Climate impact due to aviation emissions is an important issue. Nowadays global aviation contributes only about 5 % to the anthropogenic climate impact . However, the aviation's contribution to the climate impact is expected to increase further because global air traffic strongly grew in terms of revenue passenger kilometers (RPKs) by 7.4 % in 2016 compared to 2015 . The aviation climate impact consists of carbon dioxide (CO2) emissions and of non-CO2 effects. The non-CO2 effects comprise nitrogen oxides (NOx) which lead to concentration changes of ozone and methane, water vapor (H2O), hydrocarbons (HC), carbon monoxide (CO), sulfur oxides (SOx), non-volatile particulate matter such as black carbon (BC), persistent linear contrails, and contrail-induced cirrus clouds . These effects change the radiative balance of the Earth's climate system and cause radiative impact. The radiative impact potentially drives the climate system into a new state of equilibrium through temperature changes. stated that the CO2 emissions have the main impact and that the estimated radiative forcing (RF) of aviation CO2 in 2005 was 28.0 mWm-2 (15.2–40.8 mWm-2, 90 % likelihood range). The non-CO2 emissions and the induced clouds also have a large effect on RFs; for example, the estimated RFs in 2005 for total NOx and for persistent linear contrails were 12.6 mWm-2 (3.8–15.7 mWm-2, 90 % likelihood range) and 11.8 mWm-2 (5.4–25.6 mWm-2, 90 % likelihood range), respectively . In particular, the radiative impact of contrails remains uncertain, and recent studies report higher RF. estimated the contrail cirrus RF of 37.5 mWm-2 for the year 2002; reported the RF of 63 mWm-2 for the year 2006; and estimated the RF of 56 mWm-2 for the year 2006. As for timescales of their impacts, the emitted CO2 becomes uniformly mixed in the whole atmosphere, and its perturbation remains for millennia. In contrast, the non-CO2 effects occur on short timescales, e.g., the emitted NOx remains for a few days to months; the contrails last several hours. Thus, the non-CO2 effects depend strongly on the ambient (local) atmospheric conditions . To investigate measures for reducing the aviation climate impact, the impact of both CO2 and non-CO2 effects must be considered; therefore, geographic location, altitude, the time of released non-CO2 emissions and induced clouds, and corresponding local atmospheric conditions need to be considered.

In recent years, and have proposed a climate-optimized routing as an important operational measure for reducing the aviation climate impact. This routing allows a significant reduction of the climate impact by optimizing flight routes to avoid regions where released emissions (including contrails) have a large climate impact. The climate-optimized routing is immediately applicable to present airline fleets, whereas other, more technological measures e.g., efficient engines, blended wing–body configurations, and laminar flow controls; require several years before implementation. Moreover, the routing can be used in addition to the technological measures for reducing the aviation climate impact.

Benefits of the climate-optimized routing have been examined before ; for example, and developed climate cost functions (CCFs) for the climate-optimized routing. They calculated global-average RFs resulting from local unit emissions (CO2, NOx, H2O, and contrails) over the North Atlantic for typical weather patterns by using the European Center HAMburg general circulation model (ECHAM) and Modular Earth Submodel System (MESSy) Atmospheric Chemistry (EMAC) model . Those RFs were used to calculate the global and temporal average near-surface temperature response over 20 years, which describes the climate impacts (i.e., future temperature changes) caused by those emissions on a per unit basis. The resulting data set is called the CCFs. The CCFs describe the climate impact which is induced by aviation's CO2 and non-CO2 effects (H2O, ozone, methane, ozone originating from methane changes, and contrails including the spread into contrail-cirrus), and the CCFs of those effects except CO2 are a function of geographic location, altitude, and time. Because of the long residence time of CO2, its impact is the same regardless of location, altitude, and time of emission. The obtained CCFs can be used as a measure of the climate impact of aviation and form the basis for the climate-optimized routing. calculated the CCFs for a winter day and optimized 1 d transatlantic air traffic (391 eastbound and 394 westbound flights) using the CCFs in the system for traffic assignment and analysis at macroscopic level SAAM; . They reported that the climate impact decreased by up to 25 % with a small increase in economic costs of less than 0.5 %. This revealed a great potential for the climate-optimized routing. On the other hand, a trade-off between climate impact and economic cost existed; i.e., the climate-optimized and the cost-optimized routings were conflicting strategies. extended this study and investigated the feasibility of the climate-optimized routing for realistic conditions. Similar transatlantic air traffic simulations (about 800 flights) were performed for five representative winter and three representative summer days, which took safety aspects into account. They found that a decrease in potential climate impact of 10 % was achieved at a cost increase of only 1 %.

The benefits of the climate-optimized routing were investigated by using different climate metrics. optimized flight trajectories for a total climate cost which was calculated by the absolute global temperature change potential (AGTP) pulse AGTP values for three time horizons; due to CO2 emissions and contrails. A total of 960 transatlantic flights (482 eastbound and 478 westbound flights) were analyzed for a specific summer day. They reported that the climate-optimized routing reduced the total AGTP (for the medium-term climate goal of 50 years) by 38 % with an additional flight time of 3.1 % and with extra fuel use of 3.1 % for the eastbound flights, whereas the routing reduced the total AGTP by 20 % with an additional flight time of 3.0 % and with extra fuel use of 3.7 % for the westbound flights. Generally, aircraft operating costs depend on time and on fuel. Thus, those results indicate the aforementioned trade-off between climate impact and economic cost; this trade-off was also found for the short-term (25 years) and long-term (100 years) climate goals. compared the trade-off between economic costs and climate impact from the transatlantic air traffic simulations described above with respect to three climate metrics: the average temperature response with future increasing emissions (F-ATR20) and the absolute global warming potential with pulse emissions at a 20-year time horizon (P-AGWP20) for short-term climate impacts and P-AGWP100 (time horizon of 100 years) for long-term climate impacts. The trade-offs obtained with the three metrics were very similar. Although many studies show the benefit of the climate-optimized routing, this routing is not used for today's flight planning; today's aircraft routing focuses on minimum economic cost. However, if additional costs, such as environmental taxes, for aviation climate impact of CO2 and non-CO2 effects are included in the operating costs, a cost increase due to the climate-optimized routing is possibly compensated for . This inclusion can change the current routing strategy and incentivize airlines to introduce a climate-optimized flight planning.

Here we present an air traffic simulation model which serves as a basis for the following ultimate two aims: to investigate an eco-efficient aircraft routing strategy that reduces the climate impact of global air traffic over the next few decades and to estimate its mitigation gain for different aircraft routing strategies. For these aims, the submodel AirTraf (version 1.0) was developed as one of the submodels of EMAC . AirTraf can simulate global air traffic in EMAC (online) for various aircraft routing strategies (options). Every flight trajectory is optimized for a selected routing option under daily changing local atmospheric conditions. AirTraf can take into account where and when aviation emissions are released or contrails form. The road map for our overall study has been shown elsewhere .

This paper presents a technical description of the new version of the submodel AirTraf 2.0. The simple aircraft routing options of great circle (minimum flight distance) and flight time (minimum time) were developed in the previous version of AirTraf 1.0 . In AirTraf 2.0, seven new aircraft routing options have been introduced: fuel use, NOx emissions, H2O emissions, contrail formation, simple operating cost (SOC), cash operating cost (COC), and climate impact estimated by the algorithmic climate change functions (aCCFs) . The climate change functions were previously referred to as the climate cost functions mentioned above. These options represent the objects to be minimized. Overall the nine options have been integrated into AirTraf 2.0, which enables air traffic simulations for the ultimate aims of our study (hereinafter the aircraft routing options are referred to simply as, e.g., the “fuel option”). Thus, the development described in this paper is an indispensable update. Moreover, this paper provides example applications of AirTraf 2.0. Some simulations of the nine routing options were carried out for transatlantic routes for a typical winter day. Optimum flight trajectories and characteristics of the routing options were analyzed.

Here we mention the importance of the variety of the routing options. Various routing options have been made available in AirTraf 2.0 because not only the climate and the cost options but also the other options are important subjects for air traffic routing studies. The time option is useful for delay recovery. Because delays cause costs to airlines, pilots are often forced to temporarily use the time option during a flight to maintain flight schedules, although the use of this option increases fuel costs . The NOx and contrail options have been examined as a routing strategy towards climate impact reduction. Moreover, conflicting scenarios (trade-offs) between different routing strategies have been studied; for example, avoiding contrail formation generally increases fuel use and CO2 emissions. assessed the trade-off between contrail avoidance and increased CO2 emissions (∼ increased fuel use) for a single flight. AirTraf 2.0 enables the analysis of those subjects all at once because all the options are integrated. Normally, one or two specific routing options are available for a flight trajectory optimization in other models. Another aspect to be emphasized compared to other models is that AirTraf performs air traffic simulations not under International Standard Atmospheric (ISA) conditions and not under a fixed atmospheric condition for a specific day but under comprehensive atmospheric conditions which are calculated by EMAC; that is to say that AirTraf can simulate air traffic for long-term periods in EMAC, which enables one to examine effects of aircraft routing strategies on climate impact on a long-term timescale. Last but not least, the aCCFs are new proxies for the climate-optimized routing. An important aim of the AirTraf development is to verify the aCCFs themselves and the routing strategy based on the aCCFs (i.e., the climate option) in multi-annual (long-term) simulations .

This paper is organized as follows. Section 2 describes an overview of AirTraf 2.0. Particularly, key changes in the model components are stated. Section 3 presents the results and discussion for the example applications of AirTraf 2.0 using the nine routing options. Section 4 verifies the consistency of the results with literature data. Finally, Sect. 5 concludes this study.

This paper presents the extended version of the submodel AirTraf which offers additional aircraft routing options for defining overall target functions for the flight trajectory optimization. To confirm the consistency of AirTraf simulations, the relative changes in the performance measures among the routing options (listed in Table  in parentheses) are compared with previous studies. The quantitative values of the changes in the performance measures vary depending on different methodologies, atmospheric conditions, simulation periods, flight plans, aircraft/engine types, cost/climate impact metrics, etc. Thus, a direct comparison in magnitude of our results with published studies is difficult; the sign of the relative changes in the measures is compared. Note that the great circle and the time options have been verified before . In addition, the H2O option yields the same results as the fuel option (see Sect. 2.5.3 and Table ); the SOC option is comparable to the COC option (see Sect. 3.3 and Table ). Thus, we omit any discussion of the H2O and the SOC options here.

First, the time, the fuel, and the COC options are analyzed. As defined in Sect. 2.5.6, COC is a combined function of flight time and fuel. To minimize COC, one may attempt to reduce both factors simultaneously; however, a trade-off between the flight time and the fuel generally exists. Table  shows that the time penalty of flying minimum fuel trajectories is 2.4 percentage points, whereas the fuel penalty of flying minimum time trajectories is 20.3 percentage points. A similar trade-off was reported by two published studies. addressed a single-objective flight trajectory optimization on total flight time and fuel use under ISA conditions. A typical single-aisle aircraft (150 passengers) with twin turbofan engines was assumed; the aircraft speed and the flight altitude in eight flight segments were optimized for a given flight trajectory (a quasi-full flight profile optimization). Compared to the minimum time trajectory, the fuel optimum trajectory decreased the fuel use by 31.7 percentage points with an increased flight time of 14.0 percentage points. compared performances for the minimum time and the minimum fuel trajectories for a flight from Frankfurt (Main) to Dubai for a Boeing B777 freighter on 2 February 2016 at 12:00 GMT. The comparison showed that the fuel optimum trajectory decreased fuel use by 8.0 % with an increased flight time of 3.7 %. These studies imply that the minimum COC solution lies between the minimum time and the minimum fuel solutions. In fact, Table  shows that the COC option has more flight time than that of the time option and that the COC option consumes more fuel than that of the fuel option. The COC option yields the values of compromise (i.e., not minimum) of flight time and fuel. Nonetheless, this option achieves the minimum COC. The submodel AirTraf 2.0 can consistently differentiate those three solutions.

To support the discussion above, the fuel and the COC options are compared in detail. compared the minimum fuel and the minimum direct operating cost (DOC) trajectories for a short-haul route for a Boeing 727-100 aircraft on the basis of optimum control theory under United States standard atmospheric conditions. They showed that flying “minimum fuel” reduced fuel use by 6.9 %, whereas the time and the DOC penalties of the trajectory were 23 % and 6 %, respectively (constrained thrust case). Our results in Table  show that the fuel option reduces fuel use by 0.1 %, whereas the time and the COC penalties of the option are 0.1 % and 0.03 % compared to those measures of the COC option. The signs of these relative changes obtained from our results agree with those shown by . In addition, the time and the COC options are compared in a perspective of airline operating economics. Although the time option increases fuel use, NOx emissions, H2O emissions, SOC, COC, and ATR20total (fuel use and COC increase by 20.2 % and by 6.1 %, respectively), the option decreases flight time by 2.3 % compared to that of the COC option. In other words, the time option reduces flight time with the extra cost of 19 034.74 USDh-1 (=269.66 EURmin-1, converted as 1USD=0.85EUR on 18 September 2018; ). In a context of delay recovery, this extra cost is the same order of magnitude to flight delay costs. If the flight delay costs exceed the extra cost due to the time option, operators would determine to fly faster by using the time option to recover the delay. reported that the flight delay costs, which are associated with delayed passengers, additional fuel use, flight crew, cabin crew, and marginal maintenance costs, reached several hundred Euros per minute. The extra cost calculated from our results agrees well with this report.

Compared to the COC option, the NOx option decreases the NOx emissions by 0.5 %, leading to a COC increase of 0.2 %. analyzed the effects of varying cruise conditions on NOx emissions and on DOC from the cruise NOx simulation model by assuming a cruise range of 5800 km with a Boeing 747-400 aircraft under ISA conditions. They clearly concluded that a reduction of NOx emissions caused a cost increase. Our results agree well with this conclusion. Moreover, the NOx option differs from the fuel option because the amount of NOx emissions depends not only on fuel use but also on the NOx emission index, as defined in Eq. (). The emission index depends strongly on the ambient atmospheric conditions at every waypoint (see Sect. 2.6 of ). Table  shows that the NOx option decreases the NOx emissions by 0.3 percentage points, whereas this option increases flight time by 0.2 percentage points and fuel use by 0.2 percentage points compared to those measures of the fuel option. addressed a single-objective flight trajectory optimization on total fuel use and on NOx emissions with the same simulation setup described above. Compared to the minimum fuel trajectory, the minimum NOx trajectory decreased NOx emissions by 10.4 percentage points, whereas the trajectory increased time by 1.0 percentage point and fuel use by 3.9 percentage points. The signs of the relative changes obtained from our results are in good agreement with those shown by .

The contrail option drastically decreases contrail distance by 79.8 % and ATR20total by 43.4 %, whereas this option increases fuel use by 23.0 % and COC by 12.0 % compared to those measures of the COC option. The contrail option is effective in order to reduce the climate impact, as pointed out by previous studies introduced in Sect. 1. Here those relative changes in the measures are compared with two published studies. performed a 1 d European air traffic optimization on 25 July 2016. The total number of 13 584 flights over Europe (containing 16 aircraft types) was employed; their three-dimensional flight profiles were optimized for airline costs (termed as the cost performance indicators, CPI) and environmental impacts (termed as the ecological performance indicators, EPI). They revealed that an additional contrail avoidance intent decreased contrail costs by 31.5 % (contrail formations were converted into a monetary value) and EPI by 5.2 %, whereas the intent increased fuel use by 0.05 % and CPI by 0.5 % over those of the minimum cost strategy. The signs of the relative changes obtained from our simulations are consistent with those shown by . Furthermore, applied a contrail reducing strategy to aircraft flying between 12 airport pairs (287 flights) in the United States on 12 April 2010. The three-dimensional contrail reducing strategy showed a trade-off between contrail formation time (time spent in traveling through contrail formation regions) and fuel consumption. Representative points on the trade-off curve showed that the contrail formation time decreased by 4415 and by 5301 min with an additional fuel use of 20 000 and of 131 000 kg(fuel), respectively, over those of a wind-optimal strategy (this strategy is regarded as an economically optimal strategy; see Sect. 2.4 of ). This study clearly indicated the fuel increase by avoiding contrail formations. Our results agree well with the finding of .

Table  clearly shows a trade-off between economic cost and climate impact (see also Supplement Fig. S4). Compared to the COC option, the climate option decreases ATR20total by 67.9 % with an additional COC of 9.8 %. A similar trade-off certainly exists between the minimum COC and the minimum climate impact trajectories for each airport pair. The trade-off obtained from our results agrees with that indicated by many studies (see Sect. 1). Moreover, performed an aircraft trajectory optimization for nine North Atlantic flight routes varying weighting factors on average temperature response over 100 years (ATR100) and on COC under ISA conditions. They showed a clear trade-off between the cost and the climate impact. The minimum climate impact trajectories, on average, reduced ATR100 by 28.4 % with an additional COC of 7.1 % compared to those measures of the minimum COC trajectories. Our results agree with those shown by . As discussed above, many previous studies corroborate the consistency of the AirTraf simulations.

We introduced updates to the air traffic simulation model AirTraf in the chemistry–climate model EMAC. The submodel AirTraf 2.0 was developed according to the MESSy standard and was described in detail in this paper. This submodel introduces seven new aircraft routing options for air traffic simulations: the fuel use, the NOx emissions, the H2O emissions, the contrail formation, the simple operating cost, the cash operating cost, and the climate impact options. Our flight trajectory optimization methodology consists of genetic algorithms; the methodology was similarly used and was validated beforehand . The particular strength of AirTraf is to enable a flight trajectory optimization for a global flight movement set in the atmosphere which is comprehensively described by EMAC. The novel routing option, i.e., the climate impact option, has been integrated in AirTraf 2.0. This option uses meteorological variables in terms of (spatially and temporally varying) aviation climate impact estimated by the aCCFs, and optimizes flight trajectories by minimizing their anticipated climate impact. As the aCCFs are new proxies for the climate-optimized routing, AirTraf takes a role in verifying the aCCFs themselves and the climate impact option based on the aCCFs in multi-annual (long-term) simulations.

To test the submodel AirTraf 2.0, example simulations were carried out with 103 North Atlantic flights of an Airbus A330 aircraft for a typical winter day. AirTraf 2.0 simulates the 1 d air traffic successfully for the newly developed routing option concerning different optimization objectives, e.g., contrail avoidance, cash operating cost, and climate impact (represented by average temperature response over 20 years) and finds the different families of optimum flight trajectories which minimize the corresponding objective functions. The characteristics of these routing options include that aircraft are flown as the minimum economic cost with both the SOC and the COC options. These options are comparably effective for economic cost indices. AirTraf 2.0 differentiates the minimum time, the minimum fuel, and the minimum COC options. The COC option lies between the minimum time and the minimum fuel options and thus minimizes COC by taking the best compromise between the flight time and the fuel use into account. The NOx option minimizes NOx emissions; this option differs from the fuel and the COC options. The contrail and the climate options decrease the climate impact (indicated by ATR20total), which causes extra operating costs. A trade-off between the cost and the climate impact certainly exists. Compared to the COC option, the climate and the contrail options decrease ATR20total by 67.9 % and by 43.4 % with an increase of COC of 9.8 % and of 12.0 %, respectively. Thus, the climate option seems to be more effective on the cost–benefit performance than the contrail option. We believe that these climate benefits are most likely an upper limit. The simulation results were compared with literature data. The relative changes in the performance measures among the various routing options agree well with those shown by many previous studies. This comparison has limitations because of different methodologies, different atmospheric conditions, etc. Nonetheless, a lot of literature data offer evidence to indicate the consistency of the AirTraf simulations.

The integration of AirTraf into EMAC allows one to optimize flight trajectories and to study aircraft routings under historical, present-day, and future conditions of the climate system. We acknowledge that the simulation results depend on the atmospheric conditions of the target day. Thus, it is important to examine whether the findings, e.g., the trade-off between the cost and the climate impact, are common under any atmospheric conditions. Recently, examined this for representative weather types over the North Atlantic by using EMAC with AirTraf 2.0. Furthermore, the integrated aircraft routing options could be extended to conflicting scenarios. investigated a trade-off between flight time and contrail formation for transatlantic flights by combining the time and the contrail options. Another option could easily be created by adding a corresponding objective function. The AirTraf development presented in this paper leads to a further detailed understanding of characteristics of various aircraft routing strategies.