicit MFSP model. Besides, it is adapted to index the hydrogen price on the yearly energy price (equivalent of feedstock for biofuels). For hydrogen production, electrolysis, steam methane reforming and coal gasification are modeled. Carbon Capture and Storage can be added to the fossil pathways. Reference technological values on CapEx, OpEx and efficiencies are taken from 171819. When hydrogen is directly used, the cost of other production steps has to be added to its total cost. For instance, for volume reasons, its use in aircraft could require its liquefaction, and the supply chain (transport, storage and refuelling) would be modified as well. Those costs are also modelled in the module. The carbon abatement cost is thus computed using the equation above as well. The economic modelling of electrofuels is similar, though a last cost component should be accounted for: the CO2, whose direct air capture is a major cost driver.

Lastly, the expenses for kerosene are also modelled according to its market price specified by the user. By default, it is set to its average historical price (0.41/L). Note that alternative fuel market is not modelled. MFSPs are therefore a lower bound of their potential prices. Kerosene production CapEx (plant renewal and/or expansion) is not modelled so far.

The user is also able to specify a uniform carbon tax, that is applied to all energies (fossil, biofuel, e-fuel and hydrogen) using their emission factors. Two metrics are computed: a supplement to the previous MFSP and the total expenses (or fiscal revenue) for each pathway using the associated consumption as well. By default, a fictional carbon tax implementing in full the French Value for Climate Action 20 is used.

Direct operating cost (DOC) model

Airline costs can be split into two informal categories: the costs directly related to operating an aircraft and those related to general business operations named non-operating costs (administration, sales, ...). For the former category, they can be further split between Direct Operating Cost (DOC) and indirect operating costs. Like non-operating costs, indirect operating costs are not directly linked to the aircraft operation but rather to passenger service. With a simplified approach, there are five main categories in the DOC: capital (owning an aircraft), crew, fuel, maintenance, and fees/taxes. In AeroMAPS, a further simplification is made by using three categories: fuel (or energy), non-energy and carbon taxes.

Explicit direct operating cost models are presented in 21, on a per flight hour basis. These models depend directly on the aircraft characteristics. They were recalibrated using United States Bureau of Transportation Statistics data and adapted to a per flight basis in 12. Since AeroMAPS uses a global top-down approach to model flights by simulating the evolution of the Revenue Passengers Kilometres (RPK) for different markets rather than aggregating many flights, the direct use of these cost models would be of little interest. Therefore, average values for selected aircraft and distance categories were extracted from the results of 12 based on the full simulation of a year (2019) of US airlines flight. Note that it introduces an obvious geographical bias, some costs being widely dependent on the country or the airline (crew, capital structure, age of the fleet, ). However, the lack of reliable detailed financial data to recalibrate the cost model made this limitation necessary.

For non-energy DOC, average costs per aircraft type (regional jet, single-aisle aircraft on short and medium-range routes and long-range), per Available Seat Kilometre (ASK) are used as a starting point. Their evolution is modelled using two different possibilities, like aircraft efficiency. Either simple models implement an annual, category-wide evolution in non-energy DOCs, or bottom-up fleet renewal models are used with discrete DOC values for each aircraft introduced.

Concerning the fuel DOC, it is directly linked to the energy cost module described before. Indeed, the fuel cost is simply obtained by multiplying each aircraft category energy consumption by the average fuel price from the energy cost module. For the moment, each aircraft type in the drop-in fleet is considered to use a blend of all the pathways of the scenario (for example, a situation in which a new generation aircraft uses 100% SAFs while the older generation uses only fossil kerosene is not considered).

Manufacturing cost model

This model is under implementation, but a beta version is described in 13.

Sustainability assessment

In the following, the methodologies used to assess the environmental sustainability of scenarios are presented, based on estimates of induced environmental impacts. Only climate and energy issues are considered. Indeed, these two environmental issues are the most impacting when considering air transport (see for instance 22).

Climate sustainability

Climate sustainability assessment can be performed using various methodologies. For example, carbon budgets. It is an interesting concept used by the IPCC in the context of global warming mitigation strategies. It is defined as the maximum remaining cumulative CO2 emissions that can be emitted to limit the temperature increase below a certain value (for example +1.5 C). For instance, Tab.3 summarizes estimates of carbon budgets for different temperature targets. The emissions considered are net emissions: they are the difference between gross anthropogenic CO2 emissions and anthropogenic carbon sinks. Cumulative CO2 emissions and mean temperature increase are linked by a quasi-linear relationship, which facilitates the estimation of carbon budgets 23. Therefore, the use of carbon budgets allows for example to simply evaluate the relevance of transition scenarios to reach climate objectives based on their CO2 emissions alone 24.

Temperature [ C] 17th 33rd 50th 67th 83rd
1.5 900 650 500 400 300
1.6 1200 850 650 550 400
1.7 1450 1050 850 700 550
1.8 1750 1250 1000 850 650
1.9 2000 1450 1200 1000 800
2.0 2300 1700 1350 1150 900

Tab.3 Estimates of carbon budgets depending on TCRE percentile according to IPCC AR6 (in GtCO2).

However, these carbon budgets are defined globally and not by country or sector (like aviation). In the following, a method which can be applied to aviation CO2 emissions is proposed. This later is also extended to include non-CO2 effects using two solutions.

CO2 effects

First, a global gross carbon budget \(GCB\) is considered. As a reminder, it is defined as the sum of a net carbon budget and a CDR (Carbon Dioxide Removal) capacity (afforestation, BECCS, DACCS...). It is assumed that this budget will be entirely consumed by 2100. This constraint is expressed in the following equation via cumulative emissions, considering \(E_{CO_2,k}\) emissions for year \(k\) from 2020.

\(GCB = \sum_{k=2020}^{2100} E_{CO_2,k}\)

An infinite number of trajectories for CO2 emissions can satisfy this constraint. In the following, a simplified model of emissions decay at a fixed annual rate \(x\) is considered. The previous equation can then be written as the following one. This is a geometric series which can then be expressed more simply. This equation can then be solved implicitly to determine the annual rate of decrease of emissions \(x\).

\(GCB = \sum_{k=2020}^{2100} E_{CO_2,2019}~(1-x)^{k-2019} = E_{CO_2,2019}~ \frac{(1-x)-(1-x)^{82}}{x}\)

Here, the scope of the scenario studies is limited to 2050. Therefore, the following equation is used to determine the adjusted global gross carbon budget to 2050 \(GCB_c\).

\(GCB_c = E_{CO_2,2019}~\frac{(1-x)-(1-x)^{32}}{x}\)

Finally, it is necessary to allocate a share of this carbon budget to aviation. Thus, the carbon budget for aviation (by 2050) \(GCB_A\) is simply calculated using the following equation via an allocated share \(F\).

\(GCB_A = F~GCB_c\)

The choice of the share allocated to the aviation sector is a political one and may involve multiple criteria (technical, economic, societal, etc.). Discussions on this allocation are proposed in 25. An interesting reference value is the recent contribution of aviation to CO2 emissions (also called grandfathering approach). For example, it is 2.6% on the perimeter of commercial aviation considering global CO2 emissions 25. This value can be interpreted as the share that would be allocated to the aviation sector under a non-differentiated approach where all sectors reduce their emissions at the same rate. Allocations below or above this value can also be considered. However, allocating a larger share mechanically requires other sectors to reduce their emissions faster than the average to meet the global carbon budget. This type of trade-off may require multi-sectoral approaches, as for example proposed in 26. In this scenario, cumulative direct CO2 emissions from aviation would represent 3.4% of the considered carbon budget of 1055 GtCO2 over the period 2011--2050.

Therefore, the climate sustainability of a scenario (regarding CO2 emissions) can be assessed by comparing the cumulative CO2 emissions with the allocated carbon budget for aviation. If the cumulative emissions are less than or equal to the carbon budget, the climate target is met.

CO2 and non-CO2 effects

For assessing the sustainability of aviation climate impact, a first solution is to directly compare the temperature increase from air transport to a climate objective (via an allocation or an absolute target) which is for instance performed in 1027.

Another solution is to extend the previous approach in order to maintain a methodology similar to that used for CO2 emissions. So-called equivalent carbon budgets are then calculated. For this purpose, a global equivalent gross carbon budget \(EGCB\) is calculated via the following equation, which has been adapted from simplified models for estimating carbon budgets described in 28. The \(T_{non-CO_2}\) term depends on the temperature objective considered: it is for example equal to 0.1 C for a +1.5 C target and to 0.2 C for +2 C.

\(EGCB = GCB + \frac{T_{non-CO_2}}{TCRE}\)

The same approach as for CO2 emissions is then used to define an equivalent carbon budget for aviation. Allocation rules must also be defined. The reference value considered this time is 5.1%, on the perimeter of commercial aviation, over a recent period and including global CO2 emissions and non-CO2 effects 25.

Therefore, as before, the climate sustainability of a scenario (for all effects) can be assessed by comparing the cumulative equivalent emissions with the equivalent carbon budget calculated for aviation. As introduced previously, the equivalent emissions are also calculated using the GWP* climate metric. The total cumulative equivalent emissions are thus the sum of the cumulative emissions of CO2 and the sum of these annual equivalent emissions for each non-CO2 effect from 2020 to 2050.

Energy resource sustainability

The assessment of energy resource sustainability is based on an approach similar to the one presented for climate issues. This time, rather than comparing cumulative emissions to carbon budgets, the energy consumption of a scenario is compared to available energy resource budgets. Only biomass and electricity energy resources are studied in this work. To simplify the comparisons, the availabilities are checked in 2050. A more comprehensive approach would be to check the availability of energy resources on an annual basis.

In the same way as for carbon budgets, an arbitrary allocation of energy resources for aviation is assumed. The choice of a reference value can, for example, be based on the contribution of the sector to world energy or oil consumption (of the order of 2 to 3% or 7 to 8%). Thus, a scenario can be considered sustainable from an energy point of view if the consumption of energy resources in 2050 does not exceed the energy resource budget considered.

In the following, some examples of reasonable values are proposed.

Biomass availability

The estimation of the available biomass at the global level is complex and depends on several criteria. In this work, a statistical analysis of IRENA (International Renewable ENergy Agency) data is performed. The resource categories described for the biofuel pathways are used. The results are given in Tab.4. The lower and upper fences are determined to exclude extreme values (outliers).

Resource Lower fence Q1 Median Q3 Upper fence
Waste 9 10 12 20 27
Agricultural residues 10 30 57 103 204
Forest residues 5 15 17 39 59
Energy crops 8 37 63 109 217
Algae 5 8 15 31 50
Total 37 100 164 302 557

Tab.4 Global biomass availability (in EJ) scenarios to 2050.

The estimates in Tab.4 are refined using an analysis of the references 2930 to obtain detailed results for different resources. Concerning waste, used cooking oil represents a deposit of about 1 EJ, the rest being municipal solid waste. Energy crops are divided into 63% lignocellulose, 9% vegetable oils and 28% sugar or starch-based materials.

The results obtained are consistent with 31, which concludes that likely estimates are less than 300 EJ. Similarly, the results by resource type are of the same order of magnitude as those given in 32.

Electricity availability

Concerning electricity at the global level, the estimation is also complex due to technical, economic or political factors. Multiple availability scenarios are proposed by academic, industrial and institutional actors. Several scenarios are thus represented on Fig.1, with the estimation of the availability but also of the emission factor of the electricity mix. It is interesting to note the reference point in 2019 and the wide dispersion of the scenarios. Moreover, all the scenarios forecast an increase in electricity production and a decrease in the emission factor. For comparison, the emission factors at the global level for low-carbon production means are lower than 50 gCO2-eq/kWh, with values of the order of 10 gCO2-eq/kWh for wind or nuclear power 33.

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