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Differences between Carbon Budget Estimates Unravelled

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Several methods exist to estimate the cumulative carbon emissions that would keep global warming to below a given temperature limit. Here we review estimates reported by the IPCC and the recent literature, and discuss the reasons underlying their differences. The most scientifically robust number-the carbon budget for CO2 -induced warming only-is also the least relevant for real-world policy. Including all greenhouse gases and using methods based on scenarios that avoid instead of exceed a given temperature limit results in lower carbon budgets. For a >66% chance of limiting warming below the internationally agreed temperature limit of 2 °C relative to pre-industrial levels, the most appropriate carbon budget estimate is 590-1,240 GtCO2 from 2015 onwards. Variations within this range depend on the probability of staying below 2 °C and on end-of-century non-CO2 warming. Current CO2 emissions are about 40 GtCO2 yr -1, and global CO2 emissions thus have to be reduced urgently to keep within a 2 °C-compatible budget.
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NATURE CLIMATE CHANGE | VOL 6 | MARCH 2016 | www.nature.com/natureclimatechange 245
T
he ultimate objective of international climate negotiations is
to prevent dangerous anthropogenic interference with the cli-
mate system
1
. At the 2015 Paris Conference, this objective was
further specied as limiting global-mean temperature increase to
well below 2 °C relative to pre-industrial levels and pursuing further
eorts for limiting temperature increase to below 1.5 °C (ref. 2).
Over the past decade, a large body of literature has been published
that shows that the maximum global-mean temperature increase as
a result of CO
2
emissions is nearly linearly proportional to the total
cumulative carbon (CO
2
) emissions
3–11
. Maximum warming is also
inuenced by the amount of non-CO
2
forcing leading up to the time
of the peak
12–14
. is has culminated in the most recent assessment
of the IPCC in the form of several estimates of emission budgets
compatible with limiting warming to below specic temperature
limits. Here, we rst explain the underlying scientic rationale
for such budgets and then continue with a detailed account of the
strengths and limitations of the various budgets reported in both the
IPCC Fih Assessment Report (AR5) and the recent literature, and
of the dierences between them.
The purpose of budgets
e IPCC AR5 Working Group I (WGI) report
15
indicated that the
total net cumulative emission of anthropogenic CO
2
is the principal
driver of long-term warming since pre-industrial times. erefore,
to limit the warming caused by CO
2
emissions to below a given tem-
perature threshold, cumulative CO
2
emissions from all anthropo-
genic sources need to be capped to a specic amount, sometimes
referred to as the carbon budget or quota (which, in the context
of this Perspective, refers to global values and not to the emission
allowances of single countries).
Dierences between carbon budget
estimates unravelled
Joeri Rogelj
1,2
*, Michiel Schaeer
3,4
, Pierre Friedlingstein
5
, Nathan P. Gillett
6
, Detlef P. van Vuuren
7,8
,
Keywan Riahi
1,9
, Myles Allen
10,11
and Reto Knutti
2
Several methods exist to estimate the cumulative carbon emissions that would keep global warming to below a given temperature
limit. Here we review estimates reported by the IPCC and the recent literature, and discuss the reasons underlying their dier-
ences. The most scientifically robust number — the carbon budget for CO
2
-induced warming only — is also the least relevant
for real-world policy. Including all greenhouse gases and using methods based on scenarios that avoid instead of exceed a given
temperature limit results in lower carbon budgets. For a >66% chance of limiting warming below the internationally agreed
temperature limit of 2°C relative to pre-industrial levels, the most appropriate carbon budget estimate is 590–1,240GtCO
2
from 2015 onwards. Variations within this range depend on the probability of staying below 2°C and on end-of-century non-CO
2
warming. Current CO
2
emissions are about 40GtCO
2
yr
–1
, and global CO
2
emissions thus have to be reduced urgently to keep
within a 2°C-compatible budget.
e near-linearity between peak global-mean temperature rise
and cumulative CO
2
emissions is the result of an incidental interplay
of several compensating feedback processes in both the carbon cycle
and the climate: the logarithmic relationship between atmospheric
CO
2
concentrations and radiative forcing, the decline of ocean heat-
uptake eciency over time, as well as the changes in the airborne
fraction of anthropogenic CO
2
emissions
15
. is compensating rela-
tionship is robust over a range of CO
2
emissions and over timescales
of up to a few centuries, with very few exceptions
16
. Such a relation-
ship is not generally shown for other anthropogenic radiatively
active species. An approximate proportionality exists for other long-
lived greenhouse gases (GHGs) for warming during this century
12
,
whereas for short-lived climate forcers the rate of emissions leading
up to the time of peak warming is important
12–14
.
e unique characteristics of the Earth systems response to
anthropogenic carbon emissions allow the denition of a quantity
called the transient climate response to cumulative emissions of
carbon (TCRE). TCRE is dened as global average surface tempera-
ture change per unit of total cumulative anthropogenic CO
2
emis-
sions, typically 1,000PgC. In AR5, TCRE was assessed to be ‘likely’
to lie (that is, with greater than 66% probability
17
) between 0.8 to
2.5°C per 1,000PgC for cumulative CO
2
emissions less than about
2,000PgC and until the time at which temperature peaks.
e constancy of TCRE means that it can also be assessed for the
real world by dividing an estimate of CO
2
-induced warming to date
by an estimate of anthropogenic CO
2
emissions
5,10
. Such an approach
relies on a calculation of GHG-attributable warming using a regres-
sion of observed warming onto the simulated response to GHGs and
other forcings, and an estimate of the ratio of CO
2
to total GHG radi-
ative forcing or temperature response. Alternatively TCRE may be
1
ENE Program, International Institute for Applied Systems Analysis (IIASA) Schlossplatz 1, A-2361 Laxenburg, Austria.
2
Institute for Atmospheric and
Climate Science, ETH Zurich, Universitätstrasse 16, CH-8092 Zürich, Switzerland.
3
Climate Analytics, Karl-Liebknechtstrasse 5, 10178 Berlin, Germany.
4
Environmental Systems Analysis Group, Wageningen University and Research Centre, PO Box47, 6700AA Wageningen, the Netherlands.
5
College
of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, UK.
6
Canadian Centre for Climate Modelling and Analysis,
Environment Canada, University of Victoria, PO Box1700, STN CSC, Victoria, British Columbia V8W 2Y2, Canada.
7
PBL Netherlands Environmental
Assessment Agency, PO Box303, 3720AH Bilthoven, the Netherlands.
8
Copernicus Institute of Sustainable Development, Faculty of Geosciences,
Utrecht University, Budapestlaan 4, 3584CD Utrecht, the Netherlands.
9
Graz University of Technology, Ineldgasse, A-8010 Graz, Austria.
.10
ECI,
School of Geography and the Environment, University of Oxford, Oxford OX1 3QY, UK.
11
Department of Physics, University of Oxford, Parks Road,
Oxford OX1 3PU, UK. *e-mail: rogelj@iiasa.ac.at
PERSPECTIVE
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assessed from observations by applying observational constraints to
the parameters of a simple carbon-cycle climate model
7,8
, and evalu-
ating the ratio of warming to emissions for the constrained model.
For a carbon budget approach to make sense, TCRE must be
reasonably independent of the pathway of emissions. Earlier studies
have indeed shown that this is the case
7,8,18,19
, at least for peak warm-
ing and monotonously increasing cumulative carbon emissions. If a
set carbon budget limit is exceeded, CO
2
needs to be actively removed
from the atmosphere aerwards
20–22
to bring emissions back to
within the budget. Figure1 illustrates this path independency (even
for moderate amounts of net negative CO
2
emissions), and shows
with the simple carbon cycle and climate model MAGICC
7,23,24
that
even with large variations in the pathway of CO
2
emissions during
the twenty-rst century, the transient temperature paths as a func-
tion of cumulative CO
2
emissions are very similar — a characteristic
also found in other models
18,25
. Once all pathways achieve the same
end-of-century cumulative CO
2
emissions, the temperature projec-
tions are virtually identical (Fig.1).
Given these considerations, carbon budgets are a useful guide for
dening and characterizing the emissions pathways that limit warm-
ing to certain levels, such as 2°C relative to pre-industrial levels.
An abundance of carbon budgets
Despite the simplicity of carbon budgets, many (oen very dierent)
estimates have been published. Here we provide an overview of how
these budgets are dened and calculated.
Budget for CO
2
-induced warming only. e most direct application
of TCRE is to derive cumulative carbon budgets consistent with lim-
iting CO
2
-induced warming to below a specic temperature thresh-
old. For instance, WGI indicates
26
that limiting anthropogenic
CO
2
-induced warming to below 2 °C relative to 1861–1880 with
an assessed probability of greater than 50% will require cumulative
CO
2
emissions from all anthropogenic sources since that period to
stay approximately below 4,440GtCO
2
. Alternatively, doing so with
a greater than 66% probability would imply a 3,670GtCO
2
budget.
ese values assume a normal distribution of which the standard
deviation (1σ) range is given by the assessed likely TCRE range of
0.8to 2.5°C per 1,000PgC (that is, about 3,670GtCO
2
), and make
use of the near-linearity of the ratio of CO
2
-induced warming to
cumulative CO
2
emissions
15
.
Although this is the most robust translation of the TCRE concept
into a cumulative carbon budget, it is at the same time also the least
directly useful to policy-making. In the real world, non-CO
2
forcing
also plays a role, and its global-mean temperature eect is superim-
posed on the CO
2
-induced warming. A carbon budget derived from
a TCRE-based estimate should thus not be used in isolation.
e near-linear relationship of TCRE does hence not necessarily
apply to the ratio of total human-induced warming to cumulative
carbon emissions (as might be suggested by Fig. SPM.10in ref.26).
e latter relationship is scenario dependent, because, for example,
the percentage contribution of non-CO
2
climate drivers to total
anthropogenic warming increases in the future in many scenarios.
erefore, to take into account the inuence of non-CO
2
forcing on
carbon budgets, the TCRE-based approach can be extended using
multi-gas emission scenarios. Multi-gas emission scenarios pro-
vide an internally consistent evolution over time of all radiatively
active species of anthropogenic origin. ey are oen created with
integrated assessment models (IAMs), which represent interactions
within the global energy–economy–land system (for examples, see
refs27–29).
reshold exceedance budgets. Here we dene a straightforward
methodology of extending TCRE-based carbon budgets for CO
2
-
induced warming to budgets that also takes into account non-CO
2
warming as ‘threshold exceedance budgets’ (TEBs) for multi-gas
warming (Table1).
is approach uses multiple realizations of the simulated response
to a multi-gas emission scenario. ese realizations can either be
multi-model ensembles or perturbed parameter ensembles. An
example of the former would be simulations of the Representative
Concentration Pathways
30,31
(RCPs) by Earth system models (ESMs)
that were contributed to the Fih Phase of the Coupled Model
Intercomparison Project
32
(CMIP5). An example of the latter would
be the use of a simple climate model in a probabilistic setup
7,23,24
, as
used in the assessments of the IPCC
33–35
as well as in other recent
studies
36–38
. From such multi-model or perturbed parameter ensem-
bles, the carbon budget is estimated at the time a specied share
(for example, 50% or one-third) of realizations exceeds a given tem-
perature limit (that is, 50% or two-thirds of the ensemble members
remain below the limit; see orange scenario in Fig.2).
e TEB approach was used by WGI for determining carbon
budgets that account for non-CO
2
forcing
15
. Applying this meth-
odology to the CMIP5 RCP8.5 (ref. 39) simulations of ESMs
10,40
and ESMs of intermediate complexity
41
(EMICs), they found that
compatible CO
2
emissions since 1870 are about 3,010GtCO
2
and
2,900GtCO
2
to limit warming to less than 2°C since the period
1861–1880 in more than 50% and 66% of the available model runs,
respectively. Other recent studies
36
have used an extended version
of this approach that computes TEBs based on perturbed param-
eter ensembles of a subset of scenarios from the IPCC AR5 Scenario
Database (hosted at the International Institute for Applied Systems
Analysis (IIASA); https://secure.iiasa.ac.at/web-apps/ene/AR5DB).
2000 2020 2040 2060 2080 2100
0
2
4
6
8
10
12
Year
Carbon emissions from fossil fuel
combustion and industry (PgC yr
−1
)
2000 2020 2040 2060 2080 2100
0.8
1
1.2
1.4
1.6
1.8
2
2.2
Year
Global mean temperature
increase relative to 1850
−1875 (°C)
a
b
Figure 1 | Proportionality of global-mean temperature increase to
cumulative emissions of CO
2
. a,b, Four CO
2
emission pathways with
identical cumulative carbon emissions over the twenty-first century (a) and
their corresponding temperature projections (b). The grey area in b shows
the central 66% uncertainty range of temperature projections around the
thick purple line. Figure adapted with permission from ref.15, © 2013 IPCC.
PERSPECTIVE
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e results of a TEB approach are most useful if the warming
due to non-CO
2
forcing as a function of cumulative CO
2
emissions
is similar across scenarios, meaning that the conclusions are not
strongly dependent on the scenario chosen. However, Fig.3a shows
that there is quite a large variation in non-CO
2
forcing for a given
level of cumulative CO
2
emissions when looking at all scenarios
available in the IPCC AR5 Scenario Database. Caution is therefore
advised when deriving carbon budgets on the basis of one single
multi-gas scenario (see below). Finally, the use of TEBs for limiting
warming to below a given temperature limit assumes that non-CO
2
warming never increases beyond the level it reached at the time the
TEB was computed (Fig.2). Non-CO
2
forcing thus needs to be kept
within limits over time.
reshold avoidance budgets. Carbon budgets dened in the pre-
vious section are derived at the time a given scenario exceeds a spe-
cic temperature threshold or limit. A complementary approach is
to consider multiple emission scenarios and evaluate carbon budg-
ets for the subset of scenarios that avoids crossing such a threshold
with a given probability. We name these budgets threshold avoid-
ance budgets (TABs, Table1). Because, by denition, such scenarios
do not exceed the limit of interest at any specic point in time (with
a given probability), a time horizon needs to be dened up to which
a budget is computed. is time horizon can either be a predened
period, for example the 2011–2050 or the 2011–2100 period, or
more variable in nature, for example the time period until peak
warming (see yellow scenario in Fig.2). Both of these approaches
were used in AR5, and more sophisticated approaches based on the
TAB methodology have been used in the literature
7
.
IPCC Working Group III (WGIII) computed TABs for the
periods 2011–2050 and 2011–2100 by assessing probabilistic
temperature projections in 2100
34,35
. For this, WGIII categorized
a large number of scenarios on the basis of end-of-century CO
2
-
equivalent concentrations. e reported TAB values — for example,
in Table6.3 in the WGIII Report
35
or Table SPM.1 in the Synthesis
Report
33,34
(SYR) — are therefore the result of an assessment of
the exceedance probability outcomes found in each of the CO
2
-
equivalent concentration categories. Alternatively, scenarios could
have been categorized on the basis of median temperature, prob-
abilities to limit warming to below a specic temperature limit,
or even carbon budgets. For scenarios that limit end-of-century
warming to below 2°C with a likely probability, the WGIII assess-
ment
34
reports that the TABs in terms of cumulative CO
2
emissions
in the periods 2011–2050and 2011–2100are 150–1,300GtCO
2
and
630–1,180GtCO
2
, respectively.
In the IPCC SYR
33
, TABs are also computed on the basis of
the scenarios available in the IPCC AR5 Scenario Database — see
Table2.2in ref.33. However, the SYR categorizes scenarios directly
based on their probability of keeping peak warming to below a
specic temperature threshold (1.5 °C, 2 °C or 3 °C) during the
twenty-rst century. For example, the IPCC SYR reports TABs
for limiting warming to below 2 °C with at least 66% chance of
2,550–3,150GtCO
2
from 1870 until peak warming.
The numbers compared
To understand what the dierent approaches mean in terms of the
actual values of carbon budgets, we compare the available budg-
ets relating to the 2°C limit. Table2 provides an overview for all
of the numbers discussed in this section, relative to two com-
mon base years (2011 and 2015). Taking into account that about
2,050GtCO
2
(approximately 560PgC) had already been emitted by
the end of 2014
36
, a CO
2
-only budget approach would indicate that
1,620 GtCO
2
(or 440PgC) remain to have a >66% probability of
limiting warming to below 2°C relative to pre-industrial levels (here
dened as the 1861–1880 period
26
). Using a TEB approach and
assuming non-CO
2
forcing as in RCP8.5, this amount is reduced to
850GtCO
2
(or 230PgC). When assessed with the latter approach, a
1,620GtCO
2
budget would limit warming to below 2°C in less than
33% of the available models
42
.
It is worth noting that the IPCC assessment of the CO
2
-only
budget is based on an assessed uncertainty range of TCRE, drawing
on many lines of evidence. e WGI numbers including non-CO
2
forcing are based on CMIP5 simulations of the response to RCPs,
which — although being a valid approach — provide a narrower
scientic basis. At least for the four RCPs used by WGI, a similar
warming as a function of cumulative CO
2
emissions is found (see
Fig. TFE.8in ref.42), despite having dierent non-CO
2
evolutions
(Fig.3a). is counterintuitive result is explained further below.
When extensively varying the non-CO
2
assumptions for TEBs
using a subset of baseline and weak mitigation scenarios from the
IPCC AR5 Scenario Database (which all exceed the 2°C limit), a
range of 850–1,550GtCO
2
(5th–95th percentile range across all TEB
scenarios, from 2015 onwards) is associated with limiting warming
to below 2°C with 66% probability
36
. e dierence between this
range and the 850GtCO
2
number quoted above is, on the one hand,
caused by the dierent modelling frameworks and, on the other
hand, by the fact that the non-CO
2
forcing evolution of RCP8.5is
situated amongst the highest percentiles of the non-CO
2
forcing in
other high-emission scenarios that exceed the 2°C threshold (Fig.3).
When considering TABs until peak warming, based on the strin-
gent mitigation scenarios of the IPCC AR5 Scenario Database, a
range of 590–1,240GtCO
2
is found for limiting warming to below
2 °C with >66% probability
33
(10th–90th percentile range, as
reported by WGIII, from 2015 onwards). Finally, for TABs calcu-
lated over the 2015–2100 period, an assessment of the stringent mit-
igation scenarios available in the IPCC AR5 Scenario Database and
their temperature outcomes results in a range of 470–1,020GtCO
2
(10th–90th percentile range) for limiting warming to below 2 °C
with a likely chance
35
.
In conclusion, moving from a CO
2
-only budget
42
to a multi-gas
multi-scenario TEB budget
36
removes around 420GtCO
2
(that is,
the average of the 70–770GtCO
2
range) from the CO
2
budget from
Table 1 | Three dierent types of carbon budgets and their definitions.
Carbon budget type Abbreviation Definition and description
Budget for CO
2
-induced
warming
CO
2
-only budget Amount of cumulative carbon emissions that are compatible with limiting warming to below a specific
temperature threshold with a given probability in the hypothetical case that CO
2
is the only source of
anthropogenic radiative forcing. This budget can be inferred from the assessed range of TCRE.
Threshold exceedance
budget
TEB Amount of cumulative carbon emissions at the time a specific temperature threshold is exceeded with a given
probability in a particular multi-gas emission scenarios. This budget thus takes into account the impact of
non-CO
2
warming at the time of exceeding the threshold of interest.
Threshold
avoidance budget
TAB Amount of cumulative carbon emissions over a given time period of a multi-gas emission scenario that limits
global-mean temperature increase to below a specific threshold with a given probability. This budget thus takes
into account the impact of non-CO
2
warming at peak global-mean warming, which is approximately the time
when global CO
2
emissions become zero and global-mean temperature is stabilized.
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2015 onward for limiting warming to below 2°C with 66% chance.
Subsequently moving to a TAB budget until peak warming
33
or
over the 2015–2100 period
35
and a >66% chance would also remove
about 260–310GtCO
2
and 380–530GtCO
2
, respectively. (Note that
these values are illustrative as they are obtained by comparing ranges
that are dened in dierent ways.)
e TAB range for limiting warming to below 2°C with greater
than 66% probability of 470–1,020GtCO
2
for the 2015–2100 period
is thus 35 to 70% below what would have been inferred from a CO
2
-
only budget with a TEB approach.
Strengths and limitations
e various approaches to computing carbon budgets each come
with their respective strengths and limitations. Understanding what
can lead to possible dierences in budget estimates is critical to
avoid misinterpretation of the numbers.
e budget type denition, the underlying data and modelling,
the scenario selection, temperature response timescales and the
accompanying pathway of CO
2
and non-CO
2
emissions are identi-
ed as possible key drivers of the dierence between the various
budget options discussed above.
at the budget type denition will have an inuence on the
resulting numbers is almost trivial. For example, when dening
TABs from 2011 to 2100 instead of until peak warming, the cumu-
lated net negative emissions that can be achieved until the end of
the century will lead to consistently lower 2015–2100 TABs com-
pared with TABs dened until peak warming levels. Negative emis-
sions occur when CO
2
is actively removed from, instead of emitted
into, the atmosphere by human activities. For instance, for TABs
compatible with limiting warming to below 2°C with >66% chance,
the dierence between TABs dened until peak warming and over
the 2015–2100 period would be of the order of 120–220GtCO
2
.
Furthermore, the budget type denition also inuences other fac-
tors, such as scenario selection, whose impact on the carbon budget
is explained in more detail below.
Underlying data and modelling. Some of the dierences between
the quantitative budgets estimates are simply driven by dierences in
the underlying data and models. In general, these dierences apply
to TEBs and TABs alike. For example, although the WGI CO
2
-only
budget is based on the interpretation of an assessed uncertainty
range, the other TEB and TAB budgets were computed either from
CMIP5 RCP results (in the WGI report and the SYR) or from a sim-
ple climate model (MAGICC) in a probabilistic setup
7,23,24
(in the
WGIII report and the SYR).
Budget estimates can dier depending on whether a single-sce-
nario multi-model ensemble is used (for example, all CMIP5 runs
for RCP8.5) or alternatively a single-model multi-scenario perturbed
parameter ensemble is used (for example, the IPCC AR5 WGIII
approach, which uses MAGICC). e former approach allows us to
use information from a wide range of the most sophisticated mod-
els and incorporate state-of-the-art Earth system interactions in the
budget assessment. However, this approach comes at a high compu-
tational cost, resulting in only a limited ensemble of opportunity of
model runs being available for any assessment. e latter method,
on the other hand, uses a much simpler model, and hence comes
with great computational eciency, which allows for hundreds if not
thousands of realizations per scenario. us variations in scenario
assumptions on the pathways and evolution of non-CO
2
forcing over
time can be explored in more detail.
ese dierences in the underlying data and modelling can result
in changes in the budget estimates. However, although a simple climate
Global methane emissions
(TgCH
4
yr
−1
)
0
1
2
3
Temperature increase relative
to pre-industrial levels (°C)
Threshold
Timing of
peak warming
Timing of
exceeding threshold
1950 2000 2050 2100
0
200
400
600
800
1,000
1950 2000 2050 2100
Global carbon emissions
(PgC yr
−1
)
1950 2000 2050 2100
0
10
20
30
CO
2
emissions
CH
4
emissions
2
2
Dierent carbon budgets
Threshold exceedance budget (TEB)
Threshold avoidance budget (TAB)
(until peak warming)
3
1
1
2
Varying non-CO
2
emissions
Figure 2 | An illustration of the methods for computing TEBs versus TABs. In the first step (arrows labelled 1), temperature outcomes are computed
from multi-gas emission scenarios that either exceed (orange) or avoid (yellow) a given temperature threshold. Based on either the timing of exceeding
the chosen threshold or the timing of peak warming, carbon budgets compatible with the chosen temperature threshold are computed in the second step
(arrow labelled 2) by summing the carbon emissions of the underlying scenarios until the timing of exceeding the threshold or peak warming for the TEB
or TAB (arrow labelled 3), respectively.
PERSPECTIVE
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model does not provide the detail of ESMs, it can closely emulate
their global-mean behaviour
43
and can represent the uncertainties
in carbon-cycle and climate response in line with the assessment of
AR5
7,24,44
. Of importance here is that the MAGICC setup applied in
WGIII and the SYR is consistent with the CMIP5 ensemble for tem-
perature projections and TCRE (Fig.12.8in ref.15 and Fig.6.12in
ref.35). It is therefore expected that these dierences are limited.
A nal aspect related to the data and modelling is the interpreta-
tion of the nature of the uncertainties that accompany the various
data. Uncertainty ranges can be the expression of a variety of under-
lying uncertainty sources
45
, and they can be interpreted in dierent
ways. In the context of the quantication of carbon budgets, at least
three kinds of uncertainty ranges can be distinguished: an uncertainty
range resulting from an in-depth assessment of multiple lines of evi-
dence (a so-called assessed uncertainty range); an uncertainty range
emerging from a sophisticated statistical sampling of the parameter
space; or an uncertainty range that represents the spread across an
arbitrary collection of model results (a so-called ensemble of oppor-
tunity). Each of these uncertainty ranges can be interpreted in dif-
ferent ways, and they decline in robustness going from an assessed
uncertainty range over targeted statistical approaches to ensembles of
opportunities. ese aspects thus also inuence the robustness of any
carbon budget estimates based on them. For example, the budget for
CO
2
-induced warming from WGI is derived from an assessed uncer-
tainty range, whereas the WGI budgets that also take into account
non-CO
2
forcing are based on an ensemble of opportunity, which
makes them much less robust (see also Technical Focus Element 8in
ref.42).
Scenario selection. Applying the denitions of TEBs and TABs to
a large scenario ensemble for the assessment of CO
2
budgets in line
with a particular temperature limit results in the selection of two
disjoint subsets of emission scenarios: a subset of baseline and weak
mitigation scenarios that exceed the temperature limit with a given
probability in the case of TEB budgets and a disjoint subset of more
stringent to very stringent mitigation scenarios that all keep warm-
ing to below the specied temperature limit with a given probability
in the case of TAB budgets.
0 1,000 2,000 3,000 4,000
0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Non-CO
2
radiative forcing (W m
−2
)
Cumulative CO
2
emissions from 2015 onwards (Gt)
a
Count per subset
Non-CO
2
forcing at time of deriving carbon budget (W m
−2
)
0.2 0.4 0.6 0.8 1 1.2
0
20
40
60
80
100
Cumulative relative
frequency over subset (%)
0
20
40
60
80
100
5−95% range
25−75% range
Median
b
c
RCP2.6
RCP4.5
RCP6
RCP8.5
RCP2.6
RCP4.5
RCP6
RCP8.5
Carbon budget (GtCO
2
)
Estimated temperature contribution from
non-CO
2
forcing at time of deriving carbon budget (°C)
(0.16, 1,890) and (−0.05, 2,476)
0.2 0.3 0.4 0.5 0.6 0.7 0.8
200
600
1,000
1,400
1,800
d
0.70
0.53
Count per subset
Estimated temperature contribution from
non-CO
2
forcing at time of deriving carbon budget (°C)
Cumulative relative
frequency over subset (%)
0
20
40
60
80
100
TEB
TAB
0.2 0.3 0.4 0.5 0.6 0.7 0.8
0
20
40
60
80
100
153
Figure 3 | Non-CO
2
forcing and cumulative CO
2
emissions. a, Non-CO
2
forcing as a function of cumulative CO
2
emissions from 2015 onwards for scenarios
of the IPCC AR5 Scenario Database. Scenarios are split up into two subsets: those that limit warming to below 2°C relative to pre-industrial levels with
at least 66% probability (yellow, used for TABs), and those that lead to global-mean temperatures exceeding the 2°C limit with at least 34% (orange,
used for TEBs). b, Distribution of non-CO
2
forcing at the time point critical for deriving TEB (orange) and TAB (yellow) budgets, that is, the moment the
2°C limit is exceeded for TEBs and peak warming for TABs. c, Distribution of the estimated temperature contribution from non-CO
2
forcing at the same
time point as in b (see Box1). The four RCPs are also included for comparison. d, Variation within the TEB and TAB budget subsets as a function of the
estimated temperature contribution from non-CO
2
forcing as in c. Numerical values in d are R
2
values for the two linear fits.
e estimated temperature contributions of non-CO
2
forcing,
shown in Fig. 3c, are derived by the following equation, as
described in the Supplementary Material to the WGI chap-
ter on ‘Anthropogenic and Natural Radiative Forcing’
53
(equation 8.SM.13).
R
T
(t)
= exp
M
j=1
d
j
c
j
t
d
j
)
)
Σ
where R
T
is the climate response to a unit of forcing, c
j
the
component of the climate sensitivity, d
j
the response times, and
t the time. For the two-term approximation (M=2) presented by
ref.54, values of c
1
, c
2
, d
1
, and d
2
are taken from table8.SM.9in
ref.53. is estimate is to be considered an illustrative approxi-
mation of the temperature eect of non-CO
2
forcing.
Box 1 | Non-CO
2
temperature contributions.
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A rst implication of the use of these disjoint scenario sets results
from only very few scenarios being available that have, for example,
precisely a 66% probability for limiting warming to below a given
temperature threshold. Although TEBs are consistently computed for
each scenario at the time a scenario exceeds a temperature limit with
a given probability, the value of TABs is further driven by the choice
of the range of probabilities that is used to select appropriate TAB
scenarios. For example, the IPCC SYR selected all scenarios that have
a 66 to 100% probability of limiting warming to below a given thresh-
old (compared with exactly 66% for TEBs). is resulted in an average
probability of staying below 2°C across the subset of TAB scenarios
that comply with the above-mentioned selection criterion of about
75%. is can explain about one-third to half of the 260–310GtCO
2
dierence between the TEB estimates from Friedlingstein et al.
36
and the IPCC SYR TAB estimates. Moreover, for some temperature
levels, for example around 3°C, the scenarios available in the IPCC
AR5 Scenario Database do not sample the possible range extensively,
which can lead to further biases in the numbers obtained.
Temperature response timescales. A second aspect that is dierent
in the disjoint scenario subsets are the CO
2
emission pathways and
hence the annual CO
2
emissions at the time the compatible carbon
budget is derived. In the TAB subset, CO
2
emissions will typically
approach zero or become negative to stabilize global temperatures,
and will thus be very low at the time of maximum warming dur-
ing the twenty-rst century. In the TEB subset this is not the case.
Because of the timescales of CO
2
-induced warming
46,47
this leads to
dierences in the carbon budget estimates.
Recent research indicates that, at current emission rates,
maximum CO
2
-induced warming only occurs about a decade aer
a CO
2
emission
46,47
. us, even in a CO
2
-only world, TABs and TEBs
with complementary probabilities (for example, a 66% probability
to limit warming below 2°C and a 34% probability of exceeding
2°C) would not be entirely identical. In case of the TEB approach,
the maximum warming of the CO
2
emissions of the last decade
before the temperature limit was exceeded has possibly not yet
fully occurred. In a TAB approach the emissions in the last dec-
ade would be signicantly lower, if not zero, and this would allow
a much larger fraction of the warming to already be realized. e
TEB approach thus leads to a consistent overestimate of the CO
2
budget compatible with a given temperature limit, whereas this
is not the case with the TAB approach. At least one-third of the
approximately 260–310 GtCO
2
dierence between the TEB esti-
mates from Friedlingstein etal.
36
and the IPCC SYR TAB estimates
can be explained by accounting for the approximately one decade
delay between CO
2
emissions and their maximum warming.
Non-CO
2
warming contribution. A third and last aspect that dif-
fers between the two disjoint TEB and TAB scenario subsets is the
mixture of CO
2
and non-CO
2
forcers. is mixture diers over time
and therefore, depending on when the compatible carbon budget
is determined, the TABs and TEBs are derived under possibly very
dierent non-CO
2
forcing (Fig.3b). e relationship between CO
2
emissions and non-CO
2
forcing is complex, as it covers the total
non-CO
2
forcing that results from both positive and negative cli-
mate forcers. Climate policy inuences these non-CO
2
forcers
Table 2 | A selection of carbon emission budgets related to a global temperature limit of 2°C relative to pre-industrial levels from
various sources.
Source Type Specification Value from 2011
(GtCO
2
)
Value from 2015
(GtCO
2
)
IPCC AR5 WGI
26
CO
2
-only
budget
To limit warming to less than 2°C since the period 1861–1880 with greater than 66%
(or 50%) probability
1,780 (or 2,550) 1,620 (or 2,390)
IPCC AR5 WGI
26
TEB To limit warming to less than 2°C since the period 1861–1880 in more than 66% (or
50%) of the model runs when accounting for the non-CO
2
forcing as in the RCP8.5
scenario
1,010 (or 1,120) 850 (or 960)
IPCC AR5 WGIII
35
TAB To limit warming in 2100 to below 2°C since 1850–1900 with a ‘likely’ (>66%)
probability, accounting for the non-CO
2
forcing as spanned by the subset of stringent
mitigation scenarios in the IPCC AR5 Scenario Database*. (10–90% range over
scenarios in IPCC WGIII scenario category 1)
630 to 1,180 470 to 1,020
IPCC AR5 WGIII
35
TAB To limit warming in 2100 to less than 2°C since 1850–1900 with a ‘more likely than
not’ (>50%) probability, accounting for the non-CO
2
forcing as spanned by the subset
of stringent mitigation scenarios in the IPCC AR5 Scenario Database*. (10–90%
range over scenarios in IPCC AR5 scenario category II without overshoot)
960 to 1,430 800 to 1,270
IPCC AR5 SYR
33
TEB To limit warming to less than 2°C since the period 1861–1880 in more than 66% (or
50% or 33%) of the model runs of the CMIP5 RCP8.5 ESM and EMIC simulations.
(These correspond to the IPCC AR5 WGI TEB budgets reported above)
1,010 (1,110 or
1,410)
850 (960 or
1,250)
IPCC AR5 SYR
33
TAB To limit warming to below 2°C since 1861–1880 with 66–100% probability,
accounting for the non-CO
2
forcing as spanned by the subset of stringent mitigation
scenarios in the IPCC AR5 Scenario Database. (10–90% range)
750 to 1,400 590 to 1,240
IPCC AR5 SYR
33
TAB To limit warming to below 2°C since 1861–1880 with 50–66% probability, accounting
for the non-CO
2
forcing as spanned by the subset of stringent mitigation scenarios in
the IPCC AR5 Scenario Database. (10–90% range)
1,150 to 1,400 990 to 1,240
Friedlingstein et al.
36
TEB To limit warming to less than 2°C since 1850–1900 with a 66% probability,
accounting for the non-CO
2
forcing as spanned by the subset of baseline and weak
mitigation scenarios in the IPCC AR5 Scenario Database*. (5–95% range)
1,310 (1,010 to
1,710)
1,150 (850 to
1,550)
Friedlingstein et al.
36
TEB To limit warming to less than 2°C since 1850–1900 with a 50% probability,
accounting for the non-CO
2
forcing as spanned by the subset of baseline and weak
mitigation scenarios in the IPCC AR5 Scenario Database*. (5–95% range)
1,610 (1,210 to
2,010)
1,450 (1,050 to
1,850)
1,890GtCO
2
were already emitted by 2011, and about 2,050GtCO
2
by 2015. All values are rounded to the nearest 10. Budget types are defined in Table 1. *The temperature difference between 1861–1880 and
1850–1900 is 0.02°C, based on ref. 55.
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both directly (via abatement measures) and indirectly (via changes
induced in the energy system), and this is captured in dierent ways
in IAMs. For example, stabilizing and peaking global temperatures
requires global CO
2
emissions to be reduced to close to net zero.
Such very low CO
2
emissions are achieved through a fundamental
transformation of the global energy–economy–land system
35
, which
in turn leads to changes in non-CO
2
emissions because of the phase-
out of common sources of CO
2
and non-CO
2
emissions
14,48
. is
can lead to important dierences in non-CO
2
forcing as a function
of total cumulative CO
2
emissions (Fig.3a). Figure3b shows that
median non-CO
2
forcing at the time that is of importance for deriv-
ing the carbon budget (that is, the time of exceedance for TEBs, and
peak warming for TABs) is about 0.2Wm
–2
higher in the subset of
scenarios used for TEBs compared with the subset used for TABs.
However, the non-CO
2
forcing at either peak warming or the
time of exceeding a given temperature threshold does not tell the
entire story. When estimating the actual non-CO
2
-induced warm-
ing at these time points of interest (see Box1), very little dierence
can be found between the TEB and TAB scenario subsets (Fig.3c).
is suggests that when a suciently large scenario sample is avail-
able, variations in non-CO
2
forcing cannot be used to explain the
variations between TEB and TAB estimates for limiting warming
to below 2°C. e precise inuence of this dierence on the carbon
budgets has not been quantied.
Incidentally, this feature is not obviously visible when looking at
the four RCPs only, because both the lowest, RCP2.6, and the high-
est, RCP8.5, are outliers in terms of non-CO
2
warming, at opposite
sides of the scenario distribution (Fig.3b,c).
Finally, although non-CO
2
forcing does not fully explain the var-
iations between TEB and TAB estimates, it plays an important role
for the variation within the TEB and TAB subsets. Figure3d shows
that respectively 70% and 50% of the variance within the TEB and
TAB subsets can be explained by non-CO
2
warming at the time of
determining the carbon budget.
Future non-CO
2
warming under stringent mitigation remains
nonetheless very uncertain at present. Its magnitude will depend
on the extent to which society will be successful in bringing about
assumed future improvements in agricultural yields and practices
or dietary changes
49
, amongst many other factors. ese are very
uncertain. Furthermore, how much non-CO
2
forcing is reduced
compared with CO
2
depends on the relative weight that is given
to CO
2
and non-CO
2
emissions in mitigation scenarios, and also
on other mitigation choices
50
. ese weights are mostly constant in
IAMs (for example, by using global warming potentials as a xed
exchange rate), but can also change over time and depend on the
question posed.
Air pollution controls can inuence the rate of near-term
warming and, depending on the precise mix of air pollutants that
is reduced by air pollution controls, non-CO
2
warming can be
increased, decreased or stay constant
14
. e estimated eect of air
pollution controls on carbon budgets, in particular on TABs, is very
small
51
. is is important information for policy-making, as it can
be used to consider trade-os between the uncertainty in non-CO
2
mitigation, possibly larger CO
2
budgets, and a larger amount of
committed warming at the multi-century scale due to larger cumu-
lative CO
2
emissions.
Applicability. Earlier we indicated that budgets that only take into
account CO
2
-induced warming are scientically best understood
as — per denition — they do not depend on extra uncertainties
associated with other forcings. However, at the same time, they are
impractical and largely irrelevant for use in the real world, because
of their obvious limitation of neglecting any contribution other than
CO
2
. e other approaches that go beyond this CO
2
-only approach,
might therefore be more practical. Using a CO
2
-only estimate for
real-word decision-making would lead to an overestimation of the
allowable carbon budget, that is, a very high risk of exceeding a given
climate target when emitting that particular carbon budget.
e strength of TEBs is that they are easily comparable to TCRE-
based budgets for CO
2
-induced warming only. Hence the inuence
of non-CO
2
forcing on the size of carbon budgets can be assessed.
However, because of the limitations related to scenario selection
(TEBs are derived from scenarios that fail in limiting warming to
the temperature level of interest) and the timescales of the tempera-
ture response, TABs are preferred over TEBs. e strength of TABs
lies exactly in their use of scenarios that represent our best under-
standing of how CO
2
and other radiatively active species would
evolve over time when CO
2
emissions are stringently reduced.
Conclusions
Several possibilities are available to compute cumulative carbon
budgets consistent with a particular temperature limit. We have
shown that each of the carbon budget approaches has strengths but
also comes with important limitations. e devil is in the detail here.
e most scientically robust number — the budget for CO
2
-induced
warming — is also the least practical in the real world. Selecting
budgets based on multi-gas emission scenarios that actually restrict
warming to below a given temperature threshold, results in the low-
est, but most relevant CO
2
emission budgets in a real-world multi-gas
setting. Any practical implementation of a carbon budget mitigation
strategy would require parallel mitigation eorts for non-CO
2
agents.
At the time of the IPCC AR5, no established methodologies were
available to ensure easy comparability of carbon budget estimates
across working groups. In hindsight and anticipating future assess-
ments, three recommendations can be formulated. First, insofar
as important topics can already be identied, coordinated model
simulations, intercomparisons, and methods could be initiated at
an early stage to ensure consistency and traceability. Second, con-
sistency across — and collaboration and integration between — the
IPCC working groups could be improved by setting up stronger ties
between them. And third, IPCC reports should be clearer about the
policy-applicability of the numbers they provide, without being pol-
icy prescriptive.
For limiting warming to below 2 °C relative to pre-industrial
levels with greater than 66% probability, the remaining CO
2
budget
from 2015 onwards for CO
2
-induced warming only is 1,620GtCO
2
.
e corresponding TAB budget would be 590–1,240 GtCO
2
. e
latter is equivalent to about 15to 30 years of CO
2
emission at cur-
rent (2014) levels (about 40 GtCO
2
yr
–1
, ref.52). No matter which
approach is taken, the CO
2
budget for keeping warming to below
2°C always implies stringent emission reductions over the coming
decades and net zero CO
2
emissions in the medium to long term. For
policy-making in the context of the UNFCCC, we suggest using the
590–1240GtCO
2
estimate from 2015 onwards for a likely chance of
limiting warming to below 2
o
C, as this is derived from an assessment
of scenarios that eectively limit warming to below the 2°C limit.
Further eorts will be required to limit warming below 1.5 °C.
Received 10 April 2015; accepted 15 October 2015;
published online 24 February 2016
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Acknowledgements
We acknowledge the work by IAM modellers that contributed to the IPCC AR5 Scenario
Database and the climate modelling teams contributing to CMIP5. We thank IIASA for
hosting the IPCC AR5 Scenario Database, and M. Meinshausen for detailed comments
and feedback on the manuscript.
Author contributions
All authors contributed to parts of the underlying research during the writing process
of the IPCC AR5. J.R. coordinated the conception and the writing of the paper. J.R.
carried out the research with signicant contributions from M.S., and developed the TEB
and TAB conceptual framework. J.R. produced the gures and wrote the rst dra of
the manuscript. All authors contributed to interpreting and discussing the results, and
writing the paper.
Additional information
Reprints and permissions information is available online at www.nature.com/reprints.
Correspondence should be addressed to J.R.
Competing financial interests
e authors declare no competing nancial interests.
PERSPECTIVE
NATURE CLIMATE CHANGE DOI: 10.1038/NCLIMATE2868
© 2016 Macmillan Publishers Limited. All rights reserved
... However, since these models are highly complex and based on many assumptions, comparing all the details is beyond the scope of a primarily legal analysis. Nevertheless, we provide a general overview [28,29] as a basis for discussing legal issues and challenges regarding the underlying empirical data in the following two chapters. ...
... Therefore, reducing CO2 sources could reduce (these) aerosols, resulting in short-term warming but long-term cooling [15] (pp. 3-19ff) [28,31,35,56,57]. The storage capacity of the oceans for CO2 and heat also affects the projections; the colder they are, the higher their storage capacity for GHG emissions, yet climate change induced storms are likely to increase the release of CO2 [58][59][60]. ...
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... Here, we have adopted the formal definition of the RCB following Matthews et al. [2] and Rogelj et al. [5], the latter of which defines the RCB as "the finite total amount of CO 2 that can be emitted into the atmosphere by human activities while still holding global warming to a desired temperature limit". This RCB definition implies that the temperature target in question is avoided, meaning that warming from slow responding processes in the climate system is considered and is therefore consistent with the definition of the "avoidance budget" that was defined in Rogelj et al. [20]. Alternatively, some studies have estimated the amount of CO 2 emissions up until the point when a particular temperature target is reached (and subsequently exceeded), which Rogelj et al. [20] termed an "exceedance budget" (e.g. ...
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... Zhang et al. (2021) and Ali et al. (2019) developed universal index such as DSI, which based on MODIS data of NDVI, and ET/PET. Abuzar et al. (2019) reported that MODIS-based ET products have achieved extremely a good indicator for drought monitoring, while NDVI has the potential to link vegetation responses to climate change (Rogelj et al. 2016). Drought conditions persist, especially in the south-west of the country (Huang et al. 2016;Adnan et al. 2018a, b). ...
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... Previous work shows that the temperature rise is, to first order, not strongly dependent on when carbon emissions occur, only on their cumulative sum [7][8][9][10][11][12][13], however the RCB is strongly dependent on both how much and when different types of non-CO 2 emissions occur [14][15][16][17][18][19]. As a result, the RCB requires some set of scenarios describing co-evolutions of CO 2 and other emissions to estimate. ...
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... Cumulative carbon emissions have the means and methods to count and collect CO 2 emissions. Rogelj et al. (2016) summarized approaches that estimate cumulative carbon emissions to keep global warming below a given temperature. Allen et al. (2018) suggested that temperatures in future decades will be strongly influenced by short-term climate pollutants, thus complicating the estimation of cumulative emission budgets for ambitious reduction targets. ...
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Thesis
Countries lack resonant metrics to monitor environmental sustainability from a strong sustainability perspective. Building on the Sustainability Gap approach, which was developed in the late 1990s to address this indicator gap, this thesis formulates the Environmental Sustainability Gap (ESGAP) framework with a stronger focus on implementation. ESGAP comprises two novel indices of environmental sustainability: the Strong Environmental Sustainability Index (SESI) and the Strong Environmental Sustainability Progress Index (SESPI). SESI measures the performance of 21 natural capital indicators against science-based reference values of environmental sustainability that reflect whether the environmental functions provided by natural capital are threatened. Based on observed and desired trends, SESPI describes whether the country is making progress towards, or away environmental sustainability as defined by those environmental sustainability reference values. The analysis focuses on European countries due to good data availability. European countries perform quite poorly with SESI, which indicates that several environmental functions are threatened. Broadly speaking, European countries perform better in the functions related to the provision of natural resources and human health and welfare, but get lower scores in the functions associated with pollution and life support systems. As shown by SESPI, current trends are also insufficient to reach environmental standards by 2030, although relevant differences emerge depending on the countries and indicators. The results contrast with the generally high performance attributed to European countries in other environmental indices such as the Environmental Performance Index or the Sustainable Development Goals (SDG) Index. A qualitative assessment of the environmental SDG indicators suggests that the SDG indicators fail to represent strong sustainability, which can ultimately lead to misleading messages around environmental sustainability. Combined, SESI and SESPI can make the messages on environmental sustainability more digestible to relevant audiences, while complementing existing metrics, including those used in the context of the Beyond GDP literature.
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The ratio of warming to cumulative emissions of carbon dioxide has been shown to be approximately independent of time and emissions scenarios and directly relates emissions to temperature. It is therefore a potentially important tool for climate mitigation policy. The transient climate response to cumulative carbon emissions (TCRE), defined as the ratio of global-mean warming to cumulative emissions at CO2 doubling in a 1% yr(-1) CO2 increase experiment, ranges from 0.8 to 2.4 K EgC(-1) in 15 models from phase 5 of the Coupled Model Intercomparison Project (CMIP5)-a somewhat broader range than that found in a previous generation of carbon-climate models. Using newly available simulations and a new observational temperature dataset to 2010, TCRE is estimated from observations by dividing an observationally constrained estimate of CO2-attributable warming by an estimate of cumulative carbon emissions to date, yielding an observationally constrained 5%-95% range of 0.7-2.0 K EgC(-1).