Introduction
In the long term, future climate changes will largely be determined by future
cumulative CO2 emissions ,
but the timing and magnitude of emissions are uncertain and a strong function
of future climate policy . Linking specific CO2 emission
scenarios to future transient climate change requires a model of the
interacting climate–carbon-cycle system. Comprehensive Earth system models (ESMs) explicitly
simulate the physical processes that govern the coupled evolution of
atmospheric CO2 concentrations and the associated climate response
. However, the use of such models may be
computationally intensive, require large ensembles to distinguish climate
change signals from internal variability and often substantial
post-processing of output. Therefore ESMs are often only run for a few
representative future emission scenarios . For analysis of
arbitrary emission scenarios, as required for the integrated assessment of
climate policy, a computationally efficient representation of the Earth
system is needed , particularly in order to sample Earth
system response uncertainty comprehensively in probabilistic frameworks.
Simplified representations of the coupled climate–carbon-cycle system take
many forms . A key test for simplified ESMs is whether they
correctly capture the physics of the co-evolution of atmospheric CO2
concentrations and global mean temperature under both idealised settings and
under possible projections of future emission scenarios. Following a
CO2 pulse emission of 100 GtC in present-day climate conditions, ESMs
(and Earth system models of intermediate complexity – EMICs) display a
rapid drawdown of CO2 with the concentration anomaly reduced by
approximately 40 % from peak after 20 years and by 60 % after
100 years, followed by a much slower decay of concentrations which leaves
approximately 25 % of peak concentration anomaly remaining after
1000 years . The speed and shape of this decay is dependent
on both the background climate state and the size of the pulse, but a
substantial fraction of the emission is simulated to remain in the atmosphere
after 1000 years in all cases. The effect of this longevity of fossil carbon
in the atmosphere, combined with the gradual “recalcitrant” thermal
adjustment of the climate system , is to induce a global mean
surface temperature response to a pulse emission of CO2 characterised by
a rapid warming, over approximately a decade, to a plateau value of global
mean surface temperature anomaly . Warming does not
noticeably decrease from this value over the following several hundred years,
indicating that, short of artificial CO2 removal (CDR) or active solar
geoengineering, CO2-induced warming is essentially permanent on
human-relevant timescales.
The correct representation of the temporal evolution of the warming response
to a pulse emission is required for computationally simple
climate–carbon-cycle models. Aside from the simple climate–carbon-cycle
models analysed in , many simple models, including some used
in integrated assessment models (IAMs; see e.g. ), have
not explicitly been evaluated in terms of their pulse-response behaviour, and
it remains unclear how well the physical dependences of the pulse response
are represented in such models. The social cost of carbon is conventionally
calculated by applying a pulse emission of a specified magnitude in near to
present-day conditions as a perturbation on top of a specified future
emission scenario . As calculating the social cost of carbon
is a key element of many cost–benefit analyses of climate change policy,
simple climate–carbon-cycle models used in IAMs should aim to reproduce the
pulse-response dependencies on pulse size and background state that have been
highlighted in ESMs and EMICs .
A second important feature of ESMs is the increase in airborne fraction (the
fraction of emitted CO2 that remains in the atmosphere after a specified
period) over time in scenarios involving substantial emissions or warming
. An emergent feature of the CMIP5 full-complexity
ESMs appears to be that this increase in airborne fraction approximately
cancels the logarithmic relationship between CO2 concentrations and
radiative forcing, yielding an approximately linear relationship between
cumulative CO2 emissions and CO2-induced warming
. This relationship has given rise to the
concept of an all-time cumulative “carbon budget” to restrict warming to a
certain level , which has quickly become an important tool
in evaluating the required energy-system transitions that are needed to limit
warming to below particular thresholds , as well as
the climate implications of the existing capital stock
. As simple climate–carbon-cycle models are
often used to compute particular carbon budgets in integrated assessment
scenarios (e.g. the MAGICC model as used in ), the
ability to reproduce the approximate linearity of the relationship between
warming and cumulative emissions is a desirable property.
Representing climate response uncertainty is also a crucial factor in the
integrated assessment of climate policies. Despite significant advances in
climate system understanding, non-negligible uncertainties remain in the
response of the coupled climate–carbon-cycle system to emissions of CO2
, implying that climate policies have to be constructed and
assessed in the light of this continued uncertainty .
Integrated assessment activities require a representation of the physical
climate system that can transparently and simply sample physically consistent
modes of climate response uncertainty, partly to assess the possibility of
extreme and highly costly responses within the Earth system (often called
“fat-tailed” outcomes) .
In this paper we show that although the impulse-response functions provided
for the calculation of multi-gas equivalence metrics in IPCC AR5
provide a simple and easy to use climate–carbon-cycle
model, this model is insufficient to fully capture the emergent responses of
the coupled climate–carbon-cycle system. Such a state-independent
impulse-response model cannot simultaneously reproduce the relationship
between emissions, concentrations, and temperatures seen over the historical
period and in the projected response over the 21st century to both
high emissions and mitigation scenarios as simulated by ESMs and EMICs.
Indeed, such a model formalism would inherently fail to capture the
dependence of the evolution of the airborne fraction following a pulse
emission on both the background state of the climate and pulse size, as
simulated by ESMs in . We therefore propose a simple
extension of the standard IPCC AR5 impulse-response model, coupling the
carbon cycle to the thermal response and to cumulative carbon uptake by
terrestrial and marine sinks in order to reproduce the behaviour of the ESMs
under a variety of idealised experiments and future emission scenarios.
Section 2 describes the formalism of the models that we contrast throughout
this paper and describes the methodological details of the experiments that
we use to analyse the responses of these models. We show and discuss the
results of these model validation experiments in Sect. ,
beginning, in Sect. , with why a state-dependent modification
to the IPCC AR5 carbon-cycle impulse-response function is required,
motivating the modified Finite Amplitude Impulse-Response (FAIR) model
described in Sect. 2. Section then evaluates the ability of
FAIR and the unmodified IPCC AR5 impulse-response models to replicate the
dependencies of the response to a pulse emission on background conditions and
pulse size shown in ESMs and EMICs. Section evaluates the
models' behaviour under a set of idealised experiments in which CO2
concentrations are increased by a fixed percentage each year, starting from
preindustrial values. Section discusses uncertainty in FAIR
and how probabilistic assessments of climate response to CO2 emissions
could be made using the model. Section 4 provides a concluding summary and
discussion.
Model description and methods
The IPCC AR5 Impulse-Response (AR5-IR) model
The IPCC AR5 proposed an idealised simple climate–carbon-cycle model for
metric calculations, incorporating a “two-box” or “two-time-constant” model
of the temperature response to radiative forcing with a “four-time-constant”
impulse-response model of the CO2 concentration response to emissions
. This model represents the evolution of atmospheric
CO2 by partitioning emissions of anthropogenic CO2 between four
different reservoirs (all of which are empty in preindustrial equilibrium)
of atmospheric carbon anomaly that each decay with a fixed time constant.
Four carbon pools are determined to be sufficient to empirically represent
the response of atmospheric CO2 concentration anomalies following a
pulse emission of 100 GtC, above a specified background concentration of
389 ppm, over the 1000 years following the pulse . These
carbon pools do not directly correspond to individual physical processes and
instead represent the combined effect of several carbon-cycle mechanisms;
however, processes that are guiding analogues to the timescale of the pool
decays are summarised in Table . The evolution of the carbon
concentration anomaly in each pool, Ri, is given as
dRidt=aiE-Riτi;i=1-4,
where E is the annual CO2 emissions, in units of ppm year-1
(1 ppm = 2.12 GtC), ai is the fraction of carbon emissions
entering each reservoir, and τi the decay time constant for that pool.
Coefficients ai and τi are as given in AR5 Chapter 8,
Tables 8.SM.9, and 8.SM.10 except for τ0, which is
here given a finite value and not set to infinity (all results presented in
this paper are insensitive to this choice). Atmospheric CO2
concentrations are given by C=C0+∑iRi , and radiative forcing
by
F=F2×ln(2)lnCC0+Fext,
where C0 is the preindustrial CO2 concentration,
F2×
the forcing due to CO2 doubling (F2×=3.74 Wm-2), and
Fext the non-CO2 forcing. Global mean surface temperature
anomalies (T) are computed as the sum of a two components (Tj)
representing the contributions to global mean surface temperature anomalies
controlled by the equilibration timescale of the upper/deep ocean
respectively:
dTjdt=qjF-Tjdj;T=∑jTj;j=1,2.
The two thermal response timescales, dj, have been ordered to run from
longest to slowest, as with the carbon-cycle response timescales, and are
chosen to match the multi-model means of . By considering
the analytic solutions of Eq. () under an instantaneous
doubling of CO2 concentrations and a 1 % year-1 increase in
CO2 concentrations, qj can be related to the equilibrium climate
sensitivity (ECS) and transient
climate response
(TCR) via the expressions
ECS=F2×(q1+q2)
and
TCR=F2×q11-d1701-exp-70d1+q21-d2701-exp-70d2.
Equations () and () can be inverted to give
expressions for qj in terms of ECS and TCR assuming response timescales
(dj) as given in Table . We choose
default values for qj corresponding to TCR = 1.6 K and
ECS = 2.75 K (q1=0.33 KW-1 m2 and
q2=0.41 KW-1 m2), indicative of a typical mid-range climate
response to radiative forcing in ESMs .
We use two versions of the AR5-IR model in this paper, calibrated to the
present-day (AR5-IR) and preindustrial (PI-IR) climate response to a pulse
emission respectively. The AR5-IR model is used for the calculation of
absolute global temperature potentials in IPCC AR5 and has
carbon-cycle coefficients that best represent the ESM simulated evolution of
a 100 GtC pulse emission under approximately present-day conditions. The
PI-IR model uses an alternative set of coefficients that are selected to
represent the evolution of a 100 GtC pulse emission in preindustrial
conditions. These parameters are derived from a fit to the multi-model mean
of the ensemble of ESMs and EMICs from (see
Table for parameter values).
Default parameter values for the simple impulse-response
climate–carbon-cycle models used in this paper.
Parameter
Value – AR5-IR
Value – PI-IR
Value – FAIR
Guiding analogues
a0
0.2173
0.1545
0.2173
Geological re-absorption
a1
0.2240
0.1924
0.2240
Deep ocean invasion/equilibration
a2
0.2824
0.2424
0.2824
Biospheric uptake/ocean thermocline invasion
a3
0.2763
0.4108
0.2763
Rapid biospheric uptake/ocean mixed-layer invasion
τ0 (year)
1 × 106
1 × 106
1 × 106
Geological re-absorption
τ1 (year)
394.4
276.7
394.4
Deep ocean invasion/equilibration
τ2 (year)
36.54
30.75
36.54
Biospheric uptake/ocean thermocline invasion
τ3 (year)
4.304
4.459
4.304
Rapid biospheric uptake/ocean mixed-layer invasion
q1 (KW-1 m2)
0.33
0.33
0.33
Thermal equilibration of deep ocean
q2 (KW-1 m2)
0.41
0.41
0.41
Thermal adjustment of upper ocean
d1 (year)
239.0
239.0
239.0
Thermal equilibration of deep ocean
d2 (year)
4.1
4.1
4.1
Thermal adjustment of upper ocean
r0 (year)
–
–
32.40
Preindustrial iIRF100
rC (year GtC-1)
–
–
0.019
Increase in iIRF100 with cumulative carbon uptake
rT (year K-1)
–
–
4.165
Increase in iIRF100 with warming
FAIR model
In the AR5-IR and PI-IR models the carbon-cycle response to a pulse emission
is not explicitly affected by rising temperature or CO2 accumulation and
hence these models only represent the specific response to a particular
perturbation scenario. In more comprehensive models, ocean uptake efficiency
declines with accumulated CO2 in ocean sinks and
uptake of carbon into both terrestrial and marine sinks are reduced by
warming .
In an attempt to capture some of these dynamics within the simple
impulse-response model structure, we attempt a minimal modification of the
AR5-IR model to allow it to mimic the behaviour of ESMs/EMICs in response to
finite-amplitude CO2 injections, which we call a FAIR model. To introduce a state-dependent carbon uptake
as simply as possible, we apply a single scaling factor, α, to all
four of the time constants in the carbon cycle of the AR5-IR model, such that
the CO2 concentrations in the four “carbon reservoirs” are updated thus:
dRidt=aiE-Riατi;i=1-4.
To identify a suitable state dependence, we focus on parameterising
variations in the 100-year integrated impulse-response function,
iIRF100. A focus on the integrated impulse response (average airborne
fraction over a period of time, multiplied by the length of time period), as
opposed to the airborne fraction at a particular point in time, is more
closely related to the impact of CO2 emissions on the global energy
budget, and also to other metrics such as global warming potential.
With other coefficients fixed, iIRF100 is a monotonic (but nonlinear)
function of α:
iIRF100=∑iαaiτi1-exp-100ατi.
As Eq. () is derived using the approximation that α
is independent of time, the right-hand side of Eq. () is
only exactly equivalent to the iIRF100 for infinitesimal pulse emission
perturbations from a constant background climate state (in which the
approximation of time-independent α becomes exact). We assume
iIRF100 is a function of the accumulated perturbation carbon stock in
the land and ocean (equivalent to the amount of emitted carbon that no longer
resides in the atmosphere), Cacc=∑tE-(C-C0), and
of the global mean temperature anomaly from preindustrial conditions, T. A
simple linear relationship appears to give an adequate approximation to the
behaviour of ESMs and EMICs (as will be shown subsequently in
Sect. ):
iIRF100=r0+rCCacc+rTT.
At each timestep we first compute the required iIRF100 using
Cacc and T from the previous timestep
(Eq. ). We then numerically solve Eq. ()
for the compatible value for α, which is then in turn used to update
the carbon pool concentrations (Eq. ). The total radiative
forcing is then computed with Eq. (), before changes in global
mean temperature are computed with Eq. ().
Values of r0=32.4 years, rC=0.019 years GtC-1,
rT=4.165 years K-1, ECS = 2.75 K, and TCR = 1.6 K are
here used as model default parameters. We choose these parameters to approximately
replicate the relationship between warming-driven outgassing of carbon in the
bulk of CMIP5 ESMs (see Sect. ), whilst also diagnosing
near-observed values of present-day CO2 emissions to achieve present-day
concentrations. The values given here as default parameters are intended to
be taken only as approximate CMIP5-representative values that capture
important carbon-cycle dynamics in ESMs. These values have not been
explicitly optimised to any particular goal and can be tuned (along with the
other model parameters) to reproduce specific aspects of individual ESM/EMIC
behaviour (e.g. see Fig. ). Best-estimate values for the
FAIR parameters will depend on exactly what feature of ESM behaviour is the
desired target for the optimisation.
Values of iIRF100 larger than 100 years correspond to a net carbon
source to the atmosphere in response to a perturbation and, as perturbations
to the carbon stock in the atmosphere would grow indefinitely, makes the
model unstable. In this regime there is no solution for α, so we set
iIRF100 to a maximum value of 96.6 years, corresponding, with the
parameters as given in Table , to α=100. This
physically corresponds to a near-absence of carbon sinks in the Earth system
following a very large injection, with very slow rates of decay of
atmospheric concentrations. This limit is only reached after 2250 in RCP8.5
of the scenarios considered in this paper and is
unimportant for the results presented in Sect. .
Experimental setup
In this section we describe the features of several experimental protocols
that have been used to examine coupled climate–carbon-cycle feedbacks in ESMs
and EMICs. These experiments, conducted with the AR5-IR, PI-IR, and FAIR
models, form the core of our analysis of these models in
Sect. .
Pulse-response experiments
documented the response of an ensemble of ESMs and EMICs to
pulses of various sizes and under various background conditions (black lines
in Fig. ). In the PD100 experiment (100 GtC pulse in
approximately present-day background conditions), background emissions are
diagnosed that stabilise CO2 concentrations at 389 ppm (after rising as
historically observed). In a second experiment, a 100 GtC pulse is added to
these diagnosed background emissions in the year that CO2 concentrations
reach 389 ppm and the resulting CO2 concentration and temperature
evolutions are compared to the case without the pulse emission to isolate the
response to the pulse emission alone. Experiments were also conducted for a
pulse of 100 and 5000 GtC in preindustrial background conditions (PI100 and
PI5000 respectively) for a smaller subset of models.
We simulate these experiments with the impulse-response climate–carbon-cycle
models by following the experimental protocol exactly as described in
. Emissions are derived consistently with the background
concentration profile using an inversion of the carbon-cycle equations for
the AR5-IR and PI-IR models (Eq. ) and the FAIR model
(Eq. ). A declining but nonzero low level of diagnosed
emissions is required to stabilise atmospheric concentrations at the
389 ppm level for all of the models considered.
As well as investigating the response of the default FAIR parameters in these
pulse-response experiments, we also investigate how parameter perturbations
could allow FAIR to span the range of responses observed in the PD100 and
PI100 experiments for the individual models of the ensemble.
We fit the FAIR parameters to the individual model responses in a two-step
process. First, the carbon-cycle parameters (ai, r0, rT, and
rC) of the FAIR model are optimised to minimise the total combined
residual sum of squares of the FAIR fit to the multi-model
mean airborne fraction across both the PD100 and PI100 experiments. As a
constraint on this fit, we fix the ratio between the rT and rC
parameters at the value of this for the default parameters given in
Table . This is both to reduce the number of free parameters
in the fitting process (the model is underconstrained as pulse-response
experiments do not distinguish between temperature-induced and CO2
uptake-induced carbon-cycle feedbacks) and because the representation of the
temperature-induced carbon-cycle feedbacks in the “radiatively coupled”
prescribed concentration increase experiment (see
Sect. ) is more sensitive to parameter perturbations
that change this ratio than to perturbations that do not alter it (not shown).
After fitting the multi-model mean as described above, we then fit the
responses for individual models by minimising the combined PD100 and PI100
residual sum of squares whilst allowing only the r0, rT, and rC
parameters to vary from the model parameters found in the multi-model mean
fit (the ratio between rT and rC is again fixed at the value for
the default parameters). The time series of change in global mean surface
temperature due to the pulse emission are taken as simulated by the
individual models when conducting both stages of these fits.
We also consider the response of the FAIR and AR5-IR models under the
idealised pulse experiments of .
conducted several experiments with the UVic Earth System Climate Model (UVic ESCM) of
intermediate complexity . We here emulate the PULSE
experiments of by integrating the FAIR and AR5-IR
models with historical fossil fuel and land-use CO2 emissions together
with estimates of the historical non-CO2 radiative forcing, both
backed out from historical concentrations using the MAGICC model
. Pulse emissions of various sizes were then applied
over a 2-year period from 2008 in order to restrict total all-time
cumulative emissions to specified totals (see , for
details). Non-CO2 forcings are held constant at 2008 levels after
following RCP8.5 trajectories for 2005–2008.
Exponential CO<inline-formula><mml:math id="M156" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> increase experiments
To explore the response to sustained emissions, rather than an emission
pulse, we consider the experiments of and
, in which ESMs are subjected to specified rates of increase
in CO2 concentrations. Concentrations were increased from preindustrial
values at 0.5, 1, and 2 % year-1 respectively and consistent
emissions were diagnosed for different configurations of the ESMs: a
“biogeochemically coupled” experiment, where the carbon cycle is only
allowed to respond to the direct effect of increasing CO2 concentrations
and not to the resultant warming; a “radiatively coupled” experiment in
which the climate system is allowed to respond to the radiative forcing of
CO2 but the carbon cycle is only allowed to respond to the simulated
warming and not to increasing CO2; and a “fully coupled” experiment in
which the carbon cycle is allowed to respond to both warming and increased
CO2. Such idealised scenarios can be highly informative regarding the
physical drivers of carbon-cycle feedbacks under increasing emissions.
Within the FAIR framework we recreate the biogeochemically coupled
experiment by setting rT=0 and approximate the radiatively coupled
experiment by evaluating the difference between the fully coupled and
biogeochemically coupled experiments (a net out-gassing of carbon, the
simulated response to the radiatively coupled experiment in the ESMs,
cannot be directly simulated in impulse-response models where a pulse
emission of carbon always decays over time). Although
found that the relationship between the experiments was not simply a linear
summation at high CO2 concentrations, this serves as an adequate
approximation for our purposes since our objective is the correct
representation of aggregate feedbacks from different effects in the FAIR
model as opposed to a more complex linear and nonlinear partitioning. In all
experiments concentrations are increased at the prescribed rates until they
reach four times their preindustrial values.
Uncertainty sampling with FAIR
Uncertainty in the thermal response to radiative forcing typically tends to
be the dominant factor in the uncertainty in the response of the global
climate system to CO2 emissions . ECS and TCR co-vary
in global climate models , with TCR typically
considered the more policy-relevant parameter and better constrained by
climate observations to date . Hence varying ECS alone in a
probabilistic assessment risks introducing an implicit distribution for TCR
that is inconsistent with available observations. observed
that, within the coupled models of the CMIP5 ensemble, the TCR and the ratio
TCR : ECS (referred to as the realised warming fraction or RWF) are
approximately independent. IPCC AR5 provided formally assessed uncertainty
ranges for TCR and ECS but not for their ratio. RWFs for
the CMIP5 models lie within the range 0.45–0.7, while
observationally constrained estimates typically lie in the upper half of this
range .
We assess the impact of uncertainty in the FAIR parameters on the response to
a 100 GtC pulse emission of CO2 in 2020 (against a background RCP2.6
concentrations; ) via a large ensemble (300 members) of draws
from distributions representative of assessed uncertainty in these
parameters. As IPCC AR5 likely (>66 % probability) ranges for a
physical climate parameter attempt to capture structural uncertainties that
might be present in all studies, IPCC AR5 likely intervals are generally
comparable to the 90 % confidence intervals in the underlying studies as
opposed to the central 66 % of the distribution. IPCC AR5 gives no
assessment of the shape of the distribution associated with structural
uncertainty as, by definition, this encompasses “unknown unknowns” that are
not included in any model or study available. For quantitative modelling
purposes, likely ranges are best interpreted as 5–95 percentiles of input
distributions for IPCC AR5 assessed parameters, provided a similar
“structural degradation” is applied to interpret the 5–95 percentiles of
output quantities as corresponding only to a likely range, propagating the
possibility of structural uncertainty in the assessed parameter through the
study.
We here assume a bounded (between 0 and 1) Gaussian distribution for RWF
(with 5–95 percentiles of 0.45–0.75) and a log-normal distribution for TCR
(with 5–95 percentiles of 1.0–2.5 K), reproducing the positive skewness
(fat high tail) of many estimated distributions for this parameter. A
log-normal distribution has some theoretical justification as an appropriate
shape for the distribution of a so-called “scale parameter” (one in which
uncertainty increases with parameter size) which is arguably the case for TCR
. Convolving these distributions gives a corresponding ECS
5–95 percentile range of 1.6–4.5 K, in good agreement with the IPCC AR5
assessed likely range (1.5–4.5 K).
The short thermal response timescale, d2, is an important determinant of
the initial pulse-adjustment time (the initial e-folding adjustment
time of the temperature response to a pulse emission of CO2,
). We sample d2 using a log-normal distribution (as
d2 is a positive definite parameter) with 5–95 % probability
interval of 1.6–8.4 years, corresponding to the minimum of the CMIP5 range
given in as the 5th percentile and the HadCM3 value of
8.4 years as the 95th percentile. We consider uncertainties in the carbon
cycle by sampling a single Gaussian random variable which is used to obtain
draws from assumed Gaussian distributions of r0, rT, and rC for
which the 5–95 % probability intervals are equal to ±13 % of
their default value (corresponding to a present-day iIRF100 5–95 %
probability interval of ±7 years). The 300 random draws from all of the
above distributions are then used as model parameters for the integration of
the 2020 100 GtC pulse-response scenario described above, leading to a
300-member ensemble of climate outcomes indicative of the propagated
uncertainty in the FAIR input parameters.
Results and discussion
The necessity for a state-dependent impulse-response model
When the AR5-IR model is integrated under estimated historical emissions from
the Global Carbon Project (GCP) starting from an assumed
quasi-equilibrium in 1850, atmospheric CO2 concentrations increase
faster than observed (Fig. a). This is indicative of the
under-efficiency of the AR5-IR carbon sinks when continuously integrated over
the observed period, resulting in a bias of over 30 ppm in 2011 CO2
concentrations. Similarly, this under-efficiency of carbon sinks requires
lower than observed emissions to simulate the observed time series of
atmospheric CO2 concentrations (Fig. b). Whilst sinks are
maintained at their preindustrial efficiency throughout (by definition) for
the PI-IR model, it is only after approximately 1980 that the FAIR airborne
fraction rises above the PI-IR airborne fraction (Fig. c). This
arises due to a combination of a lower preindustrial iIRF100 in the
FAIR model for a 100 GtC pulse (see Sect. ) as α<1 in
the FAIR preindustrial state, annual emissions much less than 100 GtC
(reducing the iIRF100 relative to a 100 GtC pulse in FAIR but not
PI-IR), and the PI-IR model (and the AR5-IR model) not capturing temporary
reductions in the airborne fraction associated with volcanic-forced cooling
(Fig. d) mediated through the temperature-induced feedback on
the carbon cycle in FAIR. Figure c shows large amplitude
variations in the observed instantaneous airborne fraction that are likely to
be driven in large part by unforced variability in the Earth system and as
such we would not expect these oscillations to be reproduced by any of the
simple climate–carbon-cycle models. More complex carbon-cycle models are
required to understand the drivers of these variations and any implications
that they have for future carbon-cycle responses. Observed anomalies of
global-mean temperature are reproduced well in the FAIR and PI-IR models
(Fig. d), but present-day warming is too large in the AR5-IR
model, driven by substantially higher-than-observed present-day CO2
concentrations.
Historical validation of the FAIR (blue), AR5-IR (red), and PI-IR
(orange) models. (a) shows simulated CO2 concentrations when
driven by historical emissions (and historical non-CO2 forcing) as
estimated by MAGICC. (b) shows diagnosed CO2 emissions
consistent with historical concentrations. (c) shows the evolution
of annual airborne fraction (smoothed with a 7-year running mean for the
observations), and (d) the warming anomaly when driven by historical
emissions. Historical observations are shown as black dots in all
panels. (a, b, c) show and HadCRUT4
is shown in (d). All simulations are commenced
from assumed quasi-equilibrium carbon-cycle states in 1850.
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Another key test of simple coupled climate–carbon-cycle models is the ability
to replicate the response of ESMs to possible scenarios of future emissions.
Commonly used future scenarios are generally defined in terms of
concentration pathways and therefore do not have a
model-independent set of emissions associated with them. In this paper we
drive all three simple impulse-response climate–carbon-cycle models by a
single set of emissions for each future scenario that are diagnosed from the
MAGICC model in order to allow a comparison of
simulated concentrations between simple models driven by identical inputs.
MAGICC has been shown to be a good emulator of the CMIP5 ensemble and
therefore offers a comparison by proxy to the projections of CMIP5 ESMs
. Whilst the PI-IR model might do a better job than
the AR5-IR model of reproducing historical concentrations under high future
emission scenarios such as RCP8.5, it underestimates end-of-century
concentrations, relative to MAGICC, to an even greater extent than the AR5-IR
model (Fig. a) and concentrations fall from their peak even
quicker than MAGICC under the high-mitigation RCP2.6 scenario
(Fig. b). The lack of saturation of carbon sinks in the AR5-IR
model prevents the simulated concentrations keeping pace with MAGICC by the
end of the 21st century (under RCP8.5) despite having higher concentrations
than MAGICC over the historical period and until approximately 2070. AR5-IR
concentrations peak significantly higher than MAGICC under RCP2.6 and also
decline faster after the concentration peak than simulated in MAGICC and
FAIR. The deviation of both of these two models from MAGICC clearly indicates
that any state-insensitive impulse-response model is therefore unsuitable,
unless modified, for long integrations with historical and projected
emissions.
CO2 concentrations under RCP8.5 (a) and
RCP2.6 (b). FAIR (blue), AR5-IR (red), PI-IR (orange), and MAGICC
(green) are shown in both panels.
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The FAIR model compares well to MAGICC in both RCP8.5 and RCP2.6, scenarios
that span the range of plausible future emission trajectories.
Concentrations simulated by FAIR are marginally higher than MAGICC after 2100
in RCP8.5, but the behaviour of MAGICC (or indeed any other model) under
these more extreme forcing scenarios has not been verified. Additionally,
concentrations in FAIR peak at a slightly lower value than MAGICC in the
RCP2.6 scenario. Whilst comparing the performance of one simple model to
another is not as rigorous a test of model performance as comparing directly
to the behaviour of ESMs, it is encouraging that the FAIR model shows a close
correspondence with a well-known and well-used simple model that has been
used extensively to emulate the response of ESMs .
Response to pulse emission experiments of
. (a) shows the response to a 100 GtC imposed on
present-day (389 ppm) background conditions (PD100
experiment), (b) the response to a 100 GtC pulse in preindustrial
conditions (PI100 experiment) and (c) the response to a 5000 GtC
pulse in preindustrial conditions (PI5000 experiment) with the warming
normalised by the increase in pulse size between (b) and (c). Airborne
fraction (left-hand axis) is represented by solid lines in all panels and
warming (right-hand axis) by dashed lines. FAIR is shown as thick blue lines,
AR5-IR as red, and PI-IR as orange. The black lines in all panels shows the
multi-model mean for airborne fraction (solid) and warming
(dashed), with the grey shading indicating 1 standard deviation uncertainty
across the ensemble. Thin blue lines denote the biogeochemically coupled
version of FAIR.
![]()
Response to pulse emission experiments
Figure shows the response to a pulse emission of CO2 of
differing magnitudes and against different backgrounds. For a 100 GtC pulse
of carbon set against an approximately present-day (389 ppm) concentration
background (PD100 – Fig. a), the FAIR simulated concentration
anomaly associated with the pulse decays to 0.43 of its initial value after
100 years, slightly greater than the multi-model average of the ESM responses
(0.41). The FAIR iIRF100 of 50.5 years lies within the ESM multi-model
spread (see Table ). Excluding temperature feedbacks on the
carbon cycle in FAIR (the biogeochemically coupled version of FAIR –
setting rT=0) increases the decay of the concentration response to the
pulse over the century following the pulse emission, reducing the
iIRF100 by 10 %. The AR5-IR, PI-IR, and the FAIR model all show
temperature anomalies due to the pulse initially adjusting rapidly followed
by near-constant temperature over the remainder of the century as displayed
by the multi-model mean (with internal variability
superimposed on top of this signal). Peak temperature anomaly is achieved
after 12 years, consistent with the value of 10 years found by
.
Figure b and c show the response to a 100 GtC
and a 5000 GtC pulse respectively (named PI100 and PI5000), applied in
preindustrial conditions. In Fig. c the pulse size is 50 times
that in Fig. d, and thus we divide the temperature response in the
PI5000 experiment by 50 in Fig. c to allow the response per
100 GtC to be visually comparable across the PD100, PI100, and PI5000
experiments. The 100 GtC preindustrial pulse decays faster than the
present-day case (as in the ESMs and EMICs) due to reduced saturation of the
land and ocean carbon sinks in the background state. FAIR simulates an
iIRF100 approximately 32 % lower in the preindustrial case
(34.3 years) relative to the present day, lying just within the ensemble
spread of PI100 iIRF100 simulated by the models of
(34–47 years). The magnitude of the FAIR simulated temperature response is
similar in both the PD100 and PI100 cases due to the increased radiative
efficiency of a pulse of CO2 at lower background concentrations
counteracting the faster decay of carbon out of the atmosphere. FAIR
simulates a 100 % increase of iIRF100 in the 5000 GtC
preindustrial pulse relative to the 100 GtC preindustrial pulse,
consistent with the approximate doubling observed in the ESMs. This clearly
demonstrates that FAIR can capture the dependence of the pulse response on
pulse size as well as background conditions, whilst the AR5-IR model displays
identical pulse response independent of pulse size or background conditions.
The very rapid drawdown of CO2 simulated by FAIR in the initial timestep
following the 5000 GtC pulse is in part a function of the annual timestep in
the model (carbon sinks remain at their preindustrial efficiencies over the
entirety of the first year despite accumulating a substantial amount of
carbon over that period) and could be alleviated by using a smaller timestep.
Restricting temperature-induced feedbacks on the carbon cycle does not result
in a substantial reduction in the iIRF100 for the preindustrial
100 GtC pulse experiment (the fully coupled and
biogeochemically coupled experiments lie on top of each other in
Fig. b), whereas a 13 % reduction in iIRF100 is
observed for the Bern3D-LPJ model examined in . This is due
to the FAIR formalism, global mean temperature increase, and cumulative carbon
uptake increases iIRF100 from a fixed preindustrial value (r0),
therefore preventing substantial fractional differences between the
fully coupled and biogeochemically coupled PI100 experiments as
iIRF100 remains close to r0 throughout both these experiments. For
the 5000 GtC preindustrial pulse experiment we see a reduction in the
iIRF100 (17 %) associated with suppression of the
temperature-induced feedbacks on the carbon cycle in FAIR, consistent with
the approximate 15 % reduction in iIRF100 for Bern3D-LPJ. As the
impact of the temperature-induced carbon-cycle feedbacks have only been
assessed in a single EMIC, it is unclear how consistent or not FAIR is with
the range of behaviour that would be simulated by the full ESM and EMIC
ensemble.
Fitting individual models from with
FAIR. (a) shows the remaining airborne fraction for the PD100
experiment and (b) for those models that additionally completed the
PI100 experiment. Solid lines show the original model response coloured by
the iIRF100 values. Emulations with FAIR are shown by the same coloured
dashed lines. The multi-model mean is shown by a solid black line with the
FAIR fit denoted by a dashed grey line.
![]()
In Fig. we show emulations of the individual models in the
ensemble using a single set of parameters for both the PD100
(Fig. a) and PI100 (Fig. b) simulations. In
the fitting process we choose to fix the ratio of the rT and rC
parameters to the default value (see Sect. ) as the fully
coupled PD100 and PI100 experiments do not distinguish between
temperature-induced and CO2-induced feedbacks. Whilst significant
diversity is seen in the range of responses to the PD100 and PI100
experiments across different ESMs/EMICs, attributable to a range of
differences in carbon-cycle process representations within these models,
variations in just a subset of the FAIR parameters are sufficient to span
the ranges of responses in both the PD100 and PI100 experiments (fits are
worse for models in which interannual variability is simulated), as well
achieving the correct ratio between the PD100 and PI100 responses for models
across the ESM/EMIC ensemble.
iIRF100 values in the experiments and models shown in
Fig. . The star indicates that the values for suppressed
climate–carbon-cycle feedbacks are calculated assuming the 13 % (PI100)
and 15 % (PI5000) reductions in iIRF100 from the fully coupled
experiment observed from the Bern3D-LPJ model in , the only
model which conducted the experiments. Brackets indicate the ±2 standard
deviation ranges around the multi-model mean in .
Experiment – iIRF100 (year)
AR5-IR
PI-IR
FAIR
PD100
52.5
40.8
50.5
52.4 (±11.3)
PD100 (no climate–carbon-cycle feedbacks)
–
–
45.2
–
PI100
52.5
40.8
34.3
40.6 (±4.2)
PI100 (no climate–carbon-cycle feedbacks)
–
–
33.8
35.3∗
PI5000
52.5
40.8
68.6
76.9 (±6.2)
PI5000 (no climate–carbon-cycle feedbacks)
–
–
60.0
65.4∗
Temporal dependence of CO<inline-formula><mml:math id="M220" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>-induced warming on pulse size
used a version of the AR5-IR model to find that the maximum
warming from a pulse emissions of CO2 occurs approximately a decade
after emission but does not account for important sensitivities of the timing
of peak warming on the size of the emission pulse .
Figure shows that under a variety of magnitudes of present-day
pulse emission magnitudes (from – see
Sect. ), the AR5-IR model warms rapidly to a near-term
peak followed by a decline over the next century and then subsequently rises
again as the long-timescale thermal response to radiative forcing begins to
dominate the cooling effect of atmospheric CO2 decay. The timing of the
near-term warming peak is largely insensitive to the magnitude of the pulse
emission in the absence of explicit feedbacks between the carbon cycle and
thermal climate system. Unlike in the AR5-IR model, FAIR shows a dependence
of the temporal evolution of warming after present-day carbon pulses more
similar to that seen in the UVic ESCM (see
), in which warming reaches a maximum later for larger pulse
sizes (black lines in Fig. ), as the balance between
carbon-cycle cooling and long-timescale thermal warming takes centuries to
reach equilibrium. FAIR does simulate a small near-term warming peak for the
smallest pulse size, although warming only decreases by less than 2 %
before subsequently rising again. As the magnitude of future cumulative
emissions are uncertain and could exceed multiple TtC under minimal climate
policy scenarios (e.g. RCP8.5) correctly capturing the dependence of peak
warming on injection size in simple climate–carbon-cycle models is important
for correctly assessing the multi-millennial impacts of climate policy
.
Dependency of the timing of maximum warming on pulse size. Global
mean surface temperature response is expressed as a fraction of the maximum
warming under the pulse experiments of . Responses are
shown for the FAIR (blue), AR5-IR (red), and UVic ESCM (black). Different
cumulative emission totals (see ) are denoted by
different line styles.
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Response to idealised concentration increase experiments
The set of fully coupled, biogeochemically coupled, and
radiatively coupled experiments from (see
Sect. ) can help to isolate the contributions from
temperature-induced and direct carbon-induced effects on overall carbon-cycle
feedbacks. Coupling between temperature changes and the carbon cycle in the
FAIR model acts to suppress carbon uptake, shown by the difference between
the fully coupled and biogeochemically coupled (thick and thin blue
lines in Fig. a) under a 1 % year-1 CO2
concentration increase scenario, consistent with the behaviour shown by the
ESMs from (thick and thin pastel coloured lines). This is a
mechanism that is absent (by construction) in the AR5-IR model.
Figure b shows Cacc as a function of atmospheric
CO2 concentration for several rates of prescribed concentrations
increase; again, the FAIR model captures the concave-downward form of this
diagnostic shown by the ESM ensemble for all rates of concentration increase,
in contrast to the AR5-IR model.
Response to idealised concentration increase experiments from
for the FAIR (blue) and AR5-IR (red) models. Light pastel
colours show the ESMs from for the 1 % year-1
concentration increase scenario only. (a) shows the cumulative ocean
and land carbon uptake over time in the “fully coupled”
1 % year-1 concentration increase scenario. (b) shows the
evolution of cumulative ocean and land carbon uptake as a function of
atmospheric concentration in the “biogeochemically coupled” experiment for
1 % year-1 (solid), 2 % year-1 (dashed), and
0.5 % year-1 (dotted) experiments. (c) shows the
cumulative uptake as a function of temperature in the “radiatively coupled”
experiments. (d) shows the evolution of the cumulative airborne
fraction as a function of the proportional concentration increase for the
“fully coupled” experiments.
![]()
Oceanic carbon-cycle feedbacks are almost exclusively driven by
biogeochemical effects . However, simple global
climate–carbon-cycle models need to also capture dependencies of the land
carbon uptake on warming. Aside from three ESMs that display global-mean
carbon cycles relatively insensitive to warming, Fig. c shows a
relationship between temperature increases and the size of the carbon
outgassing back to the atmosphere in the radiatively coupled FAIR
experiment similar, in both shape and magnitude, to that displayed in the
ESMs under the 1 % year-1 concentration increase experiment of
. 1, 0.5, and 2 % year-1 experiments in FAIR all
lie along the same line in Fig. c, indicating minimal scenario
dependence of this effect in FAIR, in contrast to the two ESMs analysed in
.
As simulated by FAIR, the initial decrease in cumulative airborne fraction
(the fraction of all past emissions remaining in the atmosphere) followed by
a subsequent increase is a feature of the response of many ESMs under a
1 % year-1 increasing CO2 scenario (Fig. d). In
contrast, the IPCC AR5 model shows a steady decrease in the cumulative
airborne fraction with higher concentrations due to the state-invariant rates
at which a pulse of carbon is removed from the atmosphere. The initial
decrease in cumulative airborne fraction followed by subsequent increase can
be understood in terms of the saturation of carbon sinks. If atmospheric
anomalies of carbon decay with fixed timescales, τi (as in the AR5-IR
model case), then the instantaneous airborne fraction remains constant in
time, which necessarily means that cumulative airborne fraction must decline
over time (as emissions from previous years decay further, so the cumulative
fraction of the emitted carbon continually decays from the instantaneous
airborne fraction). However, if carbon sinks become saturated, the
instantaneous airborne fraction would be expected to increase with time (this
is represented in the FAIR model by increases to the decay timescales through
the parameterised increase in iIRF100). Therefore, as more recent
emissions (which increase monotonically with time in the prescribed
concentration increase experiments) have a higher instantaneous airborne
fraction, the initial decrease in cumulative airborne fraction slows and
stops,
and then this fraction subsequently begins to increase as the accelerating
saturation becomes the dominant effect.
Probabilistic parameter sampling within the FAIR model
The impulse-response formulation of the physical climate response to
radiative forcing used by both the AR5-IR and FAIR models
(Eq. ) offers a convenient structure for simply sampling
plausible ranges of TCR and ECS. Figures a and b
show the isolated impact of thermal response uncertainty under idealised
prescribed concentration scenarios, namely a 1 % year-1 CO2
concentration increase (Fig. a) and an instantaneous
quadrupling of CO2 concentrations from preindustrial values
(Fig. b). A unique combination of TCR and ECS (for fixed
response timescales dj) is associated with a unique combination of the
model parameters qj (Eqs. and ). The blue
shading in panels (a) and (b) of Fig. show the simulated
temperature response for the likely range of TCR and ECS as assessed by
IPCC AR5 (TCR: 1.0–2.5 K; ECS: 1.5–4.5 K). Expressed in terms of
qj, the top end of the IPCC AR5 thermal uncertainty range
(TCR = 2.5K; ECS = 4.5 K) corresponds to
q1=0.57 KW-1 m2 and q2=0.63 KW-1 m2, with
the lower end (TCR = 1.0 K; ECS = 1.5 K) corresponding to
q1=0.14 KW-1 m2 and q2=0.26 KW-1 m2. The
thermal response model given by Eq. () fully spans the range
of responses seen in the CMIP5 ensemble for these fixed concentration
integrations under with the ranges of parametric uncertainty given above.
AR5-IR results are not shown in Fig. a and b as for prescribed
CO2 concentrations uncertainty in warming arises from thermal
response uncertainty only – which is identical in the FAIR and AR5-IR/PI-IR
models.
Climate response uncertainties in the FAIR (blue), AR5-IR (red), and
CMIP5 (black) models. (a) shows the temperature responses to a
1 % year-1 concentration increase scenario. The green bar indicates
the IPCC AR5 TCR likely range. The blue shading in (a and b) shows the
response of FAIR under IPCC AR5 upper and lower likely TCR and ECS
ranges. (b) shows the responses to an instantaneous quadrupling of
atmospheric CO2, which is held fixed subsequently. The green bar
indicates the assessed equilibrium warming compatible with the IPCC AR5 ECS
likely range. (c) shows concentrations as a function of cumulative
emissions in the 1 % year-1 scenario. The plumes
in (c and d) show the FAIR simulated response under the IPCC AR5 likely
TCR and ECS ranges, with an additional ±13 % perturbation to the
r0, rT, and rC parameters for the high/low end response. The
dashed grey line indicates a constant cumulative airborne fraction that is
consistent with the present-day state of the climate system (green
diamond). (d) shows warming as a function of cumulative emissions in
the 1 % year-1 scenario. The green bar shows the IPCC AR5 likely
0.8–2.5 K TtC-1 assessed range for transient climate
response to cumulative emissions (TCRE).
![]()
A robust feature of the carbon-cycle response in all ESMs is an increase in
the cumulative airborne fraction over time associated with a saturation of
carbon sinks (upward curving black lines in Fig. c). Unlike the
AR5-IR model, which displays a slowly declining cumulative airborne fraction
over time due to the state-independence of its response function, correlated
and time-invariant perturbations of ±13 % to the r0, rT, and
rC parameters (combined with perturbations to q1 and q2
consistent with the IPCC AR5 likely ranges) in the FAIR model approximately
span the range of responses seen in the CMIP5 models under a
1 % year-1 concentration increase scenario (blue shading in
Fig. c) and display increasing cumulative airborne fraction
over time at both ends of the uncertainty range.
Crucially, the FAIR model also captures the approximately linear relationship
(to first order) between cumulative carbon emissions and human-induced
warming (Fig. d) that was highlighted in the IPCC 5th
Assessment and is becoming an integral part of climate change policy
analysis . When integrated with parameter settings given in
Sect. 2, FAIR has a transient climate
response to cumulative emissions
(TCRE) = 1.3 K TtC-1 (thick blue line in Fig. d). As there is
some downward curvature apparent in the FAIR relationship between warming and
cumulative emissions across the range of cumulative emissions shown in
Fig. d (as also displayed by the CMIP5 ESMs) the numerical
value of the TCRE is only exactly valid for the first 1000 GtC of an
emission injection. Perturbations to the model parameters as described above
(and identical to Fig. c) allow the IPCC AR5 likely TCRE range
of 0.8–2.5 K TtC-1 to be spanned (Fig. d). In contrast,
the AR5-IR model, with a constant airborne fraction, shows a more-pronounced
concave-downward shape in the plot of realised warming against cumulative
carbon emissions, as the decline of the cumulative airborne fraction is
unable to compensate (as it does in more complex models) for the logarithmic
relationship between CO2 concentration and radiative forcing
. The curvature in the relationship between warming and
cumulative emissions in FAIR displays most prominent curvature at high
cumulative emissions, consistent with the behaviour of ESMs
.
Probabilistic sampling in the FAIR model. Grey lines show 300 random
draws from the input parameter distributions, as described in
Sect. . (a) shows the joint distribution of TCR and
ECS. (b) shows warming as a function of cumulative emissions in the
1 % year-1 concentration increase experiment. The brown bar
in (b) represents the IPCC AR5 likely TCRE range. (c) shows the
warming response to a 100 GtC pulse emitted in 2020 on top of the
MAGICC-derived RCP2.6 emissions. The purple dot (a) and
lines (b, c) represent the median parameters of the
distributions.
![]()
Figure shows the combined effect of uncertainty in the FAIR
model parameters, both thermal parameters (the joint distribution of TCR and
ECS is shown in Fig. a) and carbon-cycle feedback parameters.
Representative uncertainty in FAIR parameters (see
Sect. ) propagates into an emergent 5–95 % range
(based on 300 draws from the input parameter distributions) for TCRE
(Fig. b) of 1.0–2.5 K TtC-1 when integrated under a
1 % year-1 CO2 concentration increase scenario
(Fig. b), broadly consistent with the IPCC AR5 likely
range (0.8–2.5 K TtC-1). The temperature anomaly associated with a
100 GtC pulse in 2020 against an RCP2.6 background is shown in
Fig. c. Across the ensemble a range of responses in both
magnitude and shape are observed. However, we consistently observe a rapid
warming on the order of a decade followed by an approximate warming plateau
(at differing values) that persists for a century or more.
Conclusions
In this paper we have presented a simple FAIR climate–carbon-cycle model, which adjusts the carbon-cycle
impulse-response function based on feedbacks from the warming of the climate
and cumulative CO2 uptake through a parameterisation of the 100-year
integrated impulse-response function, iIRF100. We use this metric of
carbon-cycle response as a parallel to those used to assess the thermal
response to radiative forcing, namely the TCR
and the ECS.
We have shown that including both explicit CO2 uptake- and temperature-induced feedbacks is essential to capturing ESM behaviour. Neglecting
temperature-induced feedbacks on the carbon cycle would prevent a simple
climate–carbon-cycle model being able to capture the important dependences of
carbon uptake on warming displayed in radiatively coupled ESM
experiments, largely driven by responses of the land carbon cycle. Similarly,
neglecting CO2 uptake-feedbacks would fail to incorporate
well-understood physical mechanisms governing the response of ocean carbonate
chemistry to anthropogenic CO2 emissions.
Important dependences of the carbon-cycle response to pulse size, background
conditions, and the suppression of temperature-induced feedbacks are generally
well captured by the FAIR model. The inclusion of climate–carbon-cycle
feedbacks in the FAIR model offers an improvement on several simple and
transparent climate–carbon-cycle models that have been proposed for policy
analysis, which either incorporate no feedbacks on the carbon cycle or do not
fully capture the operation of these feedbacks in ESMs. Successfully
emulating the approximate balance between warming-induced and
biogeochemically induced contributions to carbon-cycle feedbacks could be
important for integrated assessment of solar radiation management scenarios
and mitigation scenarios in which the balance of contributions to warming
from CO2 and non-CO2 sources changes significantly in the future.
Throughout this paper we have used iIRF100 as a central metric of the
climate system response. This represents an inherent value choice about the
timescales of the coupled climate–carbon-cycle system prioritised for correct
representation in a simple climate–carbon-cycle model. A time horizon of
100 years captures important aspects of the climate response to a pulse
emission of CO2 relevant over typical economic discounting timescales,
whereas a longer time horizon could be used to prioritise the millennial
timescale response. For studies that are primarily focused on the climate
response over multi-millennial timescales it may be most appropriate to
retune the values of the FAIR model to capture the dependencies shown by
ESMs/EMICs over this time period (e.g. ). However, over
these time periods Earth system feedbacks not simulated in ESMs and EMICs may
become important, questioning the validity of emulating particular aspects of
very long-term ESM behaviour. Although a useful composite metric for the
coupled climate–carbon-cycle system already exists (the TCRE), future studies of carbon cycle
behaviour could usefully report on ranges of iIRF100 and, importantly
for carbon cycle feedbacks, the evolution of this metric over time under
specific emission scenarios in order to isolate the changing response of
the carbon cycle and to enable emulators such as FAIR to span the ranges and
capture the dependencies of iIRF100 that are observed in
state-of-the-art models.
We believe that the FAIR model could be a useful tool for offering a simple
and transparent framework for assessing the implications of CO2
emissions for climate policy analyses. It offers a structure that
replicates the essential physical mechanisms of the climate system's response
to cumulative emissions whilst at the same time can easily be modified to
sample representative climate response uncertainty in either the thermal
climate response component, the unperturbed carbon cycle, or the coupled
climate–carbon-cycle response to anthropogenic CO2 emissions. Tuning of
parameters within FAIR allows the range of ESM behaviour to be emulated
whilst maintaining the physically understood dependency of the carbon-cycle
pulse response on background conditions and pulse size exhibited by a
particular ESM. This model structure could thus be adapted to be an effective
emulator of CMIP6 ESM responses under a variety of scenarios.