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Carbon Offsetting & Air Travel Part 2: Non-CO 2 Emissions Calculations

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SEI Discussion Paper
Carbon Offsetting & Air Travel
Part 2: Non-CO2 Emissions Calculations
Anja Kollmuss and Allison Myers Crimmins
June 2009
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Acknowledgements
We would like to thank Dietrich Brockhagen, Robert Elleman, David Fahey, Melanie Fitzpatrick, Jan
Fuglestvedt, Sivan Kartha, Eric Kemp-Benedict, Dorothy Koch, Jessica Lane, Karen Marais, John
Putnam, Thomas Tomosky, Andrew Tron, Mary Vigilante, and Ian Waitz for their comments, edits and
suggestions.
This paper was written with funding from the Stockholm Environment Institute.
Stockholm Environment Institute - US
11 Curtis Avenue
Somerville, MA 02144-1224, USA
www.sei.se and www.sei-us.org
We welcome suggestions and comments. Please contact us at anja@sei-us.org.
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Table of Contents
ACKNOWLEDGEMENTS ........................................................................................................ 2
1. INTRODUCTION ............................................................................................................. 4
2. HOW TO MEASURE CLIMATE IMPACTS ..................................................................... 7
3. AVIATION EMISSIONS’ IMPACTS ON THE CLIMATE ................................................ 11
3.1 Direct Emissions of Greenhouse Gases 11
3.2 Indirect Impacts on Greenhouse Gases 12
3.3 Particulate Emissions 13
3.4 Contrails & Cirrus Clouds 14
4. METRICS FOR EXPRESSING TOTAL CLIMATE IMPACTS OF AVIATION ................ 16
4.1 Radiative Forcing 16
4.2 Radiative Forcing Index 19
4.3 Integrated Radiative Forcing 20
4.4 Global Warming Potential 25
4.5 Global Temperature Change Potential 26
4.6 Economic Cost Calculations of Aviation 28
5. DISCUSSION ................................................................................................................ 31
5.1 Summary of Metrics 31
5.2 Application of Metrics for Current Air Travel 33
5.3 Recommendations 35
REFERENCES ...................................................................................................................... 37
APPENDIX 1 ......................................................................................................................... 41
APPENDIX 2 ......................................................................................................................... 43
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1. Introduction
Companies and individuals are increasingly interested in calculating and minimizing their climate
footprint1. Although aviation emissions are small2 when compared to other sectors of the economy, air
travel can contribute a significant proportion of an individual’s climate footprint. For example, the
average European emits about 11 metric tons of carbon dioxide (CO2) per year. If a European takes one
transatlantic round-trip flight, say from Frankfurt to New York, they will add 0.8 2 metric tons3
of
CO2 (excluding non-CO2 effects) to their climate footprint. It is important to have an accurate metric to
calculate the climate impacts of air travel. Yet calculating air travel’s impact on climate change is a
complex task, and the currently available air travel calculator estimates can vary by up to a factor of
three (Kollmuss, 2007).
The following is the second of two papers that examine the key factors that have to be taken into
account when calculating air travel emissions for the purpose of climate footprint and offset
calculations. The first paper examined methods of calculating CO2 emissions only, and provided a
framework for how to allocate responsibility for these emissions among various aviation users (e.g.
passengers, cargo customers) (Kollmuss and Lane, 2008). This paper has a broader scope in that it
explains all the emission factors that affect climate change and discusses appropriate metrics that take
into account all these factors. However, it does not directly address allocation of responsibility at the
individual level.
In order to estimate the full effect of aviation on climate, it is necessary to account for CO2 as well as
for all other, non-CO2 warming and cooling effects. This paper is written for a non-technical audience
and explains how to account for non-CO2 impacts of air travel emissions.
Much research has been conducted over the last few years on the non-CO2 warming effects caused by
aviation4. Nevertheless, controversy and confusion exist among policy makers and the general public
about what these non-CO2 effects are, how strong their impacts are, and how and if they should be
integrated into global warming emissions calculations for aviation5
1 Usually an individual’s or a company’s contribution to climate change is called their ‘carbon footprint.’ This is
slightly misleading because, as we discuss in this paper, carbon dioxide (CO2) is just one of many greenhouse
gases that have an impact on climate. To include the impact of all greenhouse gases, we use the term ‘climate
footprint.
.
2 Aviation currently accounts for approximately 2-5% of total carbon dioxide (CO2) emissions and approximately
13% of all transportation related CO2 emissions (IPCC, 1999). If non-CO2 warming effects are included, the
contribution of aviation to global climate change is even larger. Yet civil aviation is growing rapidly at 5.9% per
year (IPCC 2007: Mitigation of Climate Change, p 334; ICAO, 2007). This is faster than any other mode of
transportation (WBCSD, 2002), and the sector’s contribution to climate change will therefore continue to
increase.
3 Estimated emissions depend on the type of airplane, occupancy rate and seat class, among other things. See our
first paper (Kollmuss and Lane, 2008) for details.
4 For an excellent but more technical update on the various scientific issues involving aviation and climate change,
see the ACCRI papers available at:
http://www.faa.gov/about/office_org/headquarters_offices/aep/aviation_climate/ or http://tinyurl.com/7oagzt
5 As no scientific debate is completely sheltered from politics, it is also relevant to note that the aviation industry
has thus far shown opposition to including non-CO2 warming effects into greenhouse gas (GHG) calculations,
whereas environmental groups (e.g. World Wildlife Fundsee references) have advocated for inclusion.
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The non-CO2 warming effects of aviation are most commonly accounted for in emissions calculators
through a Radiative Forcing Index (RFI) or a multiplier. These terms refer to a dimensionless factor
which is multiplied by the calculated CO2 emissions in order to account for all warming effects. The
multipliers used by different calculators lie between 1 (i.e. not accounting for non-CO2 warming
effects) and 3 (i.e. the total warming effect is calculated at three times that of the CO2 emissions alone).
These numbers are usually chosen in reference to the IPCC special report on aviation (IPCC, 1999).
Unfortunately, these multipliers are often scientifically flawed. This paper seeks to explain why.
Many air-travel offset calculators avoid the issue of non-CO2 warming effects and calculate only CO2
emissions (multiplier of 1). We argue that this approach is not defensible: despite the difficulties of
quantifying non-CO2 warming effects from air travel emissions, most models and studies indicate that
the magnitude of these effects is relevant. There is great urgency in addressing the climate crisis
(Hansen et al., 2008). An argument can therefore be made that all climate changing agents6 have to be
included when setting reduction targets or calculating offsetting responsibilities7
.
Our discussion shows the limitations to developing a dimensionless multiplier for the integration of
non-CO2 effects into emissions calculators. These limitations are to some extent caused by scientific
uncertainty, such as limited knowledge about the effects of cirrus clouds. Yet we also show that
developing a multiplier is influenced to a great extent by value-based decisions that underlie the chosen
approach and parameters (i.e. climate impact parameters, time frame, damage function, and discount
rate8
) and not just by the uncertainties that arise from a lack of scientific knowledge.
Though science-based reasoning discourages the use of a simple multiplier to account for non-CO2
effects, such a multiplier is desirable from a policy and climate protection point of view. We elaborate
on a number of scientific and value-related issues and conclude that a multiplier of 2 or greater
should be used for air travel emissions calculators to account for non-CO2 warming effects. The
paper is structured the following way:
6 The gases that cause global warming are generally referred to as greenhouse gases, yet not all molecules that
affect climate are gaseous (e.g. soot and other particulates). Usually these are referred to as warming agents. For
the sake of simplicity, we use the term greenhouse gases (GHGs) to refer to all warming agents.
7 We are very aware that offsetting, especially voluntary offsetting of emissions, can only be a small part of the
climate solution (Kollmuss et al., 2007, Kollmuss et al., 2008). Yet carbon markets are growing rapidly (Capoor
& Ambrosi, 2008) and consumers as well as carbon offset providers need a workable policy solution for
addressing the need to accurately calculate emissions from air travel. Furthermore, such accurate calculators may
help consumers choose between available modes of transport (e.g. train vs. air travel).
8 The discount rate reflects the degree to which society prefers to receive benefits in the present rather than the
future. In terms of the economics of climate change, there are those who argue that the future benefits provided
by greenhouse gas emissions abatement should be discounted at a rate equal to the average return on a typical
private-sector investment, or returns of 6% per year (Nordhaus, 1994). Yet critics argue that the use of high
positive (c. 6%) discount rates can support policy outcomes that are unfair to future generations because
unmitigated climate change would impose major, uncompensated costs on future generations. Similarly, some
argue that equal weight should be attached to the welfare of both present and future generations. Economists have
long recognized that the use of low (c. 1%) discount rates supports aggressive steps to stabilize global climate
(Cline, 1992).
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Chapter 2 explains how climate impacts are measured and modeled. It includes definitions of several
important terms such as climate response, climate forcing, and climate impact.
Chapter 3 describes the climate changing effects from greenhouse gases (GHGs) and other non-CO2
warming agents.
Chapter 4 examines some of the metrics that have been developed to account for non-CO2 emissions,
such as Radiative Forcing Index (RFI), Global Warming Potential (GWP), and Global Temperature
Change Potential (GTP).
Chapter 5 summarizes the issues laid out in previous chapters and discusses the most pertinent issues
that must be addressed when calculating climate impacts from air travel for climate footprint
calculations, concluding with our recommendations.
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2. How to Measure Climate Impacts
Models are used to estimate aviation’s impacts on climate change. One type of model calculates how
greenhouse gas emissions change the energy balance in the atmosphere. Another type of model goes
one step further and calculates the temperature change that will be caused by the change in energy
balance. The next types of models are even more complex and estimate how the predicted temperature
change will cause changes in physical and biological systems (e.g. rainfall patterns or biodiversity) and
how much these changes will cost human society (e.g. effects on GDP).
The results of the latter models have much higher uncertainty and depend to a much larger degree on
assumptions and value-related decisions than the results of models that calculate physical changes, such
as energy balance or temperature difference. Yet such impact models are often more policy-relevant
than purely physical models. In other words, knowing the impacts on an ecosystem and its societal costs
is more relevant and more important for risk assessment and policy actions than just understanding the
radiative forcing of GHG emissions. But because we have to make many more assumptions when
determining climate costs than when calculating radiative forcing, the results are more uncertain, and
are shaped by underlying political or ethical decisions (e.g. discount rate or damage function). This
trade-off between accuracy and relevance is also reflected in the many different approaches that have
been used to account for climate impacts from aviation (see Chapter 4).
These different modeling approaches have all been used in calculating the contribution of aviation to
climate change. In order to better understand the advantages and drawbacks of each of these approaches
it is useful to break down the process of modeling climate change into the following consecutive steps
(Figure 1):
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Figure 1: Measuring Climate Impacts
This figure is a simplified illustration of how climate impacts are
modeled and estimated. The arrows on the left indicate the fields of
expertise required to calculate the climate change parameters (blue
boxes in the middle). The arrow to the right indicates theincrease in
assumptions to calculate or model these parameters as we progress
down the list. Results therefore become more uncertain. Yet relevance
for policy making decisions increases as we move down the chain of
climate change parameters. (A similar graph can be found in
Fuglestvedt et al., 2003.)
Step 1: Calculating Greenhouse Gas Emissions from Human Activities
Humans emit greenhouse gases (GHGs) and other warming agents into the atmosphere through burning
of fossil fuels, industrial and agricultural processes, and deforestation. These anthropogenic (human-
induced) emissions raise the concentrations of these gases in the atmosphere, contributing to climate
change. To calculate emissions from transportation, we need to know the type of fuel burned (e.g.
gasoline), the greenhouse gas content of the fuel (e.g. 21 pounds of CO2 per gallon of gasoline) and the
amount of fuel burned (e.g. number of gallons).
Step 2: Calculating Atmospheric Greenhouse Gas Concentrations
To ascertain the atmospheric concentration of a particular GHG, we can either directly measure it by
taking air samples, or calculate concentrations using models. In order to calculate the concentration of a
greenhouse gas in the atmosphere, we need to know how much was emitted, how long the gas remains
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in the atmosphere, how much of it is absorbed by water and land, and how strong a greenhouse gas it is.
(These properties are explained in more detail in Chapters 3 and 4.) Atmospheric concentrations are
usually expressed in parts per million (ppm) or parts per billion (ppb); for example, the global
atmospheric CO2 concentration has risen from approximately 280ppm to 385ppm in the last
approximately 250 years.
Step 3: Determining Radiative Forcing (RF)
Once we know the atmospheric concentration of GHGs, we can calculate their impact on the global
energy balance. Greenhouse gases trap solar energy (i.e. heat) in the atmosphere. The term ‘Radiative
Forcing’ expresses the capacity of greenhouse gases to alter the temperature (energy balance) of the
atmosphere (see section 4.1). To calculate radiative forcing, we need to know the physical properties of
the gas (i.e. how much energy a molecule can absorb) and its atmospheric concentration. Radiative
forcing is expressed in watts per square meter (W/m2).
Step 4: Modeling Climate Response
Once we have calculated the radiative forcing of GHGs, we can model how the Earth will react to the
additional energy the gases trap in the atmosphere. The term ‘Climate Response’ refers to Earth’s
physical and chemical responses to changes in the atmospheric energy balance, such as changes in
average global temperature and the resultant changes in precipitation patterns.. To calculate climate
responses, we need to know not only the radiative forcing of greenhouse gases but also how natural
systems respond to these changes in the energy balance. This requires in-depth knowledge of highly
complex systems. In order to model such systems, we also need to understand the following:
Climate Feedback
The term ‘climate feedback’ refers to an initial climate response that triggers a second process
that in turn intensifies or reduces the initial response. A positive feedback intensifies the
original process, and a negative feedback reduces it. An example of a positive feedback is the
albedo effect in the Arctic: if Arctic ice melts due to warmer temperatures, the white snow
surface is replaced by a much darker ocean surface. The dark ocean absorbs much more heat
than white ice and snow surfaces. The newly-exposed dark surfaces will therefore lead to
additional warming. Including climate feedbacks in climate calculations increases the accuracy
of climate models because it better describes how much warming or cooling a GHG will cause.
To express the potential of GHG emissions to cause climate feedbacks, the term ‘climate
efficacy’ is used:
Climate Efficacy
Two greenhouse gases with the same radiative forcing do not necessarily lead to the same
temperature increase. The term ‘climate efficacy’ is defined as “the global temperature response
per unit forcing relative to the response to CO2 forcing” (Hansen et al., 2005). Climate efficacy
expresses the difference in effectiveness of different GHGs in causing warming or cooling.9 In
other words, climate efficacy expresses the initial climate response to a GHG emission as well
as the secondary climate feedbacks that the GHG causes. As we will demonstrate, many of the
current models used for aviation climate calculations do not take climate efficacy into
account10
9 For example, human-caused methane has an efficacy of about 145% compared to CO2, if indirect effects on
stratospheric H2O and tropospheric ozone are included (Hansen et al., 2005).
.
10 For more information on efficacy ranges for aviation emissions, see Ponater, M., S. Pechtl, R. Sausen, U.
Schumann, and G. Huttig (2006), Potential of the cryoplane technology to reduce aircraft climate impact: A
state-of-the-art assessment,Atmospheric Environment, 40: 6928-6944..
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Climate Sensitivity11
The term ‘climate sensitivity’ expresses how responsive the climate is to added forcing from
GHG emissions. In other words, if there are strong positive climate feedbacks to GHG
emissions, the climate sensitivity is higher than if there are no such feedbacks. Or, expressed in
terms of climate efficacy: if GHG emissions have a high climate efficacy, they will lead to
more warming, which in turn translates into higher climate sensitivity. More technically, it
refers to the change in surface air temperature following a change in radiative forcing. The
higher the climate sensitivity, the more the climate changes in response to GHG emissions.
Climate sensitivity is expressed in degrees Celsius per watts per square meter (°C/Wm2).
Step 5: Modeling Climate Impacts
The term ‘climate impact’ refers to ecosystem changes due to climate responses. Examples include:
change in species composition and extinction, increase in vector-borne diseases, and impacts on
agricultural crops. These effects can be quantified in many ways; for example, number of species
threatened with extinction or number of people displaced by sea level rise.
Step 6: Modeling Climate Damages or Costs
The term ‘climate damages or costs’ refers to climate impacts expressed in economic terms. Climate
damages are usually expressed in monetary units, such as property lost to sea-level rise or flooding,
medical costs of heat waves and disease, etc. Many assumptions are required to calculate such costs,
and to discount them to present economic values; many important climate damages, such as loss of
human life, cannot easily be expressed in monetary terms12
11 In the IPCC Reports, equilibrium climate sensitivity refers specifically to the equilibrium change in global mean
surface temperature following a doubling of atmospheric CO2 equivalent concentration.
. Simple economic models frequently
express all climate damages through a damage function, assuming a mathematically simple relationship
between climate changes (measured by temperature increase) and the total value of associated damages.
The choice of damage function relies on scientific and non-scientific assumptions and therefore leads to
results that are to a large extent value-based. (For more, see Ackerman, 2009.)
12 Prices for loss of human life are established regularly (e.g. life insurance industry) yet none of these estimates
can resolve the issues between the economic realities and ethical considerations (e.g. Is the life of a rich person
worth more than that of a poor person? Or is the life of a young person worth more than an old person?)
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3. Aviation Emissions’ Impacts on the Climate
There are four main ways that aviation emissions affect climate (Fuglestvedt et al., 2008), each of
which is described in more detail below:
1) Direct emissions of Greenhouse Gases (GHGs): notably carbon dioxide (CO2) and water vapor
(H2O)
2) Indirect impacts on GHGs: non-GHGs or weak GHGs such as nitrogen oxides (NOx) catalyze
changes in concentrations of other GHGs such as ozone (O3) and methane (CH4)
3) Emissions of aerosols13
4) Formation of contrails and cirrus clouds
: emissions of particulates that have cooling or warming effects such as
sulfates and soot
These emissions occur in the troposphere and lower stratosphere. The troposphere is the lowest part of
Earth's atmosphere and its height extends to altitudes between 8 and 15km. The stratosphere lies
between the troposphere and the mesosphere. It starts at an altitude of 8 to 15km and extends to 50 km.
3.1 Direct Emissions of Greenhouse Gases
Carbon Dioxide
Carbon dioxide (CO2) is emitted during the combustion of aviation fuel (kerosene) in direct proportion
to the kerosene consumed: 3.16 kilograms CO2 are produced per kilogram of kerosene burned (IPCC,
1999). Given the current condition of the carbon cycle, natural CO2 sinks (e.g. oceans and vegetation)
absorb CO2 from the atmosphere at approximately half the rate that anthropogenic atmospheric CO2
emissions are produced14, leading to a net accumulation. The resultant long-lived15
CO2 spreads
globally and affects climate independent of where the emissions originated. CO2 is the leading
anthropogenic (human-induced) GHG and its warming effects are well understood; it is therefore often
used as the basis for comparison of all other emission effects (see sections 4.2 and 4.4 on Radiative
Forcing Index and Global Warming Potential). The climate response to CO2 emissions is independent
of where emissions occur; CO2 from aircraft has the same effect as CO2 from other ground level sources
(IPCC, 1999).
Water Vapor
Water vapor (H2O) is another GHG that is emitted during air travel. Most subsonic aircraft water vapor
emissions are removed from the atmosphere through precipitation within one to two weeks and
therefore cause short-lived, regional effects (IPCC, 1999). These effects are greater at high altitudes
(i.e. a stronger climate response occurs when water vapor is emitted in the upper stratosphere than in
13 Fine solid or liquid particles that are suspended in a gas.
14 Climate change can also affect the capacity for land and oceans to act as carbon sinks, another example of a
positive feedback mechanism (Fung et al., 2005).
15 CO2 does not have a mean atmospheric lifetime. CO2 emissions are absorbed by oceans and by the terrestrial
biosphere. About half of CO2 emitted into the atmosphere is removed in the first 30 years, a further 30% is
removed within a few centuries and the remaining 20% will typically stay in the atmosphere for many thousands
of years (IPCC, 2007).
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the lower stratosphere16
) where water vapor stays longer and can accumulate (Holton et al., 1995). This
would have climate implications if air travel was expanded into these higher altitudes, but this is
currently not common with commercial aircraft. Current science indicates that the warming effect of
water vapor from air travel emissions is small (Sausen et al., 2005). (For information on the effects of
condensed and frozen water, see Section 3.4 on contrails and cirrus clouds.)
3.2 Indirect Impacts on Greenhouse Gases
Certain chemicals emitted by airplanes, though not direct GHGs themselves, can act to modify,
produce, or destroy GHGs. Nitrogen oxides17
(NOx) and their impacts on methane and ozone
concentration are of primary concern.
Nitrogen Oxides and Impact on Ozone and Methane
Nitrogen oxides are produced in aircraft engines under high temperature and high pressure conditions
by the reaction between oxygen and atmospheric nitrogen. Nitrogen oxides catalyze the following
chemical reactions which lead to both warming and cooling effects:
1. NOx (and hydroxides (-OH) produced from water vapor and volatile organic emissions) catalyze
production of the short-lived greenhouse gas ozone (O3). NOx released during air travel increases
ozone in the upper troposphere but destroys ozone in the lower stratosphere (IPCC, 1999).
The process of O3 formation is similar to ground level smog formation from transportation and
industrial emissions. As with ground level smog, ozone formation depends on the concentration
of NOx because NOx catalyzes not only the formation of ozone but also its destruction. This
means, paradoxically, that lower ambient NOx concentrations can lead to a greater production of
O3 than higher NOx concentrations18
. The O3 effects of a particular flight therefore depend on the
existing atmospheric conditions (Forster and Rogers, 2008).
Because of increased UV radiation at high altitude (above approximately 9 km19
To summarize, the climate response of ozone formation is a function of UV radiation, water
vapor concentration, temperature, and input of NOx, as well as input of volatile organic
compounds (VOCs), all of which have ambient concentrations and effects that differ with 1) the
) ozone is
formed more effectively there than at ground level and leads to a larger radiative forcing
(Berntsen et al., 2005). Ozone formation in the upper troposphere and the lower stratosphere is
particularly sensitive to NOx (Forster and Rogers, 2008). Furthermore, ozone occurring in the
subtropics and tropics has greater radiative forcing than ozone emitted at higher latitudes
(Berntsen et al., 1997). Thus the O3 effects of a particular flight depend on where changes occur
geographically.
16 The stratosphere lies between about 10 km (6 miles) and 50 km (31 miles) altitude above the Earth’s surface at
moderate latitudes. At the poles, the stratosphere starts at about 8 km (5 miles) altitude.
17 Strictly speaking, NO2 is also a (weak) GHG. Yet because NO2 tends to oxidize rapidly, it has a more important
role in its impacts on ozone and methane than as a GHG.
18 Lower NOx concentrations do not always lead to a greater production of O3 than higher NOx concentrations. It
depends on the proportion of NOx and volatile hydrocarbons and also on temperature, humidity, and UV light.
19 Aircraft usually travel at or above 9km (29,500 feet) for distances of more than 500 km (IPCC, 1999).
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physical and chemical background levels, 2) altitude and latitude, and 3) climate sensitivity
(Berntsen et al., 1997 and 2005).
2. NOx emissions also lead to indirect destruction of methane (CH4) through the creation of ozone.
Methane is a strong GHG with an average lifetime of approximately 12 years. Creation of ozone
results in hydroxyl radicals (-OH) that break down CH4 into CO2 and water, which are weaker
GHGs than methane.20
NOx-induced ozone production that reduces atmospheric methane
therefore results in a small net cooling. The effects of NOx on methane last a little more than a
decade (Stevenson et al., 2004).
3. Lastly, NOx emissions and the resulting reduction in methane in turn lead to a longer-term
decrease in O3, and therefore a small cooling effect over the same lifetime as the methane
reaction (Stevenson et al., 2004.) Ozone itself has an average lifetime on the order of weeks.
To summarize, NOx emissions lead to an initial increase in ozone (net warming) followed by a longer-
term decrease in methane (net cooling) and later a decrease of ozone (net cooling). However, the small
decrease in ozone does not outweigh the larger initial increase in ozone. Therefore, overall changes in
ozone concentration incur a warming effect whereas decreased methane has a cooling effect (Berntsen
et al., 1997 and 2005; Marais et al., 2008). But it would be incorrect to assume that the two effects
cancel each other out, since they occur on different time scales and have different geographical
distributions.
While the scientific understanding and modeling of NOx effects have substantially improved over the
last few years, there is still uncertainty regarding the exact extent to which NOx emissions from air
travel affect climate change (Workshop on the Impacts of Aviation, 2006). In general, uncertainties for
emissions that have indirect impacts on GHGs are higher than for direct GHG emissions, as the climate
response may be dependent on geographic location and time of emission (IPCC, 2007, p 214).
3.3 Particulate Emissions
Sulfates & Soot Aerosols
Aircraft emissions of sulfates and soot particles also affect climate. Direct sulfate emissions cause
cooling because sulfates reflect sunlight, while direct soot emissions have a warming effect, since the
dark soot particles (black carbon) absorb solar radiation and decrease albedo when deposited over
snow21. These anthropogenic (human-caused) aerosols are short-lived. The warming and cooling
impact of aerosols from aircraft emissions is currently poorly understood22
20 If NOx is added to a NOx-limited environment, there will be higher production of ozone and hydroxyl (-OH).
More -OH leads to the faster breakdown of methane into CO2. Though flight levels are usually NOx-limited, if
NOx is added to a VOC-limited regime, less ozone production will lead to less –OH production and a longer
methane lifetime.
(Penner et al., 2009;
Workshop on the Impacts of Aviation, 2006).
21 This is an oversimplification. The key is the relative change in albedo as compared to the absence of aerosols
which can affect temperature and humidity structure and thus alter the formation of clouds (Fuglestvedt et al.,
2009).
22The direct effect of particles from aircraft is fairly well understood and is estimated to be a small effect. Indirect
effects, however, are poorly understood.
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The warming effects of soot are reduced at high altitude (Pueschel, 1996). Light-scattering particles, on
the other hand, are less altitude-dependent in their effects (Hansen et al., 1997). Also, climate responses
can vary with location of emission. For example, soot emissions have a stronger warming effect when
emitted over white surfaces, e.g. aircraft flying over the snow- and ice-covered Arctic.
Aircraft sulfate particles can also impact climate change by influencing cloud formation. Water vapor in
saturated air can condense on certain particles (ice nucleation), resulting in contrails and cirrus clouds
(see Section 3.4). The exact impact of soot from air travel emissions is not well understood because of
the many factors that influence its efficacy in causing cloud formations. These factors include, but are
not limited to, natural particle concentrations, temperature fluctuations, and humidity levels (Penner et
al., 2009). The warming impact of enhanced cloud formation due to aerosols acts on a shorter time scale
than the effects of most GHGs and is currently poorly understood (IPCC, 2007, section TS2.2 of AR4
WG I Technical Summary).
3.4 Contrails & Cirrus Clouds
Clouds can have either a cooling or a warming effect: they can cause warming by trapping long-wave
(infrared) radiation from the Earth, but also cool it by reflecting short-wave (visible and ultraviolet)
solar radiation back into space. Overall, however, clouds caused by air-travel emissions are considered
to have a net warming effect.
Contrails are linear ice clouds formed in the wake of aircraft, which, when persistent, can result in the
formation of cirrus cloud cover (Williams, et al., 2002). Aircraft emissions trigger condensation of
ambient water vapor into ice crystals in the atmosphere (Lee et al., 2009). Contrail formation and
persistence depends on flight altitude and the temperature and humidity of the air through which a plane
flies; thus contrail and cirrus formation is seasonally dependent. Approximately 10-20% of all jet flights
occur in air masses with a humidity level sufficient to cause contrails. In 1992, contrails were estimated
to cover about 0.1% of the Earth’s surface on an annually averaged basis, with larger regional values.
According to the IPCC’s most likely scenario, coverage is expected to grow to 0.5% by 2050 (IPCC,
1999). Contrails are short-lived and have an overall warming effect that is similar to thin, high clouds.23
Warming effects of contrails are different during the day than at night. During the day, contrails trap
infrared radiation (a warming effect) and reflect solar radiation (a cooling effect). At night, only
infrared radiation is trapped and re-emitted downward. The warming effect of contrails is therefore
stronger at night (Stuber et al., 2006). It is important to note that because contrails are short-lived,
formed in areas of high air traffic density, and can affect existing cirrus clouds, they may cause local or
regional climate responses24
(Burkhardt et al., 2008).
23 For an interesting example of how contrails affect surface temperatures, see the study on the effect of the lack of
contrails on surface temperatures during the no-fly period following Sept 11th, 2001: "Regional variations in U.S.
Diurnal temperature range for the 11-14 September 2001 aircraft groundings: Evidence of jet contrail influence on
climate," Journal of Climate, 17: 1123-1134.
24 Line-shaped contrails cause a global radiative forcing of approximately 10 mW/m2 (see section on radiative
forcing). For the most updated research on contrails and contrail cirrus clouds, see the recent ACCRI report
(Burkhardt et al., 2008).
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Cirrus clouds are composed entirely of ice crystals and occur above ~6 km, covering approximately
30% of the Earth’s surface (Penner et al., 2009) . Extensive cirrus cloud development has been
observed after the formation of persistent contrails. The science on this relationship is still developing,
and while cirrus clouds are acknowledged to have a net warming effect, the significance of this effect is
still uncertain. The scientific understanding of cloud formation and modification due to air travel is still
limited (Burkhardt et al., 2008). As the most recent IPCC assessment report notes, “Because spreading
contrails lose their characteristic linear shape, a component of [aviation-induced cloudiness] is
indistinguishable from background cirrus” (IPCC, 2007, WG I, section 2.6.3, p 187). The warming
impact from cirrus clouds was therefore excluded from the Radiative Forcing (RF) and Radiative
Forcing Index (RFI) figures of the research discussed later in this paper (Chapter 4).
Yet to get an accurate estimate of total warming impacts from aviation, cirrus effects should be
included. Although uncertainty remains about the precise nature of aviation-induced cirrus-caused
warming, we do know how cirrus clouds form, and that they have a warming impact. According to
some researchers, this warming impact could be very significant (David Fahey, personal
communication, May 2008); Workshop on the Impacts of Aviation, 2006). For more information, see
the ACCRI papers on contrails and aviation, available at http://tinyurl.com/7oagzt.
Table 1 summarizes the climatic response to aircraft emissions of the different GHGs and forcing
agents.
Table 1: Summary of Climatic Response to Aircraft Emissions25
:
CO
2
NO
x
Ozone
increase
NO
x
Methane
decrease
NO
x
Ozone
decrease
Aerosols
(particulates)
Contrails and
Cirrus Clouds
Mean
temperature
response
warming warming cooling cooling
warming (soot)
and cooling
(sulfates)
Net warming
Duration
on the order
of:
centuries weeks to
months decade decade days to weeks
contrails: hours
aviation-induced
cirrus: hours -
days
Spatial
distribution global continental
to global
continental
to global
continental
to global
soot:
local to global
sulfates:
continental to
global
local to
continental
Scientific
understanding
(Scale: good -
fair - poor)
good fair fair fair fair poor
25 Sources : Sausen et al., 2005; Forster and Rogers, 2008
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4. Metrics for Expressing Total Climate Impacts of
Aviation
A metric is needed to calculate total contribution to climate change of current air travel so that an
individual’s or a company’s climate footprint can be accurately calculated. Such a metric must capture
the future effects of current emissions. Such a metric must:
a) Exclude warming responses from past air travel.
b) Include the future impacts of current air travel.
c) Exclude warming responses from future air travel.
This chapter explains some of the currently available metrics that try to quantify non-CO2 climate
effects: Radiative Forcing (RF), Radiative Forcing Index (RFI), Global Warming Potential (GWP),
Global Temperature Change Potential (GTP) and Economic Cost Calculations. All these metrics have
been used to determine aviation’s total impact on climate change. This chapter examines the strengths
and weaknesses of each approach and explains which of these metrics are most appropriate for
calculating the climate footprint of air travel.
4.1 Radiative Forcing
The Earth’s surface temperature is determined by the balance between incoming solar radiation and
outgoing infrared radiation. Radiative Forcing (RF) is the measurement of the capacity of a gas or other
forcing26 agents to affect that energy balance, thereby contributing to climate change. Put more simply,
RF expresses the change in energy in the atmosphere due to GHG emissions. The RF of a gas is
defined as the difference between incoming solar radiation and outgoing infrared radiation caused by
the increased concentration of that gas27. Radiative forcing is expressed in Watts per square meter
(W/m2) or the “rate of energy change per unit area of the globe as measured at the top of the
atmosphere” (IPCC, 2007, WG I, p. 136)28
.
Positive radiative forcing results in an increase in Earth’s energy budget and ultimately leads to
warming. Because GHGs absorb infrared radiation and re-emit it back to the Earth’s surface, thus
increasing the Earth’s energy balance, they have positive RF values29
.
Negative radiative forcing results in a decrease in the energy budget and ultimately leads to cooling.
Aerosol particles reflect solar radiation, leading to a net cooling, and therefore have negative RF values.
26 The use of the word “forcing” refers to the capacity to drive Earth’s radiative energy balance away from its
current state.
27 More exactly, radiative forcing of a given forcing agent is defined as the difference between incoming and
outgoing radiation, allowing the stratospheric temperatures to adjust to the forcing agent, but keeping tropospheric
and surface temperatures fixed at unperturbed values.
28 Currently, total radiative forcing of human-caused greenhouse gas emissions is approximately 1.5 W/m2.
29 The absorption of infrared radiation by many greenhouse gases grows linearly with their abundance. Yet a few
important exceptions display non-linear behavior (e.g., CO2, CH4, and N2O). For those gases, the relative radiative
forcing will depend upon abundance and hence upon the future emission scenario assumed. The relationship
between carbon dioxide and radiative forcing, for example, is logarithmic, so that the warming effect of rising
concentrations increases, but at a diminishing rate.
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The radiative forcing of a GHG is determined by its atmospheric concentration, warming capacity,
residence time, and spatial distribution:
Amount/Atmospheric Concentration is determined by the emitted quantity of a GHG and by
how much of it stays in the atmosphere. The greater the concentration of a GHG in the
atmosphere, the larger its impact will be.
Warming or Cooling Capacity refers to the “strength” or potency of an emitted gas to act as a
GHG. Not all GHGs have the same warming/cooling capacity; some gases are more effective
than others at trapping heat30
. For example, over a 100-year time frame (see section 4.4 on
Global Warming Potential), a molecule of methane is approximately 25 times more potent
(effective at trapping radiation and inducing warming) than a molecule of CO2 (IPCC, 2007,
WG 1, Table 2.14, p 212).
Duration/Residence Time in the Atmosphere refers to the time a GHG stays in the
atmosphere. Some GHGs are short-lived31
while others remain in the atmosphere for hundreds
or thousands of years. To properly asses the climate impacts of a combination of gases, the
lifetime of each gas has to be taken into account. For example, the warming impacts of CO2
persist for hundreds of years, whereas the warming impacts of ozone or contrails last only days
or months.
Spatial Distribution refers to how far GHGs spread geographically. Long-lived greenhouse
gases spread across the entire global atmosphere (e.g. CO2 and methane); their warming impact
is therefore global in scale. Other gases are short-lived and their warming effects are local or
regional. Residence time of GHGs is therefore related to spatial distribution. Globally-averaged
radiative forcing calculations (see, for example, Figure 2) do not take into account these
differences in spatial distributions.
Radiative forcing has been used as a proxy to express the climate response of different GHGs. Figure 2
illustrates the RFs from aircraft emissions in 1992 and 2000 as reported by Sausen et al. (2005)32. These
RF calculations are based on atmospheric concentrations of GHGs in 2000 due to aviation emissions
starting in the 1940s33
.
30 GHGs do not just absorb heat, they also re-radiate it. More precisely: GHGs absorb heat arriving from one
direction (the direction of the heat source, i.e, the sun, or the surface of the Earth) and re-radiate it in all directions.
GHGs may also have indirect effects on energy budgets due to chemical reactions with other gases in the
atmosphere, which can lead to warming or cooling effects.
31 We use the terms “lifetime” or “short- vs. long-lived” in reference to average atmospheric residence time of an
emitted gas.
32 Sausen et al. (2005) updates the figures reported in the 1999 IPCC aviation report and uses other sources, such
as Minnis et al, 2004 and TRADEOFF, 2003. Sausen et al. (2005) and IPCC (1999) use aircraft emissions data
based on jet fuel production reporting from IEA (the data includes commercial and military aviation, yet military
aviation accounts for only about 10-15% of the emissions).
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Figure 2: Radiative Forcing of Aircraft Emissions in 1992 and 2000 (emissions from 1940 to 2000)
(Source: Sausen et al., 2005)
Scientific Uncertainty: Figure 2 reflects scientific uncertainties of specific emissions both with error
bars and terminology along the x-axis. For example, little is known about the warming impacts of
aircraft-induced cirrus clouds, as indicated by the rating of “poor” at the bottom and by the different
graphical representation (lines instead of bars for the cirrus RF). Because of these uncertainties, total
RF on the right does not include effects of cirrus clouds.
Future Impacts Not Counted: Figure 2 does not represent future warming impacts from any of the
emissions. This underestimates the total impacts of long-lived gases such as CO2 when compared to
short-lived gases like ozone.
Past Cumulative Impacts: Figure 2 shows the RF of long-lived GHGs from air travel which have
accumulated over approximately 60 years. The RF for short-lived gases, on the other hand, does not
include past emissions, but only current emission levels, because short-lived gases decay quickly and
past emissions are therefore no longer present in the atmosphere.
In order to evaluate if RF can be used as a metric for determining the climate footprint of an air travel
passenger, it is important to understand the following characteristics of RF:
RF is an instantaneous measure: it expresses the climate forcing of a greenhouse gas at a particular
point in time. Yet it also has a temporal component: it is a backward-looking metric because it
measures the RF of a GHG that has accumulated in the atmosphere over a certain period of time (e.g.
aviation emissions over approximately 60 years in Figure 2).
Short-lived GHGs, such as ozone, do not accumulate over time because they decay rapidly. The RF
given in Figure 2 therefore shows only the RF of current concentrations of short-lived gases, whereas it
shows the RF of accumulated concentrations for long-lived GHGs. In other words: if emissions stay
constant, the RFs for short-lived GHGs stay constant over time. Long-lived gases such as methane and
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CO2, on the other hand, accumulate over time, even if emissions stay constant, and thus their RF will
increase over time.
4.1.1 What Radiative Forcing Does Not Show
Because RF is an instantaneous, backward-looking metric, it does not account for future impacts of
GHGs. Long-lived GHGs will continue to warm the atmosphere for the duration of their residence time.
Consequently, RF values do not express the total climate response of long-lived gases.
Globally-averaged RF values, such as the ones in Figure 2, do not account for regional variability in
forcings and their climate responses. This is pertinent, since the potential damage of local warming due
to locally-occurring GHGs (and their potential positive feedbacks) might be more intense than if the
warming impact of those GHGs is spread out globally (RF values in Figure 2 apply only to total global
annual emissions). If RFs are globally averaged, it might seem that cooling effects and warming effects
can neutralize each other, yet this is not necessarily the case:
Importantly, global cancellations between the responses of different forcings do not necessarily
represent regional cancellation between their responses. […]The net effect, given the regional
pattern of airline flights, is therefore a Northern Hemisphere warming and Southern
Hemisphere cooling (Forster and Rogers 2008).
It is, for example, plausible that a small global-mean temperature response could occur from
large temperature changes of opposing signs in the two hemispheres; it is unlikely that the
global-mean response would adequately reflect the impact (e.g. the damage) associated with
such a response. However, we are unaware of any simple models that have, as yet, adequately
addressed this generic weakness (Sausen et al., 2006).
To summarize, RF calculations as used in the IPCC aviation report (IPCC, 1999) and in Sausen et al.
(2005) are based on instantaneous measures of atmospheric concentration, warming capacity, residence
time, and spatial distribution of GHGs due to aviation emissions from the 1940s to 2000. Yet, to
calculate total forcing from current air travel, future impacts also have to be included. RF values
reported in the IPCC aviation report and in Sausen et al. (2005) are therefore not the correct metric for
determining current air travel’s total contribution to climatic change, or as the IPCC states:
RF provides a limited measure of climate change as it does not attempt to represent the overall climate
response. (IPCC, 2007, WG I, p. 133)
4.2 Radiative Forcing Index
The Radiative Forcing Index (RFI) has been used to quantify non-CO2 warming effects of air travel.
RFI is the ratio of total radiative forcing (RF) of all GHGs to RF from CO2 emissions alone for aircraft
emissions (IPCC, 1999).
RFI = RFtotal / RF CO2
Many air travel calculators use a dimensionless multiplier between 2 and 3 to account for non-CO2
warming effects. Usually these multipliers are based on the RFI calculated in the 1999 IPCC report on
aviation. The RFI for aviation emissions was estimated by the IPCC to be 2.7 with an uncertainty of
±1.5 (IPCC, 1999). In other words, the IPCC estimated that total RF of aviation was 2.7 times that of
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just CO2 emissions from aviation. When the IPCC estimates were updated, RFI was calculated to be
approximately 2 (Sausen et al., 2005).
Yet RFI is an inappropriate metric to use for personal air travel emissions calculators because RFI
calculations are based on RF values for aviation emissions from the last approximately 50 years. RFI
therefore includes warming responses from past air travel emissions. Furthermore, future warming due
to long-lived greenhouse gases is not included in these calculations. RFI was never intended to be used
to calculate the total effect of current aviation, and is therefore not appropriate for our purpose.
To summarize, RFI is not the correct metric for determining total climate effects of aircraft emissions in
order to calculate climate footprints of air travel passengers. Or, as the IPCC states:
[T]he RF index (RFI) introduced by IPCC (1999), should not be used as an emission metric since it
does not account for the different residence times of different forcing agents. (IPCC, 2007, WG I,
section 2.10.4, p 215)
4.3 Integrated Radiative Forcing
Researchers are aware of the limitations of RF and have been developing metrics that can express total
climate response, including future impacts.
4.3.1 Understanding RF versus Integrated RF
To express the future effects of GHGs, RFs of current (or future) GHG emissions over a chosen time
frame can be summed (in mathematical terms: integrating emissions over time). The results incorporate
future effects of GHGs. This method places an equal weight on impacts occurring at each point of time
within the chosen time frame. (See Figure 3 for a schematic illustration of integrated RF.) Integrated RF
is expressed in Watts per square meter year (W/m2y), i.e. it expresses the energy that is added to the
system during a chosen time horizon due to the GHG emissions.
Figure 3: Integrated Radiative Forcing: the sum of
RF over a chosen time period (area under the curve)
measured in Watts per square meter year (W/m2 year1)
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Figure 4: Integrated RF of All Anthropogenic GHGs Emitted in the Year 2000 over Two
Different Time Horizons.
Top graph: integrated RF over a 100-year time horizon, i.e. the bars express the cumulative
energy that will be added or subtracted from the global energy balance over the next 100 years
due to the different GHGs emitted in 2000.
Bottom graph: integrated RF over a 20-year time horizon.
(Source: IPCC, 2007, WG I, p 206)
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Choosing the time frame for integrated RF greatly influences results. For example, as Figure 4 shows,
integrated RF of CO2 is much larger over the 100-year time frame than over the 20-year time frame,
whereas the contributions from short-lived gases stay the same over the two time horizons, because they
decay much faster and do not cause additional forcing after the first 20 years.
Choosing the time horizon for integrated RF is not a scientific matter but a policy choice. If we are
concerned about the long-term warming impacts of GHG emissions, we should choose a longer time
horizon. If we are concerned about warming impacts in the short term that may lead to irreversible
changes (‘tipping points’), we should choose a shorter time horizon (Berntsen and Fuglestvedt, 2008).
4.3.2 Understanding Pulse versus Sustained Emissions
Integrated RF can be calculated using different assumptions. Figure 4 uses a pulse emission (the
emissions from the year 2000) and integrates RF as GHG emissions from that year decay over time.
Short-lived GHGs will decay faster, long-lived gases more slowly.
Yet integrated RF could also be calculated assuming sustained emissions. For example, instead of using
only the emissions from the year 2000, as in Figure 4, emissions over the chosen time frame (say 20
years) could be assumed to remain constant and cumulative integrated RF of these constant emissions
could be calculated. The RF for short-lived emissions would then stay constant (not decay). The RF for
long-lived gases would grow over time because these gases accumulate. Figure 5 is a simplified
illustration of RF for a pulse emission and RF for constant emissions. If we expect that emissions will
grow or decrease, we can also calculate integrated RF scenarios with growing or decreasing emissions.
The choice to calculate pulse or sustained emissions is a policy decision. As Figure 5 illustrates, the
results can vary dramatically depending on which method is chosen. A pulse emission is suitable for air
travel calculators, since the interest is in calculating the effects of a single flight. Sustained emissions
would be appropriate for modeling, for example, the effects of future aviation: either constant emissions
or the predicted emissions projections should be chosen in that case.
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Figure 5: Atmospheric Concentration and Radiative Forcing Over Time for a Pulse
Emission (top) and Constant Emission Levels (bottom).
Top left: A pulse emission of two hypothetical GHGs: a short-lived one (red) and a long-lived
one (blue). The concentrations of both GHGs decrease over time: the short-lived GHGs decays
much faster than long-lived GHG.
Top right: The total RF (blue line) of these two pulse emissions also decreases over time because
both gases decay over time. Integrated RF is the area under the blue curve.
Bottom left: Constant emissions of two hypothetical GHGs: concentration of the short-lived GHG
(red) stays constant; concentration of the long-lived GHG (green) accumulates over time.
Bottom right: The total RF of these two constant emissions (blue line) increases over time
because the concentration of the short-lived GHG stays constant and the concentration of the
long-lived GHG increases over time. Integrated RF for these two constant emissions is the area
under the blue curve.
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4.3.3 What Integrated Radiative Forcing Does Not Show
Temporal differences in warming
Integrated RF only sums the radiative forcings over a chose time horizon. It does not show at what
point during that time horizon warming occurs. For example, short-lived GHGs with strong warming
capacity, such as methane, will cause temperature changes early on, but will then decay and no longer
cause warming. Long-lived gases with comparatively weaker warming capacities, such as CO2, will
warm the climate more gradually, but for a much longer time. Figure 6 shows the same total integrated
RF value for two very differently-acting GHGs. Despite the fact that they share the same value for
integrated RF, their effect on the climate will play out quite differently. Neither integrated radiative
forcing nor Global Warming Potential (see next section) takes these differences into account.
Figure 6: Identical Integrated Radiative Forcing of Two Hypothetical
GHGs with Different Longevity and Warming Capacity.
The red line shows the RF of a short-lived GHG with a high warming
capacity, such as methane. The green line shows the RF of a long-lived
GHG with a weaker warming capacity, such as CO2. Both GHGs have the
same integrated RF value (area under the curve) yet because the warming
they cause occurs at different points in time and with different strengths,
their effect on the climate will not be the same. Integrated RF does not
reflect this difference.
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Thermal Inertia
Integrated RF does not account for the thermal inertia of the climate system (Fuglestvedt et al., 2008).
Thermal inertia refers to the delay in the change of Earth’s energy balance in response to climate
forcing, or the imbalance caused by a lag between the effects of forcing and the return to energy
equilibrium (Hansen et al., 2005).
To summarize, integrated RF can be used to expresses the future effects of current aviation. The chosen
time horizon greatly influences the results: short time horizons emphasize the warming due to short-
lived emissions, whereas longer time horizons emphasize the warming of long-lived gases. The choice
of pulse versus sustained emissions also influences the results: sustained emissions give more weight to
short-lived effects than pulse emissions do.
4.4 Global Warming Potential
Global Warming Potential (GWP) is based on the integrated RF of a pulse emission. It is used as a tool
to compare the potency of different greenhouse gases with that of CO2. GWP calculates the integrated
RF and lifetime of each gas relative to that of carbon dioxide34
. Carbon dioxide has an assigned GWP
of 1 and is used as the baseline unit (i.e. reference gas) to which all other greenhouse gases are
compared. Thus GWP is unit-less. GWP values can be used to convert various greenhouse gas
emissions into comparable CO2 equivalents when computing overall sources and sinks; greenhouse
gases can thus be expressed in terms of Carbon Dioxide Equivalent (CO2e) (IPCC, 2007, WG I, pp 210-
213).
Because they are based on integrated RFs, GWP values depend on the time span over which the
potential is calculated. Short-lived GHGs initially have large effects that become less significant over
time relative to CO2, since the integrated RF of CO2 increases over time. Methane, for example, has a
GWP of approximately 25 over 100 years but 62 over 20 years (IPCC, 2001). The Kyoto Protocol uses
the GWP time frame of 100 years. If a climate policy is enacted to limit long-term temperature increase,
effects of short-lived emissions may be overestimated if the time horizon chosen is too short (Berntsen
and Fuglestvedt, 2008). On the other hand, a time horizon of 100 years versus one of 20 years might
underestimate the importance of short-lived emissions (IPCC, 2007, WG I, p 206).
34 The GWP index, based on the time-integrated global mean RF of a pulse emission of 1 kg of some compound
(i) relative to that of 1 kg of the reference gas CO2, was developed (IPCC, 1990) and adopted for use in the Kyoto
Protocol. The GWP of a component is defined as (IPCC, 2007, WG I, p 210):
=
TH
r
TH
i
i
dttRF
dttRF
GWP
0
0
)(
)(
i = the greenhouse gas for which a GWP should be calculated
r = reference gas, in this case CO2
RF(t) = radiative forcing over time
TH = time horizon
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4.4.1 What GWP Does Not Show
As discussed in section 4.3.3, integrated RF and GWP do not indicate when the temperature changes
occur given the varying residence times and warming capacities of different GHGs. GWPs also fail to
account for thermal inertia of the climate system. GWP furthermore assumes that the warming response
due to the various GHGs’ forcings are all the same. Yet, as explained earlier, climate efficacy of
different GHGs can vary considerably.
To summarize, while GWP is widely accepted as a reliable proxy for the warming impacts of long-
lived, well-dispersed gases such as CO2, GWP with a 100-year time frame, as used in the Kyoto
Protocol, is not suitable for measuring the kind of short-lived emissions associated with aviation. Or, as
the IPCC states:
To assess the possible climate impacts of short-lived species and compare those with the impacts of the
LLGHGs [long-lived greenhouse gases], a metric is needed. However, there are serious limitations to
the use of global mean GWPs for this purpose. While the GWPs of the LLGHGs do not depend on
location and time of emissions, the GWPs for short-lived species will be regionally and temporally
dependent (IPCC, 2007, WG I, p 211)
4.5 Global Temperature Change Potential
Global Temperature Change Potential (GTP) goes further than GWP and integrated RF in describing
the effects of emissions: it estimates the change in global mean temperature for a selected year in the
future. In other words, this metric tries to answer the question: What will the temperature change be in
year X in response to the radiative forcing of certain GHG emissions? This metric is more complex
because it calculates climate response and not just radiative forcing (see Figure 1). GTP is based on
RF. Yet in order to model and calculate GTP, we also need to know the time scale of the climate
response: because of Earth’s thermal inertia, there is a lag between when the emissions occur and when
they cause warming. In other words, GTP accounts for Earth’s thermal inertia. In addition, the models
need to include the Earth’s climate sensitivity (see Chapter 2). This means that GTP calculations are
more complicated and are less certain than simple radiative forcing calculations.35
As illustrated in
Figure 1, although uncertainty is increased, relevance is also increased since it is more useful for policy
makers to know what the actual temperature change will be than only the amount of energy that has
been added to the system.
GTP can be calculated using a pulse emission or sustained emissions (see section 4.3 on Integrated
Radiative Forcing for a detailed explanation). Furthermore, climate efficacy can be integrated into
formulas that calculate GTP.
As with all other approaches discussed here, the chosen time frame greatly influences the results. For
example, if we choose to evaluate temperature change after 100 years, the effects of short-lived GHGs
are de-emphasized, and changes of temperature in between the time of emission and the evaluation year
are not captured (Berntsen and Fuglestvedt, 2008).
35 The absolute GTP (AGTP) is the temperature change associated with a pulse emission (usually one year) of a
specific GHG at a chosen point in time. The ratio between the AGTP for this gas and the AGTP for CO2 gives the
GTP for the specific GHG (Berntsen and Fuglestvedt, 2008). As with Global Warming Potential, this allows for
comparisons between the climate responses of other GHGs to that of CO2.
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Figure 7 shows the net future temperature change from a 1-year pulse of current emissions for different
transport modes for four future time horizons (20, 40, 60, 100 years). The difference in results between
time horizons is starkest for shipping. The emissions pulse led to cooling in year 20 because of the high
sulfate emissions associated with shipping, but a warming effect begins to become apparent in the
second graph (year 40) because shorter-lived sulfates (cooling) have disappeared while longer-lived
CO2 (warming) is still in the atmosphere. The error bars for aviation in the 20-year time frame are very
large. This is because of uncertainties surrounding the effects of contrails and cirrus clouds.
Figure 7: Contribution to Net Future Temperature Change (in milli-
Kelvin) from a 1-year Pulse of Current Emissions for Different
Transport Modes for Four Future Time Horizons (20, 40, 60, 100
years). The error bars express uncertainties primarily in the effect of
contrails and cirrus clouds. Rail D refers to direct emissions (e.g. fossil
fuel) and Rail I refers to indirect emissions (e.g. electricity) associated with
rail travel. (Source: Berntsen and Fuglestvedt, 2008)
4.5.1 What GTP Does Not Show
Two different GHGs with equal GTPs describe the same temperature change at the end of a chosen
time horizon, though not at specific points within this time horizon. In other words, two different
emissions that give the same temperature effect at a chosen time can have different paths (Berntsen and
Fuglestvedt, 2008). That means that total climate impact of these two gases might be very different, yet
GTP does not reflect these differences.
To summarize, GTP can be used to express future climate responses to current aviation emissions. As
with Global Warming Potential, the chosen time horizon greatly influences the results: short time
horizons include the warming due to short-lived emissions, whereas longer time horizons exclude those
effects.
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4.6 Economic Cost Calculations of Aviation
Economic cost calculations go further than all the previously discussed metrics. This metric tries to
answer the question: What will the economic costs in year X be due to the expected temperature
change from anthropogenic GHG emissions? This metric is more complex because it calculates
climate costs and not just radiative forcing or climate response (see Figure 1). Climate cost
calculations can be based on GTP or on calculating the sum of temperature change over time (delta T
over time: ΔT/t); both metrics in turn are based on RF. In addition to all the assumptions made in order
to calculate GTP, an additional range of parameters, such as discount rate, economic growth rates, and
damage functions need to be determined.
This means that climate cost calculations are more complicated and their results are more value-based
than radiative forcing and climate response calculations. Yet the results of climate cost calculations are
often more relevant for policy makers (e.g. it is more useful for a policy maker to know the economic
impacts than only the physical changes caused by GHG emissions.)
The U.S. Federal Aviation Administration/Aviation Environmental Portfolio Management Tool
(FAA/APMT) model36
calculates the economic costs of the climate impacts due to aviation and is based
on delta T over time.
The FAA/APMT model looks at the future impacts of current (and future) CO2 and non-CO2 emissions
(Marais et al., 2008). FAA/APMT looks at marginal air travel impacts by taking into account the
background atmospheric GHG concentrations from all anthropogenic emission sources37
.
Figure 8 shows the FAA/APMT model’s quantified impacts of one year of aviation. The FAA/APMT
model is probabilistic in order to capture to the extent possible the impacts of many of the uncertainties.
Because some of the behaviors are non-linear, this can be important. The figure shows the mean of the
response for each GHG at each point in time.
Figure 8(a) shows the impact expressed in change in surface temperature (delta T) over time. The
cooling effects of sulfate aerosols, methane decrease (in the figure legend labeled as: NOx-CH4), and
long term ozone decrease (in the figure legend labeled as: NOx-O3 long) can be observed. The total
impact (x-line) is the sum of all warming effects minus the cooling effects.
Figure 8(b) illustrates the same effects expressed as impact on US Gross Domestic Product (GDP). In
order to convert the warming impacts to an economic metric, Marais et al. (2008) assumed a discount
rate, economic growth rates, and a damage function, among other parameters. These parameters explain
the change in shape of the curves as compared to Figure 8(a).
36 The FAA/APMT model is part of a suite of software tools that are currently being developed by the U.S.
Federal Aviation Administration Office of Environment and Energy (FAA/OEE) in collaboration with Transport
Canada: “The main goal of the effort [FAA/OEE ] is to develop the capability to assess the interdependencies
among aviation-related noise and emissions, impacts on health and welfare, and industry and consumer costs,
under different policy, technology, operations, and market scenarios.” (Sausen, Shine & Wuebbles, 2006)
37 The model begins calculating current and future emissions with baseline emission concentrations from the year
1750, then adds the aviation emissions from 1940 onwards to calculate their contribution to climate change. For
more on the mathematical details of this model, see Appendix 1.
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Figure 8: FAA/APMT Model’s Quantified Climate Impacts of a One-Year
Aviation Pulse with Fixed Inputs. (a) Baseline temperature change. (b) Baseline
damage function, Nordhaus and Boyer (2000). The total impact (x line) merges with
the CO2 impact line after a few decades because the short-lived emissions no longer
cause warming after a few decades. (Source: Marais et al., 2008)
The parameters in the FAA/APMT model (e.g. the time frame or the discount rate) can be adjusted
depending on the policy option that is being researched. The parameters for this model do not have
equally strong influences on the results. The relative importance of non-CO2 effects changes depending
on the time frame for which they are calculated. Furthermore, the modelers found:
[T]he climate sensitivity, the radiative forcing of different short-lived effects, the choice of emissions
scenario and the discount rate have the most significant influence on the output metrics we considered.
Other uncertainties were less important. (Marais et al. 2008)
Some of these factors will become more accurate as scientific knowledge improves. Yet others will not:
discount rates, for example, cannot be established by scientific analysis because they are dependent on
ethical choices and value judgments. They also depend on assumed economic performance in the
future.
The FAA/APMT model can also be used to purely express the physical metric of climate impacts by
using the integrated delta T-years (the area under the change in temperature graph for each greenhouse
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gas). In other words, it expresses the changes as a theoretical number that is the sum of all the
temperature changes that occur over a given period of time. This result is then neither discounted nor
used to make any economic estimates. This is what is shown in Figure 8a.
4.6.1 What Economic Cost Calculations Do Not Show
The FAA/APMT model does not take into account the spatial effects of aviation emissions. It uses a
single variable global-mean surface temperature to express climate impacts. It therefore has the
same shortcomings as Global Temperature Change Potential (see section 4.5.1).
In addition, the number and type of assumptions that have to be made in order to estimate climate costs
mean that the results of such economic models are to a large extent value-based. For example, as
mentioned in section 4.6, many important climate damages, such as loss of human life, cannot easily be
expressed in monetary terms. Economic models frequently express all climate damages through a
damage function, assuming a mathematically simple relationship between climate changes (measured
by temperature increase) and the total value of associated damages. Yet such damage functions do not
reflect the complexities and non-linear behavior of physical, biological and economic systems. The
damage function in the FAA/APMT model is based on the climate economics model “DICE,”
developed by Nordhaus and Boyer (2000). For a critique of the DICE model and its assumptions, see
Ackerman and Finlayson (2006).
Despite their shortcomings, economic models are important because they translate climate change into
the currency that is most pertinent to policy makers and businesses: the monetary costs associated with
the expected warming. It is therefore vital for evaluating and prioritizing climate mitigation strategies
that more sophisticated models which explicitly discuss their underlying assumptions be developed.
Any model that calculates climate costs should therefore explicitly state the assumptions that were
made for the non-scientific parameters and their associated uncertainties.
To summarize, we are looking for a metric that is most suitable to calculate the effect on climate change
from air travel so that an individual or a company can accurately calculate their climate footprint due to
their current air travel. Economic cost calculations go beyond this task. A metric that compares the
different forcings or climate responses seems more appropriate for this task and is more comparable
with metrics that are used in other climate policy measures (such as the Global Warming Potential with
a 100-year time frame used under the Kyoto Protocol).
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5. Discussion
After explaining a number of different metrics that have been used to assess aviation’s contribution to
climate change, we now evaluate which one is most suitable for estimating the contribution to climate
change of individual current air travel: in this final chapter, we summarize the most pertinent features of
each metric, discuss the application of these metrics to current air travel impact calculations, and end
with a set of recommendations on how to best account for non-CO2 effects in air travel calculators.
5.1 Summary of Metrics
Figure 9: Climate Change Parameters and Their Associated Metrics.
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Numerous modeling approaches have been used to estimate aviation’s contribution to climate change.
Figure 9 is modified from Figure 1 and shows the units of measurements for the climate change
parameters and their associated metrics discussed in this paper. Radiative Forcing (RF), Radiative
Forcing Index (RFI), Integrated Radiative Forcing, Global Warming Potential (GWP) and Integrated
Change in Temperature over Time all express in some way the change in energy balance that GHG
emissions are causing:
Radiative Forcing is an instantaneous measure: it expresses the climate forcing of a greenhouse gas at
a particular point in time. Yet it also has a temporal component: it is a backward-looking metric
because it measures the RF of a GHG that has accumulated in the atmosphere over a certain period of
time (see Figures 2 and 3). Long-lived GHGs will continue to warm the atmosphere for the duration of
their residence. Consequently, RF values include effects of past air travel and exclude future effects of
current air travel. RF values reported in the IPCC aviation report (1999) and by Sausen et al. (2005) are
therefore not the correct metric for determining total climatic response of current air travel (and were
never intended to be used that way).
Radiative Forcing Index (RFI), as used in IPCC 1999, compares the non-CO2 warming effects of
aviation to those of CO2. RFI is the ratio of total radiative forcing (RF) of all GHGs to RF from CO2
emissions alone. The RFI calculations in the IPCC aviation report from 1999 are based on RF values
for aviation emissions from the last approximately 50 years. RFI has the same shortcomings as RF: RFI
includes effects of past air travel and excludes future effects of current air travel. RFI is therefore not
the correct metric for determining total climatic response of current air travel (and was never intended
to be used that way).
Integrated Radiative Forcing enables us to calculate the future effects of GHGs. It sums the RFs of
GHGs over a chosen time frame (in mathematical terms: integrating them; see Figure 3 for a schematic
illustration of integrated RF). Integrated RF expresses the energy that is added to the system during a
chosen time horizon due to GHG emissions. Integrated RF of current emissions excludes effects from
past air travel and includes future effects of current air travel. Integrated RF of current emissions could
therefore be an appropriate metric for our purposes. Yet results of integrated RF vary greatly depending
on the chosen time frame and whether a pulse emission or sustained emissions are used (see further
discussion below).
Global Warming Potential is used as a tool to compare the potency of different greenhouse gases with
that of CO2. In that way, GWP is similar to RFI. But whereas RFI is a backward-looking metric, GWP
is a forward-looking metric that includes future effects of current emissions. GWP is based on
integrated RF over a chosen time frame of each GHG relative to that of CO2e. GWP values depend on
the time span over which the forecast warming potential is calculated. GWP with a time horizon of 100
years is used in the Kyoto Protocol, yet such a long time horizon might underestimate the importance of
short-lived emissions. While GWP is widely accepted as a reliable proxy for the warming impacts of
long-lived, well-mixed gases such as CO2, GWP with a 100-year time frame may not be suitable for
measuring the kind of short-lived non- CO2 emissions associated with aviation.
Global Temperature Change Potential (GTP) goes further than the metrics described above. It
estimates the change in global mean temperature for a selected year in the future. This metric is more
complex because it calculates climate response and not just radiative forcing (see Figure 9). Although
uncertainty is increased, relevance is also increased since it is more useful to know what the actual
temperature change will be than just to know the amount of energy that was added to the system.
GTP excludes effects from past air travel and calculates future warming from current air travel.
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GTP could therefore be an appropriate metric for our purposes. Yet, as with integrated RFI, the results
of GTP vary greatly depending on the time frame and if a pulse emission or sustained emissions are
used (see further discussion below).
Integrated Change in Temperature over Time expresses the climate impacts as a theoretical number
that is the sum of all the temperature changes that occur over a given period of time. The FAA/APMT
model (described in section 4.6) can also be used to calculate such a metric, expressed in integrated-
delta T-years (shown in Figure 8a). Integrated Change in Temperature over Time could therefore be an
appropriate metric for our purposes. Yet, as with integrated RF, the results if this metric will vary
greatly depending on the time frame and if a pulse emission or sustained emissions are used (see further
discussion below).
Economic Cost Calculations go further than all the metrics discussed above: they calculate climate
costs and not just radiative forcing (see Figure 1). As mentioned above, assumptions that need to be
determined by moral or political positions lie hidden in the economic assessment of the damages (e.g.
the discount rate). This means that climate cost calculations are more complicated and their results more
dependent on value-based decisions than simple radiative forcing calculations. Despite their
shortcomings, economic models are important because they translate climate change into the currency
that is most pertinent to policy makers and businesses: the monetary costs associated with expected
climate effects. Yet economic cost calculations go beyond our purpose. A metric that compares the
different forcings or climate responses is more appropriate for our task because it is more compatible
with metrics that are used in other climate policy measures (such as the Global Warming Potential with
a 100-year time frame used under the Kyoto Protocol).
5.2 Application of Metrics for Current Air Travel
We have established that, of the examined metrics, RF and RFI are not suitable for estimating the
contribution to climate change of individual current air travel. We now discuss why value-based
decisions impact the results even if more appropriate metrics such as integrated RF or Global
Temperature Change Potential (GTP) are used. Aside from the scientific uncertainties related to certain
warming effects from aviation (e.g. cirrus clouds, see error bars in Figure 10) there are two value-
related choices that greatly influence the results: choice of time frame and choice of pulse versus
sustained emissions.
Figure 10 shows three different metrics: Pulse Global Warming Potential (PGWP), Pulse Global
Temperature Potential (PGTP) and Sustained Global Temperature Change Potential (SGTP). The
impacts have been normalized to CO2. In other words, the impacts of CO2 have been assigned the value
of 1 (similar to Global Warming Potential). The total aviation impacts are expressed as multiples of the
impacts of CO2 emissions alone. For example, the first red bar shows that over a 20-year time horizon,
the total impact of aviation, using PGWP, is four times as much as that of CO2 alone. In general, the
graph shows that at the 20-year time horizon (red bars), the effects of short-lived emissions dominate in
all three metrics. At longer time horizons (orange: 50 years; yellow: 100 years), CO2 effects become
increasingly dominant, especially using the PGTP. Depending on the metric and the time frame chosen,
total climate response to aviation is shown to be anywhere from slightly more than that of CO2 alone to
up to 6 times that of CO2 alone.
Figure 10 includes the effects from aviation-induced cirrus clouds. These have a particularly large
impact at shorter time horizons (Grassl and Brockhagen, 2007). As mentioned earlier, there is still quite
a bit of scientific uncertainty surrounding cirrus clouds and their warming effects, and more research is
needed to assess impacts more accurately (Burkhardt et al., 2008). Because of these uncertainties, the
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error bars in the 20-year time horizon are very large. Error bars for the longer time horizons are much
smaller because the effects of cirrus clouds are short-lived and no longer appear after 50 or 100 years.
The multipliers (normalized emission weighing factors) that Forster and Rogers (2008) calculate for
non-CO2 aviation emissions range between 1 and 6, depending on the time frame and metric used.
Using a time frame of 20 years and including cirrus effects, multipliers range from 2 to 6. Appendix 2
shows the complete graph from their paper.
Figure 10: Normalized Impacts of Total Warming Effects From
Aviation Compared to CO2 Alone.
Total aviation impact has been normalized to CO2 impact, creating an
emission weighting factor appropriate to the current fleet. Error bars
represent uncertainties arising from NOx and contrail forcings.
PGWP: Pulse Global Warming Potential
PGTP: Pulse Global Temperature Potential
SGTP: Sustained Global Temperature Change Potential
Red (Left Bar): 20-year time horizon
Orange (Middle Bar): 50-year time horizon
Yellow (Right Bar): 100-year time horizon
(Source: Forster and Rogers, 2008)
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5.3 Recommendations
There is no single metric, no single multiplier and no single answer to the question of how the effect on
climate change from air travel should be calculated so that an individual or a company can accurately
calculate the climate footprint of their current air travel. Metrics and underlying assumptions have to be
chosen according to the questions we are trying to answer and the goals we are trying to achieve
(Fuglestvedt et al., 2009). For example, if the main concern is the near-term impacts of climate change,
a shorter time horizon is more appropriate. Nevertheless, we would like to make the following final
observations and recommendations:
The Science:
There is still uncertainty related to quantifications of the climate impacts of non-CO2 air travel
emissions. Clearly, more research and more sophisticated models38 are needed39
. Although there is no
simple answer to what the overall impact of aviation is, it is clear that total contribution to climate
change is greater than that of CO2 alone.
It seems therefore less defensible to exclude non-CO2 effects than to choose a multiplier that is
greater than 1.
Time Frame:
As we have illustrated, the chosen time frame greatly influences the results. For example, if we choose
temperature change after 100 years for the evaluation, the effects of short-lived GHGs are de-
emphasized, and changes of temperature in between the time of emission and the evaluation year are
not captured (Fuglestvedt et al., 2008). Yet including these short-lived regional impacts into a climate
metric is important because they might trigger feedback mechanisms (Berntsen and Fuglestvedt, 2008).
For example, researchers have recently found that short-lived emissions in the Arctic result in an equal
or greater climatic response than long-lived emissions due to the positive feedback mechanisms
associated with ice albedo.. Reducing these short-lived but high impact non-CO2 emissions in the
critical near-term may be more effective in slowing Arctic warming and preventing a “tipping point”
for ice disintegration than emphasizing long-term efforts to reduce long-lived GHGs such as CO2
(Quinn et al., 2008).
For these reasons, we advocate a short time horizon (e.g. 20 years) that includes short-lived effects be
used. (This is a value-based choice and only applies to calculating effect on climate change from air
travel in order to best estimate the footprint of an individual or a company due to their current air
travel, see discussion at the end of this section.)
The Climate Challenge:
It is becoming increasingly clear that climate change is happening faster than was expected (e.g. loss of
Arctic sea ice, see e.g. Shepherd and Wingham, 2007) and triggering positive feedbacks (e.g. methane
emissions in Siberia, see e.g. UNEP, 2007) that may lead to unprecedented and possibly irreversible
38 E.g. Forster and Rogers (2008) state: Impacts of short-lived species depends on location (altitude and
geography), season, time of day, and background conditions such as temperature, chemistry and weather yet none
of the metrics take into account regional forcings and their effects on the climate.
39 For more on this topic, see the ACCRI report, “A Report on the Way Forward Based on the Review of Research
Gaps and Priorities,” available at http://tinyurl.com/4zuwhg
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changes. At the same time, anthropogenic emissions are growing faster than was predicted by even the
highest IPCC emissions scenario (Raupach et al., 2007). It is therefore no exaggeration to say that we
are facing a climate emergency. Addressing this emergency will require changes on a scale we have
never undertaken as a human society.
Given the urgency of the climate change challenge, it is an ethical imperative to proceed following
the precautionary principle and include all warming effects to the best of our knowledge.
Equity:
The wealthy are disproportionately responsible for air travel, yet the impacts of climate change will be
felt disproportionally by the poor (Grassl and Brockhagen, 2007).
We believe that an ethical argument can be made that the effects of aviation should be accounted for
to their fullest extent, so that mitigation policies and offset options are based on fully internalized
climate costs of aviation.
Multipliers or any other type of metric that tries to express the full climate impacts of aviation have to
be chosen carefully depending on their specific intended purpose. Our recommendation is specifically
intended for calculating the non-CO2 portion of the climate footprint resulting from an individual’s or a
company’s air travel. It is NOT a general recommendation for calculating the impacts of all emissions
from air travel. For example, certain aviation policy choices might lead to a decrease of short-lived
GHGs but an increase in fuel consumption and therefore (long-lived) CO2 emissions. In this case, a long
time frame would need to be used to evaluate the most climate-friendly policy, because long-term
climate effects would likely outweigh short-term benefits from reducing shorter-lived GHGs. In this
example, one policy option is being weighed against another. But for our purposes of calculating total
climate footprint, CO2 effects are already accounted for and the question we are answering is: how
much should we add (expressed as a multiplier) to account for non-CO2 effects?
For all of the reasons elaborated above, we advocate that a multiplier of at least 2 be used for air
travel emissions calculators40 to account for non-CO2 warming effects41
.
We emphasize that our recommendation is not solely based on scientific arguments, but on ethical ones
as well. It is based on our best understanding of the current knowledge of aviation emissions in
particular and climate science in general. As the science progresses, the models become more
sophisticated, and the ethical and political debates on climate change develop in the coming years, our
recommendation should be revisited and refined.
40 Coincidentally, the RFI figure of 2.7 frequently used and cited in air emissions calculators fits with our own
recommendation of a multiplier of at least two. Although the numeric figures happen to be very similar, they are
based on different metrics. We can therefore say that the results of calculators that do use the RFI figure of 2.7 are
not necessarily wrong, despite the fact that they are based on an inappropriate choice of metric.
41 An exception to this might be short-haul flights. Many non-CO2 climate change effects (such as NOx catalysis
and contrail/cirrus formation) tend to take effect when aircraft cruise in the upper troposphere/lower stratosphere.
Short-haul flights either spend a small portion of their overall air time in the UT/LS, or none at all (in the case of
turboprop short-haul aircraft). This could imply that it would be inappropriate to assign the full emissions
multiplier to these flights. It would be interesting to elaborate on this topic, which goes beyond this paper. We
welcome suggestions and comments: please contact us at anja@sei-us.org.
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Carbon Offsetting & Air Travel Part 2: Non-CO2 Emissions Calculations
40
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Appendix 1
Simplified Mathematical Background for the FAA/APMT Model
The RFI attempts to answer the question, “Given the gases currently present in the atmosphere, what is
the current impact on the Earth’s radiative energy balance?” It is an important question to answer in
order to understand climate, but is not as useful for addressing economic concerns or for comparing the
non-CO2 effects of aviation to the CO2 emissions caused by air travel. In contrast, the FAA/APMT asks,
“If someone travels today, what is his or her total impact on the Earth’s climate, considering both short-
term and long-term effects?” Thus FAA/APMT is forward-looking, while RFI is backward-looking.
The question that the FAA/APMT seeks to answer is better suited for economic analysis.
Other than the question of whether future or past cumulative impacts are being assessed, the
calculations underlying the FAA/APMT approach are very similar to those that lie behind the RFI. Yet
they differ in that the FAA/APMT model allows us to calculate future damages:
To understand the FAA/APMT approach, suppose that during year zero (t = 0), 1 kg of CO2 is emitted.
Then over time the atmospheric concentration of CO2 due to that 1 kg of emissions will change in a way
that can be predicted. Call the time-dependence of the atmospheric concentration GC(t). Then the
change in the concentration of CO2 ΔC(t) from that 1 kg over time is:
)()( tGtC C
=
.
In reality there will not just be 1 kg emitted at one time. Instead, there will be a series of emissions, one
in each year, and the effects will add up. That means the emissions have to be added up. If the
emissions over time are denoted by Q(t), then:
=
t
C
dtttGtQtC
0
')'()'()(
.
If the emissions are known, and the link between emissions and atmospheric concentration over time is
known, then the change in atmospheric concentration from those emissions can be calculated. This can
then be used to calculate the radiative forcing RF(t) , since radiative forcing depends on the atmospheric
concentration. This is a way to calculate a RF which is forward-looking. It differs from the RF which
was used in the IPCC report to calculate the RFI, which takes into account cumulative emissions but
does not take into account future effects. (Again, this is relevant only for long-lived gases because
short-lived gases will not accumulate over time).
.
The change in temperature from radiative forcing at a specific time can be delayed. For this reason,
there is not a direct connection between RF(t) and the change in temperature. Instead, it follows a
relationship much like the relationship between emissions and concentration:
=
t
T
dtttGtRFtT
0
')'()'()(
.
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These are the basic equations that lie behind the FAA/APMT approach. In order to calculate them, they
require an understanding of how the carbon cycle responds to carbon emissions (captured by GC(t)), and
an understanding of how the climate system responds to a change in radiative forcing (captured by
GT(t)). A nice feature of this approach is that it can take into account the uncertainties in those
connections by varying GC(t) and GT(t) over the range of possibilities, multiplied by the probability that
they could have one value or another.
In order to draw economic conclusions from a change in climate, it is necessary to link the change in
temperature to potential damages via a damage function. While acknowledging the difficulty of
constructing such a function, the authors of the FAA/APMT model chose the damage function of
Nordhaus and Boyer (2002), which has the form:
2
1900,21900,1 )()()( tTatTatD kkk +=
.
In this equation, Dk(t) is the percent change in GDP, k represents a region, and ΔT1900(t) is the change in
temperature since 1900 in Kelvin. To estimate the global average impact, use a1 = -0.0045 and a2 =
0.0035. In order to estimate the marginal damage from a particular effect, the damage from all
anthropogenic effects except the effect of interest is subtracted from the total damage from all
anthropogenic effects. (This roundabout approach is necessary because the damage function does not
change linearly with changes in temperature. It is also required for background CO2 emissions since the
marginal RF of CO2 depends on the background concentration of CO2 as shown in the logarithmic
relationship.) That is,
Damage[effecti] = Damage[all anthropogenic effects] Damage[all anthropogenic effects effecti].
Finally, the costs from damages are discounted over time at a particular discount rate r to calculate the
net present value (NPV) of the climate impact, using the standard financial formula
=+
=T
t
t
r
tD
TNPV
0)1(
)(
)(
,
where t runs over all of the years from the initial year zero to year T and ΔD(t) is the marginal damage
from the effect of interest.
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Appendix 2
Figure 9 from Forster and Rogers, 2008, p 35
Total aviation impact has been normalized to CO2 impact, creating an emission weighting factor
appropriate to the current fleet. Error bars present uncertainties arising from NOx and contrail forcings.
Top: Excluding the highly uncertain aviation-induced cirrus (AIC).
Middle: Including AIC.
Bottom: Excluding AIC, and assuming an efficacy of 0.6 for contrail forcing. Note that the scale on the
y-axes varies between frames. (Source: Forster and Rogers, 2008)
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