The climate impact of aviation could potentially be reduced if flights were routed to avoid regions where emissions have the largest impact (Sausen et al 1994 ; Schumann et al 2011 , Sridhar et al 2011 , Gierens et al 2008 , Grewe et al 2014b ). Here, we investigate whether the introduction of a reduced climate impact routing strategy is beneficial for climate change. The objective of our study is to show the feasibility of such a routing strategy by taking into account a representative set of weather situations for winter and summer seasons and optimizing all trans-Atlantic air traffic on those days and taking safety issues fully into account. An overview of the calculation of the climate-optimal routes, climate metrics and air traffic simulation is given in section 2 . The impact of the climate-optimized routing strategy on climate impact and cost is presented in section 3 , as well as a consideration of the use of market-based measures to incentivise the use of such a strategy, and a roadmap for implementation. Uncertainties and a comparison to previous work are discussed in section 4 .

The warming from increases in ozone dominates over the cooling due to methane decreases for the current global fleet (Lee et al 2010 ). However, locally the net effect can vary significantly (Köhler et al 2008 , Stevenson and Derwent 2009 ) and NO x emissions in some regions can lead to a global cooling (Grewe and Stenke 2008 ). Similarly, contrail formation, properties and the related climate impact vary significantly between different regions and times (Ponater et al 2002 , Marquart et al 2003 , Palikonda et al 2005 , Meyer et al 2007 , Myhre and Stordal 2001 ). Hence the climate impact of these non-CO 2 emissions depends strongly on the altitude, geographic location and time of the emission referring to the diurnal as well as the seasonal cycle (e.g. Fichter et al 2005 , Mannstein et al 2005 , Meerkötter et al 1999 , Gauss et al 2006 , Grewe and Stenke 2008 , Frömming et al 2012 ).

Nitric oxide (NO) reacts with hydroperoxyl (HO 2 ) forming a hydroxyl radical (OH) and nitrogen dioxide (NO 2 ). This initiates two other mechanisms, the production of ozone via the photolysis of the NO 2 molecule, forming an oxygen atom, which recombines with oxygen to form ozone and the reaction of the hydroxyl radical with methane. Hence the emissions of nitrogen oxides lead to an enhancement of ozone and a decrease in methane concentrations (which itself leads to a reduction in the ozone production). Both ozone and methane are greenhouse gases and changes in their concentrations cause RF.

The impact of aviation on climate, i.e. the impact on global mean near-surface air temperature, has been summarized in assessment reports (IPCC 1999 , Lee et al 2010 , Brasseur et al 2016 ). Roughly 5% of anthropogenic climate change is attributed to global aviation (Skeie et al 2009 , Lee et al 2010 ) and this number is expected to grow further. A wide range of atmospheric processes determine the impact of aviation emissions on climate, which include advection, dispersion, wash-out, chemical conversion, cloud formation (contrail-cirrus), and solar and infrared radiation. In addition to aircraft emissions of carbon dioxide, emissions of water vapor and nitrogen oxide‐ and potentially also particulates—contribute to the climate impact. Contrails only form when the mixture of the hot and moist exhaust with the ambient air becomes saturated with respect to water and only persist if the ambient air is saturated with respect to ice. Contrails influence both the budget of incoming solar radiation and the outgoing infrared radiation emitted by the Earth and its atmosphere—on average, contrails act to warm the climate, but in certain circumstances (e.g. close to sunrise and sunset) the reverse can be true (Meerkötter et al 1999 , Myhre and Stordal 2001 ). The effect of perturbations on the energy balance are quantified using the radiation imbalance at the tropopause (radiative forcing, RF) (IPCC 2013 ). Positive RF will lead to warming and vice versa.

2.1. Overview

To examine the relationship between changes in the climate impact and changes in costs for routing options, we apply a four step procedure. First, for each case study day, radiative forcings resulting from locally-confined unit emissions over the north Atlantic are calculated (section 2.2) by employing the detailed chemistry-climate model EMAC (Jöckel et al 2010, 2016) and then globally averaged. Second, the climate change induced by these emissions is calculated by applying emission metrics to these RF, resulting in climate-change functions (section 2.3, referred to in previous publications as climate-cost functions). The emissions represent a change in the routing strategy towards climate-optimized routing. Third, these CCFs are input to an air traffic simulator (section 2.4). For each flight lateral and vertical variations in the flight profile are considered, resulting in a number of possible flight paths for each flight. The climate impact of each possible flight path of the roughly 800 trans-Atlantic flights (figure 1) is calculated from the CCFs; in addition the cost of each flight is also considered. Finally, for this large set of possible traffic realizations, the optimal relation between climate impact reduction and cost increase relative to the minimum cost situation is derived by successively replacing the flight trajectories with the highest ratio of climate impact reduction versus costs increase. Details of the underlying methodology have been reported previously (Grewe et al 2014a) as have results for one individual case study day in winter (Grewe et al 2014b). Figure 1 Actual flight paths for all trans-Atlantic flights on one day, which corresponds to the first winter weather pattern (WP1). These roughly 800 flights are modified for climate-optimal routing. Download figure: Standard image High-resolution image Export PowerPoint slide

2.2. Atmospheric changes and radiative forcing

The climate impact of local emissions, i.e. the climate-change functions, are determined for five winter and three summer days, which represent frequently-occurring North-Atlantic winter and summer weather patterns (WP and SP) using the classification of Irvine et al (2013). They are classified by their similarity to the North Atlantic Oscillation and East Atlantic teleconnection patterns, which describe main circulation patterns and impact the location and strength of the jet stream. For example WP1 is characterized by a strong zonal jet stream, whereas WP3 is a blocking situation. Winter weather patterns 1–4 each occur on average between 16%–18% of the time, whereas WP5 has the highest frequency of occurrence of 26%. The summer pattern 2 (SP2) is most frequently occurring weather pattern during summer with 60% of the time and SP1 and 3 occurring each 20% of the time. For each weather pattern, one day was selected, which best represents the location and strength of the jet stream of that weather pattern. For each of these days, unit amounts of nitrogen oxide, water vapor, and carbon dioxide are released at about 500 different points in the atmosphere. At each of these 500 points 50 air parcels are started in which chemical perturbations are calculated. In addition, a flight distance is accounted for in every air parcel to simulate the effect of contrails. These emission points are located in an area over the north Atlantic, at multiple levels which cover the main North Atlantic flight levels, and the unit emissions occur at multiple times during the day. The processes simulated in the air parcels include effects from emissions of CO 2 , H 2 O, NO x , and the formation of contrail-cirrus. Emitted nitrogen oxides are converted to HNO 3 , which is rained out depending on the simulated cloud physics. HNO 3 can also be reconverted into NO x . The nitrogen oxides concentration in the air parcel further affect ozone production via the reaction of NO+HO 2 → NO 2 + OH, where NO 2 easily photolyses and the resulting O atom recombines with molecular oxygen (O 2 ) to form ozone. In addition the emitted NO x impacts the OH to HO 2 ratio in favor of OH (see reaction above). The latter is important since the increased OH reduces the background methane concentration. The same effect also results from the produced ozone, which is destroyed by photolysis. The resulting atomic oxygen reacts with water vapor to form OH, which again leads to methane loss. Water vapor is, in a similar way to NO x , emitted into the air parcels, which are transported with the winds in the atmosphere. Whenever precipitation occurs, the water vapor in the air parcels is rained out. Contrails form within the air parcels whenever the Schmidt-Appleman criterion is fulfilled. They are persistent if the air is saturated with respect to ice. Persistent contrails increase the cirrus coverage and, depending on the available water vapor and the prevailing temperature, the contrail coverage and contrail ice water content can grow due to water vapor uptake or shrink due to sublimation. Contrail ice particles sediment and sublimate whenever the air parcel is transported to warmer atmospheric layers. Wind shear acts on the contrails and results in a spreading of the contrail and hence increases the contrail coverage. The contrail coverage, however, is limited by the potential contrail coverage, which is the fraction of an EMAC grid box, which can maximally be covered by contrails. All regarded quantities are transformed from the air parcels onto the EMAC grid, where radiation changes are calculated, and then globally averaged. The resulting changes in the concentrations of—and RF from—CO 2 , ozone, methane, water vapor and contrail-cirrus then provide the relationship between a local emission and the resulting global-average RF. Further details of this modelling approach are reported in Grewe et al (2014a). The simulation of chemical and contrail effects were validated in Grewe et al (2014a) by analyzing key parameters: The temporal course of the response of nitrogen oxide, ozone and methane to an initial unit emission agrees well with results from Stevenson et al (2004). The frequency distribution of ice water content of the simulated contrails agrees well with results from in situ measurements by Voigt et al (2011), whereas the frequency of optically thin (with respect to the visible spectral range) contrails is larger in our simulation. The specific radiative forcing of contrails has been verified with the Myhre et al (2009) benchmark test, which determines the RF for a 1% cirrus increase at 11 km with an optical depth of 0.3. The results fall well within the range of other model results.

2.3. Climate metrics and climate-change functions

To choose an appropriate climate metric we pose the question, what potential reduction in climate impact could be achieved by steadily applying a climate optimizing aircraft routing strategy, especially in the next few decades? From this objective we derive an adequate climate metric (Grewe and Dahlmann 2015). We consider a business-as-usual future air traffic scenario as a reference and compare that to a scenario where we daily fly trans-Atlantic routings with a low climate impact. We use the global and temporal average near-surface temperature response over 20 years after introducing the climate-optimized routing strategy. This metric enables the different climate relevant emissions to be placed on a common scale and thus be directly compared. Other metrics, which are suitable to assess a continuous change in the routing strategy, were investigated without significantly altering the conclusions (Grewe et al 2014b). We note that had we adopted the more frequently used pulse-based metrics (e.g. Fuglestvedt et al 2010), we would have found much stronger sensitivity, and more contrast between the short- and long-lived emissions—however, these would not have been best suited to quantifying the sustained impact of a permanent change in routing strategy on near-term climate change, which is the aim here. Applying this metric to the calculated RF (section 2.2) we then obtain a relation between locally and temporarily specified emissions and the global-average impact on climate in terms of future temperature changes. We call these 4-D response patterns 'climate-change functions' (CCFs). They comprise, e.g. the contribution from NO x emissions to the global-mean climate impact via ozone. The climate impact of NO x emissions depends significantly on where they are emitted with higher impacts for emissions in the jet stream and lower values for emissions north of it (Grewe et al 2014b).

2.4. Air traffic simulation