key: cord-0683403-xzuynia2
authors: Lee, D.S.; Fahey, D.W.; Skowron, A.; Allen, M.R.; Burkhardt, U.; Chen, Q.; Doherty, S.J.; Freeman, S.; Forster, P.M.; Fuglestvedt, J.; Gettelman, A.; De León, R.R.; Lim, L.L.; Lund, M.T.; Millar, R.J.; Owen, B.; Penner, J.E.; Pitari, G.; Prather, M.J.; Sausen, R.; Wilcox, L.J.
title: The contribution of global aviation to anthropogenic climate forcing for 2000 to 2018
date: 2020-09-03
journal: Atmos Environ (1994)
DOI: 10.1016/j.atmosenv.2020.117834
sha: 4f13d7d659f66179c16dcbad804d2483a08204c6
doc_id: 683403
cord_uid: xzuynia2

Global aviation operations contribute to anthropogenic climate change via a complex set of processes that lead to a net surface warming. Of importance are aviation emissions of carbon dioxide (CO(2)), nitrogen oxides (NO(x)), water vapor, soot and sulfate aerosols, and increased cloudiness due to contrail formation. Aviation grew strongly over the past decades (1960–2018) in terms of activity, with revenue passenger kilometers increasing from 109 to 8269 billion km yr(−1), and in terms of climate change impacts, with CO(2) emissions increasing by a factor of 6.8–1034 Tg CO(2) yr(−1). Over the period 2013–2018, the growth rates in both terms show a marked increase. Here, we present a new comprehensive and quantitative approach for evaluating aviation climate forcing terms. Both radiative forcing (RF) and effective radiative forcing (ERF) terms and their sums are calculated for the years 2000–2018. Contrail cirrus, consisting of linear contrails and the cirrus cloudiness arising from them, yields the largest positive net (warming) ERF term followed by CO(2) and NO(x) emissions. The formation and emission of sulfate aerosol yields a negative (cooling) term. The mean contrail cirrus ERF/RF ratio of 0.42 indicates that contrail cirrus is less effective in surface warming than other terms. For 2018 the net aviation ERF is +100.9 mW (mW) m(−2) (5–95% likelihood range of (55, 145)) with major contributions from contrail cirrus (57.4 mW m(−2)), CO(2) (34.3 mW m(−2)), and NO(x) (17.5 mW m(−2)). Non-CO(2) terms sum to yield a net positive (warming) ERF that accounts for more than half (66%) of the aviation net ERF in 2018. Using normalization to aviation fuel use, the contribution of global aviation in 2011 was calculated to be 3.5 (4.0, 3.4) % of the net anthropogenic ERF of 2290 (1130, 3330) mW m(−2). Uncertainty distributions (5%, 95%) show that non-CO(2) forcing terms contribute about 8 times more than CO(2) to the uncertainty in the aviation net ERF in 2018. The best estimates of the ERFs from aviation aerosol-cloud interactions for soot and sulfate remain undetermined. CO(2)-warming-equivalent emissions based on global warming potentials (GWP* method) indicate that aviation emissions are currently warming the climate at approximately three times the rate of that associated with aviation CO(2) emissions alone. CO(2) and NO(x) aviation emissions and cloud effects remain a continued focus of anthropogenic climate change research and policy discussions.

atmospheric modeling systems. Given the dependence of aviation on burning fossil fuel, its significant 77 CO 2 and non-CO 2 effects, and the projected fleet growth, it is vital to understand the scale of aviation's 78 impact on present-day climate forcing. 79

Historically, estimating aviation non-CO 2 effects has been particularly challenging. The primary 80

(quantified) non-CO 2 effects result from the emissions of NO x , along with water vapor and soot that can 81 result in contrail formation. Aviation aerosols are small particles composed of soot (black and organic 82 carbon (BC/OC)) and sulfur (S) and nitrogen (N) compounds. The largest positive (warming) climate 83 forcings adding to that of CO 2 are those from contrail cirrus and from NO x -driven changes in the chemical 84 composition of the atmosphere (Lee et al., 2009 (L09) ). L09 estimated that in 2005, aviation CO 2 85 radiative forcing (RF (Wm -2 )) was 1.59% of total anthropogenic CO 2 RF and that the sum of aviation CO 2 86 and non-CO 2 effects contributed about 5% of the overall net anthropogenic forcing. 87

Understanding of aviation's impacts on the climate system has improved over the decade since the last 88 comprehensive evaluation (L09), but remains incomplete. and NO x ERFs and recalibration of other individual ERFs accounting for factors not previously applied in 98 a common framework. 99

In L09, the net RF was calculated with and without the full contrail cirrus term but including an estimate 100 for linear contrails. The exclusion was based on the lack of a best estimate derived from existing studies. 101

At that time radiative forcing estimates were limited to linear or line-shaped contrails since the modelling 102 approaches required scaling contrail formation frequency to observed coverage and only satellite 103 observations of linear contrails existed (Burkhardt et al., 2010) . The contrail cirrus term requires the 104 simulation of the whole contrail cirrus life cycle, starting from persistent linear contrails which spread and 105 often become later indistinguishable from natural cirrus. Persistent contrail formation requires ice-106 supersaturated conditions along a flight track, which are variable in space and time in the troposphere and 107 tropopause region (Irvine et al., 2013) . Estimating the RF from contrail cirrus requires knowledge of 108 complex microphysical processes, radiative transfer, and the interaction with background cloudiness 109 (Burkhardt et al., 2010) . Contrail cirrus forcing dominates that of persistent linear contrails with the latter 110 on the order of 10% of the combined forcing (Burkhardt and Kärcher, 2011) . In the present study, we 111 present a best estimate and uncertainty based on the results from global climate models employing 112 process-based contrail cirrus parameterizations. 113

Emissions of NO x from aviation lead to photochemical changes that increase global ozone (O 3 ) formation 114 while decreasing the lifetime and abundance of methane (CH 4 climate impacts to be assessed in context with other sectors, such as maritime shipping, ground 143 transportation and energy generation. This updated understanding is especially important given the 144 potential role of international aviation in meeting the goals of the Paris Agreement (Section 2) on limiting 145 future temperature increases. 146

The remaining sections address global aviation growth statistics (Section 2); a brief summary of methods 147 used in the analysis (Section 3); results for the ERF estimates of CO 2 , NO x , water vapor, contrail cirrus, 148

and aerosol-radiation and aerosol-cloud interactions with soot and sulfate (Section 4); results for the net 149

ERF of global aviation (Section 5); emission metrics (Section 6); and aviation CO 2 vs non-CO 2 forcings 150 (Section 7). The appendices contain additional detailed information on trends in aviation emissions (App. 151 A); aviation CO 2 radiative forcing calculations (App. B); radiative forcing, efficacy and ERF definitions 152

(App. C); aviation NO x RF calculations (App. D); contrail cirrus RF scaling factors and uncertainty (App. 153 E); and emission equivalency metric calculations (App. F). A Supplemental Data (SD) file is provided 154

containing the interactive spreadsheet used to calculate RFs and ERFs for each aviation term. 155

Global aviation fuel use and CO 2 emissions have increased in the last four decades with large growth 157 occurring in Asia and other developing regions due to the rapid expansion of civil aviation (Figure 2 and  158 Appendix A). Looking forward, this pattern of growth is expected to be maintained-for example, of the 159 1229 orders of Airbus and 1031 orders of Boeing in 2017, 20.3% and 37.5%, respectively, are for airlines 160 in the Asia region (Airbus, 2017; Boeing, 2018) . Airbus projects 41% of orders over the next two decades 161

to be from the Asia-Pacific region (Airbus, 2017) . The uncertainty in this expectation has increased due to 162 the slowdown in aviation operations in the early months of 2020 due to the COVID-19 pandemic (Le 163 Quéré et al., 2020) . Annual aviation emissions in 2020 are now expected to be below recent projections 164 that are based on historical growth. approximately 2.4% of anthropogenic emissions of CO 2 (including land use change) (Figure 2c) . 173 Aviation has grown strongly over time (Figure 2b ) in terms of available seat kilometers (ASK, a measure 174 of capacity) and revenue passenger kilometers (RPK, a measure of transport work). Fuel usage and hence 175 CO 2 emissions have grown at a lesser rate than RPK, reflecting increases in aircraft efficiency derived 176 from changes in technology, larger average aircraft sizes and increased passenger load factor. Aviation 177 transport efficiency has improved by approximately eightfold since 1960, to 125 gCO 2 (RPK) -1 . 178

At present and for some considerable time into the future, aviation growth is likely to be largely 179 dependent upon the combustion of kerosene fossil fuel (Jet A-1/A) (OECD, 2012), resulting in emission 180 of CO 2 . Renewable biofuels partially offset fossil fuel emissions but these have yet to be produced in 181 sufficient quantities to offset growth of fossil fuel use. Furthermore, considerable uncertainties remain 182

regarding the life-cycle emissions of biofuels, which determine the reductions in net CO 2 emissions (e.g., 183

Hari gases (e.g., short-lived (non-CO 2 ) climate forcers) will be included in future international agreements. 190

The methodologies used to calculate ERF and RF for individual aviation terms are described in this 192 section, and results of these calculations are given in Section 4. Most of the results for the non-CO 2 terms have associated statistics from which the median was chosen as  217  the best estimate, including the net aviation ERF and RF, and the net non-CO 2 ERF and RF. For CO 2 and  218  contrail cirrus, for which the sample sizes are small (3, in both cases), the mean was used as the best  219 estimate. The best estimates of the non-CO 2 terms except contrail cirrus have associated uncertainties 220 expressed as 5% and 95% confidence intervals calculated from 5, 95% percentile statistics. The 221

uncertainty distributions for all forcing terms other than CO 2 and contrail cirrus are lognormal and that for 222

net NO x has a discrete probability distribution function (PDF). The uncertainties for the ERF and RF of 223 CO 2 were taken from IPCC (2013) and fitted with a Monte Carlo analysis with a normal distribution (see 224

Section 5). The uncertainties for contrail cirrus were estimated partly from expert judgement of the 225 underlying processes, as described in Appendix E, again fitted with a Monte Carlo analysis with a normal 226 distribution. 227

The time series of aviation CO 2 emissions is shown in Figure 2 The net-NO x ERF sensitivity of 5.5 ± 8.1 mW m -2 (Tg (N) yr -1 ) -1 yields a 2018 best estimate of 17.5 (0.6, 290

28.5) mW m -2 . This best estimate includes the correction factor for non-steady state conditions as well as 291 the revised formulation of CH 4 RF (Appendix D). 292

Other potential short-term effects from NO the northern hemisphere (Forster et al., 2003) . The accumulation of water vapor emissions perturbs the 300 low background humidity in the lower stratosphere and changes the water vapor radiative balance. 301

Calculating the water vapor RF is complicated by the sensitivity to the vertical and horizontal distribution 302 of emissions, seasonal changes in tropopause heights, and short stratospheric residence times. Some 303 earlier studies do not include the water vapor effect. 304

The water vapor effects were explored in detail (see SD) using results from nine studies: IPCC (1999), 305 Marquart Table 3 ). The IPCC best 356 estimate of 50 (20, 150) mW m -2 (including the natural cloud feedback) was derived from scaling and 357 averaging two studies. IPCC assigned a large uncertainty and low confidence to reflect important aspects 358 with incomplete knowledge (e.g., spreading rate, optical depth, and radiative transfer). The RF best 359 estimate derived here for 2018 is 111 (33, 189) mW m -2 . The uncertainties in the present study are 360 reduced due to the development of process-based approaches simulating contrail cirrus in recent years. 361

The uncertainty in the new RF estimate, excluding the uncertainty in the ERF/RF scaling of individual RF 362 values, is ±70%, a value substantially lower than the factor of three stated in IPCC. 363

The ±70% uncertainty was derived differently than for the NO x forcing due to the smaller number of 364 available studies. Instead, the uncertainty was derived from the combined uncertainties associated with 365 the processes involved (see Appendix E). The processes fall into two groups: those connected with the 366 upper tropospheric water budget and the contrail cirrus scheme itself, and those associated with the 367 change in radiative transfer due to the presence of contrail cirrus. We considered uncertainty in upper 368 tropospheric ice-supersaturation frequencies and their simulation in global models and the uncertainty of 369

ice-crystal numbers due to uncertainty in soot-number emissions, ice nucleation within the plume, and lead on average to an increase in contrail cirrus RF, causing our best estimate to be conservative. The 386 estimated uncertainty relates to the average contrail cirrus RF. In specific synoptic situations, 387 uncertainties may be much larger and correlated with each other. 388

In contrast to other aviation forcing terms, the average ERF/RF ratio for contrail cirrus is estimated to be 389 0.42, much less than unity. The associated uncertainty is thought to be very large and dependent on 390 prevailing aviation traffic and its geographic distribution. The low ERF/RF value is largely due to the 391 reduction in natural cloudiness caused by increased contrail cirrus similar to the reduction in natural cirrus 392 cloudiness as reported by Burkhardt and Kärcher (2011 interactions of aviation soot and sulfate preclude best estimates of ERF contributions. Given the potential 432 importance of these ERF terms, placeholders are included in Figure 3 . Furthermore, to promote progress 433 towards future best estimates, the results of relevant modeling studies were compiled and normalized to 434 global aviation fuel usages in 2005, 2011, 2018, to a soot emission index, and to a fuel S content of 600 435 pm (except in the cases of low fuel-S content tests) (see Figure 5 and spreadsheet). As noted in the 436 caption of Figure 5 , some earlier wide-ranging values for the soot aerosol-cloud interaction have been 437

superseded by a more recent study (Penner et based on evidence and agreement in accordance with IPCC guidance ( Table 4) . 513

In Figure 3 , contrail cirrus formation yields the largest positive (warming) ERF term, followed by CO 2 514

and NO x emissions. For the 1940 to 2018 period, the net aviation ERF is +100.9 mW m -2 (5-95% 515 likelihood range of (55, 145)) with major contributions from contrail cirrus (57.4 mW m -2 ), CO 2 (34.3 516 mW m -2 ), and NO x (17.5 mW m -2 ). The aerosol and water vapor terms represent minor contributions. The 517

formation and emission of sulfate aerosol yields the only significant negative (cooling) term. Non-CO 2 518 terms sum to yield a positive (warming) ERF that accounts for 66% of the aviation net ERF in 2018 (66.6 519 (21, 111) mW m -2 ). The application of ERF/RF ratios more than halves the RF value of contrail cirrus 520 while approximately doubling the NO x value. ERF/RF ratios were not included in the L09 analysis. 521

Uncertainty distributions (5%, 95%) show that non-CO 2 forcing terms contribute about 8 times more than 522 CO 2 to the uncertainty in the aviation net ERF in 2018. The best estimates of the ERFs from aviation 523 aerosol-cloud interactions remain undetermined. 524

The time series of ERF values for individual terms is shown in Figure 6 for the 2000-2018 period. 525

Through normalization and scaling the terms are self-consistent over this period. The increase in all of the 526 terms with time is consistent with the growth of aviation fuel burn and CO 2 emissions over the same 527 period (Figure 2 fraction of aviation CO 2 emissions of total anthropogenic CO 2 emissions has averaged 2.1% (±0.15) for 546 the last two decades (see Figure 2) . Normalized relative probabilities of CO 2 and non-CO 2 ERFs for 2018 547 as derived from the Monte Carlo simulations show that non-CO 2 uncertainties are the predominant 548

contribution to the uncertainty in the aviation net ERF (Figure 7) . IPCC also separately estimated the 549 contrail cirrus term for 2011 as 50 (20, 150) mW m -2 as discussed above, which compares well with the 550 updated value of 44.1 (13, 75) mW m -2 . 551

The determination of net aviation ERFs and their uncertainties shown in Figure 3 and accompanying 552 tables required a Monte Carlo approach to summing over terms with discrete probability distributions. A 553 similar method was employed in L09. PDFs of each term were constructed from the respective individual 554 studies as normal, lognormal or discrete distributions (see SD spreadsheet). Monte Carlo samplings (one 555 million random points) of the individual forcing PDFs were then used to combine terms to yield net ERFs 556 and the uncertainties (95% likelihood range) for the sum of all terms and for only non-CO 2 terms ( Figure  557  7) . The forcing terms are generally assumed to be independent (uncorrelated) with the notable exception 558 of the NO x component terms which have strong paired correlations as shown in Appendix Figure D .1. 559

Only the short-term O 3 and CH 4 terms were included in L09 and a 100% correlation was assumed, in part, 560

because the assumption of uncorrelated effects was deemed less acceptable. A subsequent study showed 561 that these terms are indeed strongly correlated (R just aviation, which yields a lower radiative efficiency (i.e., forcing per unit emission) than in the present 583 study. Also given in Table 5 are CO 2 -equivalent aviation emissions, along with ratios of total CO 2 -584 equivalent emissions to CO 2 emissions. Such ratios are sometimes used as 'multipliers' to illustrate the 585 additional climate impact from aviation non-CO 2 terms over those from CO 2 emissions alone. show that when the C-cycle feedback is consistently accounted for, the non-CO 2 emission metrics 598

increase, but less so than initially suggested by Myhre et al. (2013) . They also find that removing the C-599 cycle feedback from both numerator and denominator give similar metric values as including it in both 600

places. Using the CO 2 IRF without the C-cycle feedback provided by Gasser et al. (2017), we calculate a 601 second set of aviation emission metrics ( warming-equivalent emissions based on GWP* indicate that aviation emissions are currently warming the 624 climate around three times faster than that associated with aviation CO 2 emissions alone ( Table 5) . 625

It is important to note that, unlike the conventional GWP and GTP metrics given in forcers, such as CO 2 , continue to accumulate in the atmosphere resulting in a constantly increasing level 634 of associated warming. Hence warming-equivalent emissions show that the widely-used assumption of a 635 constant 'multiplier', assuming that net warming due to aviation is a constant ratio of warming due to 636 aviation CO 2 emissions alone, only applies in a situation in which aviation emissions are rising 637 exponentially such that the rate of change of non-CO 2 RF is approximately proportional to the rate of CO 2 638 emissions (assuming non-CO 2 RF is proportional to CO 2 emissions, and noting that the rate of change any 639 quantity is proportional to that quantity only when both are growing exponentially). In contrast, under a 640 future hypothetical trajectory of decreasing aviation emissions, this GWP* based multiplier could fall 641 below unity, as a steadily falling rate of emission of (positive) short-lived climate forcers has the same 642 effect on global temperature as active removal of CO 2 from the atmosphere. The GWP* based 'multiplier' 643 calculated here (which depends on the ratio of the increase in net aviation warming to the increase in 644 warming due to aviation CO 2 emissions alone over the recent past), should not be applied to future 645 scenarios that deviate substantially from the current trend of increasing aviation-related emissions. The 646 broad range of values for a 'multiplier'presented here is an illustration of the limitations of using a 647 constant multiplier in the assessment of climate impacts of aviation, and a reminder that the choice of 648 metric for such a multipler involves subjective choices. 649

Since IPCC (1999), the comparison of aviation CO 2 RF with the non-CO 2 RFs has been a major scientific 651 topic, as well as a discussion point amongst policy makers and civil society (ICAO, 2019 or ICAO negotiations to mitigate climate change, in general, will include short-lived indirect greenhouse 658 gases like NO x and CO, aerosol-cloud effects, or other aviation non-CO 2 effects. Aviation is not 659 mentioned explicitly in the text of the Paris Agreement, but according to its Article 4, total global 660 greenhouse-gas emissions need to be reduced rapidly to achieve a balance between anthropogenic 661 emissions by sources and removals by sinks of greenhouse gases in the second half of this century. 662

The IPCC concludes: "Reaching and sustaining net-zero global anthropogenic CO 2 emissions and 663

declining net non-CO 2 radiative forcing would halt anthropogenic global warming on multi-decadal time 664

scales." (IPCC, 2018, bullet A2.2, SPM). Crucially, both conditions would need to be met to halt global 665

warming. Hence, to halt aviation's contribution to global warming, the aviation sector would need to 666 achieve net-zero CO 2 emissions and declining non-CO 2 radiative forcing (unless balanced by net negative 667 emissions from another sector): neither condition is sufficient alone. Some combination of reductions in 668 CO 2 emissions and non-CO 2 forcings might halt further warming temporarily, but only for a few years: it 669

would not be possible to offset continued warming from CO 2 by varying non-CO 2 radiative forcing, or 670 vice versa, over multi-decade timescales. 671

That aviation's non-CO 2 forcings are not included in global climate policy has resulted in studies as to 672 whether they could be incorporated into existing policies, such as the European Emissions Trading 673

Scheme, using an appropriate overall emissions 'multiplier'; however, scientific uncertainty has so far 674 precluded this (Faber et al., 2008 ). In addition, as noted above, the multiplier is highly dependent on the 675 future emissions scenario (Section 6). Alternatively, proposals have been made to reduce aviation's non-676 CO 2 forcings by, for example, avoiding contrail formation by re-routing aircraft ( emissions. Thus, reducing CO 2 aviation emissions will remain a continued focus in reducing future 705 anthropogenic climate change, along with aviation non-CO 2 forcings. The latter increase the current-day 706

impact on global average temperatures by a factor of around 3 (using GWP*) above that due to CO 2 707 alone. 708 Formal analysis; 720

The authors declare that they have no known competing financial interests or personal relationships that 722 could have appeared to influence the work reported in this paper. 723

We gratefully acknowledge discussions with many colleagues during the preparation of this paper, in 725 particular Andreas Bier and Bernd Kärcher. We acknowledge help with graphical displays from Beth 726

Tully ( Figure 1) and Chelsea R. Thompson (Figures 5, 6 and 7 cloudiness affect the climate system. Net positive RF (warming) contributions arise from CO 2 , water 1318 vapor, NO x , and soot emissions, and from contrail cirrus (consisting of linear contrails and the cirrus 1319 cloudiness arising from them). Negative RF (cooling) contributions arise from sulfate aerosol production. 1320

Net warming from NO x emissions is a sum over warming (short-term ozone increase) and cooling 1321 (decreases in methane and stratospheric water vapor, and a long-term decrease in ozone) terms. Net 1322 warming from contrail cirrus is a sum over the day/night cycle. These contributions involve a large number 1323 of chemical, microphysical, transport and, radiative processes in the global atmosphere. The quantitative 1324 ERF values associated with these processes are shown in that no estimate is available yet. The basis for confidence levels is presented in Table 4 . 

Global aviation CO 2 emissions for 1940-1970 were taken from Sausen and Schumann (2000) and for the 1398 years 1971-2016 were calculated from International Energy Agency (IEA) data on usage of JET-A and 1399 aviation gasoline, largely from annual 'Oil Information' digests (e.g., https://webstore.iea.org/oil-1400

information-2019). The regional data are from the same source but accessed online from the IEA Oil 1401

Information held at the UK Data Service (IEA, 2019). Note that these data are proprietary 1402 and must be purchased from IEA. Data were unavailable for 2017 and 2018, so incremental annual 1403 percentage increases in global aviation fuel usage and, therefore CO 2 emissions, for those years were taken 1404 from reports of the International Air Transport Association (IATA, 2019). Some uncertainties exist from 1405 the annual fuel estimations and to a much smaller extent, the emission factors. The IEA does not give 1406 uncertainties for annual kerosene fuel sales or usage. Sausen and Schumann (2000) , from which the 1940 1407

to 1970 data are based here, estimated that the uncertainty in cumulative fuel consumption from 1940 to 1408 1995 (their dataset) is 20%. There is a known discrepancy of IEA estimates of aviation fuel usage being 1409 greater by about 10% than that derived from bottom-up global civil aviation inventories. Actual fuel usage 1410 is likely to be somewhere between the two estimates: aviation emissions inventories are known to be 1411 incomplete, with only scheduled traffic being available from some air traffic regions, and fuel usage 1412 potentially being underestimated from flight routing and cruise altitudes; IEA data on the other hand 1413

includes military aviation fuel (not included in civil aviation inventories) and a small fraction of kerosene 1414 not used in aviation, but sold for that purpose (L09). The CO 2 emission factors for aviation fuel on the 1415 other hand are well determined, and the uncertainty is likely within 1%. 1416

The response of CO 2 concentrations, C(t), to a CO 2 aviation emissions rate, E(t), is modelled using the 1419 method described in Hasselmann et al., (1997) and is expressed as: 1420 and τ j is the e-folding time of mode j and the equilibrium response of mode j to a unit emissions of α j τ j .

The mode parameters used in this study are presented in Sausen and Schumann (2000) and approximate 1425

the carbon-cycle model in Meier-Reimer and Hasselmann (1987) . The applicability of these parameters in 1426 the context of aviation response was tested in a model intercomparison exercise . 1427

For the time horizon of 50-60 years into the future, these were found to compare well with other more 1428 sophisticated carbon-cycle models such as MAGICC 6.0, which is widely used in the IPCC Fourth 1429

Assessment Report (IPCC, 2007) . Beyond this horizon, aviation CO 2 concentrations begin to have an 1430 impact on the ocean and biosphere uptake of CO 2 and the non-linearities of the system must be accounted 1431

for. 1432 CICERO-2 express how the CO 2 impulse decays within each reservoir. The CO 2 partial pressure in each 1437 reservoir is calculated as a function of the carbon in that reservoir, and the CO 2 partial pressure in each 1438 reservoir is related to the CO 2 partial pressure in the atmosphere by explicitly solving for the 1439 atmosphere/ocean/biosphere CO 2 mass transfer. Therefore, the CICERO-2 carbon cycle takes into account 1440 the nonlinearity in ocean chemistry and biosphere uptake at high CO 2 partial pressures since it represents 1441 the atmospheric change in CO 2 as a function of total background. 1442

The FaIR SCM is described by Millar et al. (2017) and summarized as follows. FaIR is a modified version

Here RF i * is the forcing modified by the efficacy, which yields a better approximation for the surface 1482 temperature change than RF. However, the calculation of the RF i * is computationally much more 1483 expensive than the calculation of RF, as it requires the determination of the equilibrium temperature 

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Radiative forcing from aircraft NO x emissions: mechanisms and seasonal dependence

TRADEOFFs in climate effects through aircraft routing: 1230 forcing due to radiatively active gases

Why radiative forcing might fail as a predictor of climate change

The importance of the diurnal and annual cycle of air traffic for 1235 contrail radiative forcing

A methodology to relate 1237 black carbon particle number and mass emissions

CAM5 short-term O 3 RF that can be found in Khodayari et al. (2014a; b) and NASA ModelE2 1526 short-term O 3 and CH 4 RFs presented by

The scenario (SRES A1B, B1 and B1 ACARE) (the factor can be larger than 1 if the aircraft emissions are 1666 assumed to decrease in the preceding years

Uncertainties in the CH 4 correction factor are associated mainly with inter-model differences and the 1668 applied emission scenarios; the correction factor is sensitive, within ~10%, to inter-model differences 1669 (based on two models, TROPOS and AirClim) and it can vary by another ± 10% depending on emission 1670 scenario (based on a range of RCP projections up to 2050). Given that the uncertainties of the CH 4 1671 correction factor on the net-NO x RF are rather small

Contrail cirrus 1675 The global contrail cirrus RF is calculated by homogenizing existing estimates through the use of specific 1676 scaling factors. The factors relate to the choice of air traffic inventory and its basis year; the use of the full 1677 3D flight distance; the use of hourly air traffic data; the feedback of natural clouds

was corrected by redoing the CAM simulation using a 1680 lower ice crystal radius of 7 µm and a larger contrail cross-sectional area of 0.09 km 2 for the 1681 initialization of contrails at an age of about 15-20 minutes, in agreement with observations (Schumann 1682 et al., 2017b). The resulting change in cirrus cloudiness including the adjustment

• A scaling S 1 of 1.4 is applied for estimates based on the AERO2k inventory for the year 2002 instead 1685 of the AEDT inventory for the year

• A scaling S 2 of 1.14 is applied to estimates that are based on track distance instead of slant distance 1687

This scaling is based on an estimate for the impact of the temporal resolution of the air traffic data 1691 of -25% to -30% within CAM

• A scaling S 4 of 1.15 is applied to account for the underestimation of RF in radiative transfer 1694 calculations that use frequency bands instead of line by line calculations

The study details and scaling results are shown in Table E.1. Weighting each estimate equally, the best 1696 estimate of global contrail cirrus RF is approximately 66 mW m -2 . As noted in the main text

calculation is interpreted as being closer to an ERF than an RF, so was excluded from 1698 this averaging. This mean RF estimate does not include the RF due to contrails forming within natural 1699 cirrus

Uncertainties affecting our contrail cirrus estimates are, on the one hand, due to (A) 1704 uncertainties in the radiative response to the presence of contrail cirrus and, on the other hand, (B) 1705 uncertainties in the upper tropospheric water budget and the contrail cirrus scheme

Uncertainties associated with the radiative response to contrail cirrus are: A1. Uncertainty related to the model's radiative transfer scheme of approximately 35%

the vertical cloud overlap, and the use of plane parallel geometry 1712 as compared to full 3D radiative transfer

Uncertainty estimating radiative transfer in a global climate model in the presence of very small ice 1715 crystals within young contrails, which may amount to about 10%

Uncertainty due to the ice crystal habit is approximately 20% according to Markowicz and Witek

Uncertainty in the radiative transfer due to soot cores within the contrail cirrus ice crystals is 1720 thought to be large, as the change in the shortwave (SW) albedo is large

Overall, uncertainty in the radiative response to contrail cirrus (excluding A3) is estimated to be about 1723 55%, assuming independence of different uncertainties and excluding the impact of ice crystal soot cores. 1724 The uncertainty A3 is included in the uncertainty estimate under (B) because A3 and B2 are dependent 1725 uncertainties

This results from a lack of knowledge in ambient conditions due to the low vertical 1730 resolution of satellite instruments (Lamquin et al., 2012) and to the ability of models to reproduce the 1731 observed statistics of ice supersaturation

This dependency on the atmospheric state leads 1735 to a reduction in the number of nucleated ice crystals in particular in the tropics and at lower flight 1736 levels (Bier and Burkhardt, 2019) leading to a large uncertainty in the impact of tropical and subtropical 1737 air traffic. Depending on the atmospheric state and ice crystal numbers, a varying fraction of ice crystals 1738 can be lost in the contrail vortex phase (Unterstrasser, 2014)

The uncertainty in the lifetime of contrail cirrus, affecting the day-/night-time contrail cover, has 1743 only a small impact on the estimated contrail cirrus RF (Chen and Gettelman

We estimate the associated uncertainty to be

From the sensitivity of the contrail cirrus RF to the temporal resolution in the air traffic dataset in 1746 ECHAM5 and CAM, we deduce an uncertainty of about 10%

The estimate of the feedback of natural clouds, due to contrail cirrus changing the water and heat 1748 budget of the upper troposphere, is very uncertain and has not been properly quantified yet (Burkhardt 1749 and Kärcher

Uncertainty in the RF estimate of Chen and Gettelman (2013) to assumptions in the initial ice-1752 crystal radii and contrail cross-sectional areas is about 33%

From the 1756 two different sources of uncertainty (list A, radiative, and list B, contrail cirrus properties, above) we 1757 calculate an overall contrail cirrus RF uncertainty of about 70%

Note that we do not attempt to infer an estimate for the uncertainty of the factor ERF/RF. When 1760 calculating the contrail cirrus ERF, the error range given refers to the error range of contrail cirrus RF and 1761 not ERF

Emission metrics calculations

For the other 1768 species, the atmospheric decay is given by a constant e-folding time taken as the 'perturbation lifetime'. 1769 The lifetimes used here are broadly consistent with Fuglestvedt

For the calculation of the average rate of CO 2 -warming-equivalent emissions for aviation non-CO 2 forcings 1777 (E CO2e* ) under the GWP* metric in Table 5, we use the relationship between recent changes in effective 1778 RF and CO 2 -equivalent emissions from

CO2) is the absolute global warming 1781 potential of CO 2 at time horizon H. We use updated AGWP H(CO2) values incorporating the updated 1782 radiative efficiency of CO 2 as described in the previous paragraph

Advanced Emission Model 1790 AERO2K-Global aircraft emissions data project for climate impacts evaluation 1791 AGAGE-Advanced Global Atmospheric Gases Experiment 1792 CAM-Community Atmosphere Model 1793 CCMod-Contrail Cirrus Module 1794 CH 3 CCl 3 -Methyl chloroform 1795 COCIP-Contrail Cirrus Prediction Tool 1796 CTM-Chemical Transport Model 1797 ECHAM-European Centre/Hamburg Model 1798 IPCC-Intergovernmental Panel on Climate Change 1799 MAGICC-Model for the Assessment of Greenhouse Gas Induced Climate Change 1800 MOZART-Model for OZone And Related chemical Tracers 1801 NOAA-National Oceanic and Atmospheric Administration 1802 QUANTIFY-Quantifying the Climate Impact of Global and European Transport System 1803 REACT4C-Reducing Emissions from Aviation by Changing Trajectories for the benefit of Climate 1804 RCP-Representative Concentration Pathway 1805 SRES-Special Report on Emission Scenarios 1806 TAR-Third Assessment Report 1807 TRADEOFF-Aircraft emissions: contribution of different climate components to changes in radiative 1808 forcing-tradeoff to reduce atmospheric impact 1809 TROPOS-2D global TROPOSpheric model 1810 WDCGG-World

Global CH 4 lifetime reduction due to aircraft NO x emissions in TROPOS for transient emissions 1865 combining historical emissions (1950-2000) and RCP-4.5 emissions (2000-2050); and constant 1866 emissions for the years

Global CH 4 burden reduction due to aircraft NO x emissions in TROPOS for transient emissions 1869 combining historical emissions (1950-2000) and RCP-4.5 emissions (2000-2050); and constant 1870 emissions for the years

Global CH 4 burden reduction due to aircraft NO x emissions in TROPOS for transient emissions 1873 combining historical emissions (1950-2000) and RCP-4.5 emissions (2000-2050); and constant 1874 emissions for the year 2018. The dashed lines represent 2018 equilibrium (green) and transient values

of the IPCC AR5 four time-constant impulse response function (IRF) model, which represents the 1445 evolution of atmospheric CO 2 by partitioning emissions of anthropogenic CO 2 between four reservoirs of 1446 an atmospheric CO 2 concentrations change, following a pulse emission (see Myhre et al., 2013 for more 1447 details). In more comprehensive models, ocean uptake efficiency declines with accumulated CO 2 in ocean 1448sinks (Revelle and Suess, 1957 ) and uptake of carbon into both terrestrial and marine sinks are reduced by 1449warming (Friedlingstein et al., 2006) . FAIR captures some of these dynamics within the simple IRF 1450 structure, mimicking the behaviour of Earth System Models/Earth System Models of Intermediate 1451Complexity in response to finite-amplitude CO 2 injections; this is achieved by introducing a state-1452 dependent carbon uptake with a single scaling factor, α, to all four of the time constants in the carbon cycle 1453 of the IPCC AR5 impulse response model used for the calculation of CO 2 -equivalence metrics. This 1454 approach is described in more detail by Millar et al. (2017) . 1455

Radiative forcing (RF) has been introduced as a predictor for the expected equilibrium global mean of the 1457 (near) surface temperature change ∆T s that results from the introduction of climate forcers, such as 1458 additional atmospheric CO 2 or a change in the solar irradiation (e.g., IPCC, 2007): 1459 ∆T s = λ RF (C.1) 1460where λ is the climate sensitivity parameter (K (W m -2 ) -1 ). Several definitions of RF exist. According to 1461 the simplest one, the instantaneous RF is the change in the total irradiation (incoming short-wave solar 1462 radiation minus the outgoing long-wave terrestrial radiation) at the top of the atmosphere over the 1463 industrial era. However, for most of the climate forcers a better definition (with respect to the linearity of 1464Eq. (C.1)) is the stratosphere-adjusted RF at the tropopause. correlations between the net-NO x effect and its components are also apparent, especially for the short-term 1546 O 3 and net-NO x components; however, their strength is around half. The high correlations (p=1, R 2 =1) 1547across the long-term effects is expected since CH 4 -induced O 3 and SWV are all derived based on CH 4 RFs. 1548In units of mW m -2 (Tg(N yr -1 ) -1 , 49% of this ensemble short-term O 3 RF is concentrated between 20 and 1549 35, 43% of CH 4 RFs is found between -14 and -10, 41% of CH 4 -induced O 3 RFs is between -7 and -5 and 155045% of SWV RFs vary from -2.5 to -1.5. Of the normalized net-NO x RFs resulting from this ensemble, 1551 44% are observed between 5 and 10 mW m -2 (Tg(N) yr -1 ) -1 . 1552 Transient vs. equilibrium. In calculating the CH 4 RF response to aviation NO x emissions, the lack of steady-1553 state conditions is an important consideration. Since methane (CH 4 ) has a lifetime of the order 8-12 years 1554(largely model-dependent) any NO x perturbation takes on the order ~40 years to come within 2% of the 1555 steady state solution. Moreover, the timescale of removal of CH 4 from the atmosphere is made longer 1556 through a positive chemical feedback (Prather et al. 1994) . In order to overcome the necessity to run a 1557 global chemical transport model (CTM) with full chemistry for such long integrations, a parameterization 1558 to account for this perturbation was originally developed by Fuglestvedt et al. (1999) and has been widely 1559 adopted since then. However, with the significant annual increases in aviation NO x emissions over the last 1560 several decades (Figure D.2a Here, we present an updated methodology to calculate the non-steady-state aviation-NO steady-state CH 4 lifetime reductions is within 6% (on a global scale) (see Table D The present approach is in general agreement with that presented by Grewe