Solar radiation management (SRM) has been proposed as a means to reduce
global warming in spite of high greenhouse-gas concentrations and to lower the chance
of warming-induced tipping points. However, SRM may cause economic damages and its
feasibility is still uncertain. To investigate the trade-off between these (economic) gains and
damages, we incorporate SRM into a stochastic dynamic integrated assessment model and
perform the first rigorous cost–benefit analysis of sulfate-based SRM under uncertainty,
treating warming-induced climate tipping and SRM failure as stochastic elements.
We find that within our model, SRM has the potential to greatly enhance future welfare and
merits being taken seriously as a policy option. However, if only SRM and no
CO2 abatement is used, global warming is not stabilised and will exceed 2 K.
Therefore, even if successful, SRM can not replace but only complement
CO2 abatement. The optimal policy combines CO2
abatement and modest SRM and succeeds in keeping global warming below 2 K.
Introduction
Despite the Paris Agreement target to keep global mean temperature change
“well below 2 K” in order to prevent “dangerous climate change”
, no decisive reduction of CO2
emissions has yet taken place . This has sparked
renewed interest in the possibility of cooling the climate system by
geoengineering .
Among several suggested approaches, only solar
radiation management (SRM), i.e. reflecting part of the incoming solar
radiation back into space, has the potential to offset the global
mean temperature changes projected by 2100 .
Several SRM techniques have been proposed ,
although for some of them it is yet unknown whether they will be effective in cooling the planet
and whether they will be technically feasible. The scheme that is most likely to become ripe for
employment in the near future is sulfate-aerosol-based SRM
. The scheme involves injecting
precursor gases such as SO2 into the stratosphere.
This leads to the formation of reflective sulfate aerosols
in the lower stratosphere which increases the Earth's albedo and causes
surface cooling. Such cooling – of about 0.4 K over several years
– was
observed following the Pinatubo eruption ,
which injected 8–10 Mt(S) (megatonnes of sulfur), mainly as SO2,
into the stratosphere . It is
still uncertain whether SRM can completely eliminate future global
warming. High aerosol concentrations lead to faster coagulation, which
reduces albedo and accelerates deposition . One
study suggests that SRM cannot provide a stronger
negative radiative forcing than -2 W m-2, while others find that sufficiently strong
forcing can be achieved, albeit at very high injection rates
.
The potential benefits of SRM are obvious: a reduction of global warming
and warming-induced damages and a reduced
transition likelihood of temperature-related climate tipping points
. However, SRM cannot avert all climate change .
In particular, global mean precipitation is expected to decrease
,
and the spatial precipitation patterns may change.
Ocean acidification will continue unless atmospheric CO2
concentrations are reduced .
The implementation costs of sulfate SRM are estimated to be USD 2–10 billion per megatonne
of injected gas , which is modest
compared to the world GDP of USD 80 trillion (data for 2017;
).
For comparison, building and installing enough solar cells to meet global
energy demand would, at current prices, cost about USD 250 trillion,
although prices are decreasing rapidly .
However, apart from moral issues ,
sulfate SRM may have damaging effects on human health
and the environment that are still poorly understood
. A sudden discontinuation
of SRM will cause rapid warming (“termination shock”) to levels dictated by greenhouse-gas concentrations , which could
put more stress on ecosystems and societies than a gradual warming
.
At least two major uncertainties are of great importance for cost–benefit analysis
of SRM: the possibility of warming-induced tipping behaviour
(whose likelihood is reduced by SRM) and the possibility of SRM failure,
either by inefficiency or because (unforseen) damaging
side effects force one to abandon it . In this study we use a stochastic
version of the integrated assessment model DICE to compute
the (economically) optimal policy including CO2 abatement and SRM.
Here we build on earlier studies, which often included uncertainty only through
parameter sensitivity analysis or as
a simplified two-step decision problem .
Two recent studies include climate
tipping behaviour and parameter uncertainty in DICE but employ a simple four-step look-ahead
scheme that is unsuitable for long-term optimisation. We employ dynamic programming
to perform the first rigorous cost–benefit analysis
of SRM under uncertainty, albeit with a simple model.
The DICE model has been criticised for being overly simple . In
particular, it employs a very aggregated damage function for assessing the material
and immaterial cost of climate change (see , for the calibration),
which ignores irreversibility of damages and delayed damage (e.g. slow melt of ice caps) and which
in later model versions has only received minor updates
despite new studies on the subject
. Neither does it include climate adaptation.
In addition, DICE has an overly simplified energy sector with exogenous costs for CO2
reduction and does not include negative emission techniques. Finally, assuming only one
global “social planner”, it disregards the possibility of conflict or imperfect collaboration.
Despite these shortcomings, we believe DICE to be a useful test bed for exploratory studies,
which should serve as a first orientation and be expanded using more detailed models.
The paper is organised as follows: in Sect.
we present our model GeoDICE, a stochastic DICE model including geoengineering; in Sect. we describe the scenarios employed.
The results are presented in Sect. (deterministic cases) and
Sect. – (stochastic cases) with a sensitivity analysis
in Sect. . A summary and discussion is presented in
Sect. .
MethodsGeoDICE: a stochastic DICE model including geoengineering
Our code is based on , which in turn combines
the 2013 version of DICE and
the DSICE framework for stochastic treatment of DICE.
Here, we include SRM as an additional policy option (together with
CO2 abatement). To this end, we incorporate the cooling
effect, implementation costs, and environmental damages of SRM into DSICE.
A summary of the model parameters and their standard values is given
in Table .
Model parameters of the GeoDICE model
related to the representation of SRM. The carbon model parameters can be found in Table 5 of
, and others in DICE or DSICE .
SymbolMeaningValueαCO2effect CO2 on radiative forcing, see Eq. ()5.35 W m-2αSO2scales sulfate radiative forcing, see Eq. ()65 W m-2βSO2scales sulfate radiative forcing, see Eq. ()2246 Mt(S) yr-1γSO2scales sulfate radiative forcing, see Eq. ()0.23ηsulfate rad. forcing correction, see Eq. ()0.742b1strength temperature response, see Eq. ()0.126 K (J m-2)-1b2strength temperature response, see Eq. ()0.0254 K (J m-2)-1τT1timescale temperature response, see Eq. ()1.89 yearsτT2timescale temperature response, see Eq. ()13.6 yearspTprecipitation dependence on temp., see Eq. ()0.0806 mm d-1 K-1pCprecipitation dependence on CO2, see Eq. ()-0.0229 mm d-1 W-1 m2pSprecipitation dependence on SRM, see Eq. ()-0.0077 mm d-1 W-1 m2ψCecon. damage from CO2 conc., see Eq. ()1.703×10-3 K-2ψTecon. damage from warming, see Eq. ()0.4 (mm d-1)-2ψPecon. damage from precip. change, see Eq. ()3.31×10-8 (ppmv)-2ψSecon. damage from SRM, see Eq. ()9.27×10-5 (Mt(S) yr-1)-2ψfailecon. damage from SRM failure, see Sect. 0.01 (Mt(S) yr-1)-1Ωremaining fraction econ. output after tipping, see Eq. ()0.9λSimplementation cost SRM, see Eq. ()USD 14 billion per megatonne of sulfurλ0cost of abatement, see Eq. ()2.15λ1cost of abatement, see Eq. ()USD 0.418 per kilogram of carbonλ2cost of abatement, see Eq. ()2.0λ3cost of abatement, see Eq. ()0.005 yr-1κtipptipping probability per year and per degree warming, see Eq. ()0.00255 yr-1 K-1Ttipptemperature threshold for (damage) tipping, see Eq. ()2 KTalbtemperature threshold for albedo tipping, see Eq. ()1.5 Kαalbradiative forcing strength for albedo tipping, see Eq. ()1.07 W m-2 K-1κfailprobability of SRM failure per year, see Sect. 0.00056 yr-1ρpure rate of time preference (constant in time), see Eq. ()0.015 yr-1δKrate of capital depreciation, see 0.065 yr-1SRM and radiative forcing
To the radiative forcing equation, we add a contribution that depends sublinearly on
the sulfur injection rate .
The total radiative forcing F takes the form
F=αCO2ln((CPI+C)/CPI)+Fother-ηαSO2×exp[-(βSO2/IS)γSO2]≡FC+Fother+FS.
The first term FC describes the contribution of the increase
C in atmospheric CO2 concentration above the pre-industrial
value CPI and is the same as in DICE. The second term Fother
represents the effects of other greenhouse gases (e.g. CH4, N2O, halogen
compounds) and industrial aerosol. In DICE, this term is prescribed.
However, it seems unlikely that a society that makes great efforts
towards abating CO2 emissions does nothing towards
combatting other pollutants.
quantify various forcing agents, some of which we
believe can be more easily abated than others. In particular, we
assume that roughly 30 % of the current CH4 emissions (contributions
related to fossil fuel production, e.g. leakage and biomass burning),
10 % of the N2O emissions (likewise from industry and fossil fuel
production), and 100 % of the emission of halogen compounds could be
abated, whereas 70 % of the CH4 emissions (natural sources and agriculture)
and 90 % of N2O emissions (agriculture) cannot be abated.
Tropospheric ozone, another important greenhouse gas, is formed in chemical
reactions with pollutants which likewise can be partially abated. As a rough
estimate, about 50 % of the radiative forcing stemming from non-CO2
greenhouse gases could be abated. For simplicity, we assume that
this also holds for (mainly cooling) industrial aerosol. Thus we put
Fother=Fother,DICE×(1-κμ),
where κ=0.5; μ is the abatement of CO2, i.e. the fraction of CO2 emissions avoided;
and Fother,DICE is the prescribed contribution used in DICE.
The third term FS describes the influence of sulfate SRM. The sulfate injection
leads to a (negative) radiative forcing at the top of the atmosphere which
is given by αSO2×exp[(-βSO2/IS)γSO2],
as found in an atmospheric chemistry modelling study ,
where IS is the annual injection rate of sulfur into the stratosphere
(measured in Mt(S) yr-1).
To achieve a modest radiative forcing of -2 W m-2 at the top of the
atmosphere (TOA), an annual injection of 10 Mt(S) (megatonnes of sulfur),
equivalent to one Pinatubo eruption, is required, whereas to achieve a
forcing of -8.5 W m-2 (offsetting the greenhouse-gas forcing projected for 2100
under the RCP8.5 scenario), 100 Mt(S) yr-1 is needed.
However, due to fast adjustment processes, the
TOA radiative forcing is not sufficient to predict
the impact on global mean surface temperature .
For example, it is found that to compensate
7.42 W m-2 forcing from quadrupling CO2, the
solar constant would have to be reduced by (4.2±0.6)%, which
amounts to 10.1 W m-2 at TOA (taking into account
the Earth's albedo). In other words, the top of atmosphere radiative forcing
arising from changes in the solar constant is less efficient than
forcing caused by CO2 by a factor of η=0.742.
We assume here that sulfate SRM has the same efficiency factor η
as solar dimming, since both processes take place above the troposphere,
and multiply the sulfate SRM contribution to F by this factor
in Eq. ().
Note that there is still considerable uncertainty in the forcing efficiency of SRM.
For example, find higher efficiencies and an almost linear relationship
for injection rates up to 25 Mt(S) yr-1, while
suggest that the maximal radiative forcing achievable with sulfate
SRM might be limited to 2 W m-2.
This possibility that SRM is much less efficient is qualitatively included in the
“realistic storyline” scenario described below, which captures that SRM may never work at all.
For numerical reasons, we impose an upper bound of IS≤100 Mt(S) yr-1 on the
injection rates, i.e. we do not allow them to exceed ≈10 Pinatubo eruptions per year.
This upper limit is a much higher injection rate than considered in most detailed studies of
the environmental and climate effects of SRM.
The limit is never reached except in the somewhat extreme SRM-only scenario
(see Sect. ).
Carbon cycle and climate response
We replace the carbon-climate part of DSICE by an emulator of full-fledged climate model
simulations . We also include global mean
precipitation as a proxy for the residual climate change (changes remaining if SRM is
employed to keep global mean temperature constant).
As in DICE, CO2 can be emitted by fossil fuel combustion and land use
change. The former contribution is calculated within our model and the
latter is prescribed externally using the same values as DICE.
We model carbon concentrations based on the Green's function found by
.
Current CO2 concentrations
C(t) (above pre-industrial levels) can be computed from emissions E
at all previous times t′<t:
C(t)=∫t′<tGC(t-t′)E(t′)dt′,
where GC(t-t′) is the Green's function determining how a unit emission
pulse contributes to the concentrations t-t′ years later, and E(t′)
an emission pulse at time t′. Following , GC(s) can be represented as
a sum of exponentials, GC(s)=a0+∑n=1Nase-s/τn with N=3,
and the temporal evolution of C can be rewritten as
3aC(t)=C0(t)+∑n=1NCn(t),3bdC0/dt=a0E,3cdCn/dt=anE-1τnCn.
Here a0 represents the fraction of carbon emissions staying permanently
in the atmosphere. The model parameters an and τn were obtained
from a multi-model study (, see their Table 5) and
thus represent a best estimate for the behaviour of the carbon cycle,
provided that non-linear effects (e.g. saturation of carbon sinks with
increasing CO2 concentrations) are small. The initial values are
C0=39.01, C1=35.84, C2=21.74, and C3=4.14 ppmv, since our
model does not start at pre-industrial times (1765) but in 2005.
For the global mean temperature change (relative to pre-industrial temperature),
we follow the same approach, fitting the temperature response to a
1-year pulse of radiative forcing obtained by a multi-model study
onto a sum of exponentials, obtaining
4aT=T1+T2,4bdTn(t)/dt=bnF-1τTnTn,
where F is the radiative forcing from Eq. ()
and other parameters are in Table . For
the temperature response to a radiative forcing pulse, there is no
permanent response T0. The initial values (year 2005) are T1=0.466
and T2=0.436 K.
The response of global mean precipitation P to CO2-induced
or SRM-induced radiative forcing is based on and can
be split into a slower temperature-driven increase of 2.5% K-1 and an instantaneous
contribution due to CO2 and SRM .
In particular, increased CO2 concentrations cause additional absorption
of longwave radiation, warming the atmosphere and causing a more stable stratification, which
suppresses precipitation, while surface warming enhances precipitation.
For a gradual increase in CO2 and zero SRM, the temperature-driven
effect dominates over the instantaneous contribution, leading to a net moistening.
For SRM, the instantaneous contribution is much weaker than for CO2.
More specifically, the response GPf of the global mean precipitation P to
a 1-year-long 1 W m-2 pulse of radiative forcing from agent f (f stands
for CO2 or a change in the solar constant) in year
0, obtained by , can be expressed as
GPf(t)=bfδt,0+aGT(t),
where GT is the temperature response to a 1 W m-2 forcing
and δt,0=1 if t=0 and 0 otherwise. This means
that in the year of the forcing pulse, the fast response bf
plays a role, whereas in later years the precipitation response is
determined by the temperature response. As before, we use the result
for reduction in the solar constant as a proxy for sulfate SRM. By
lack of data, the fast response to other forcing agents constituting Fother is ignored.
With these results, the change in global mean precipitation w.r.t. pre-industrial precipitation levels can be written as
P(t)=pTT(t)+pCFC(t)+pSFS(t),
where pTT is the slow precipitation change mediated by warming, whereas pCFC and
pSFS are the instantaneous responses expressed in terms of the radiative forcings F.
Throughout our study, FC>0 (CO2 leads to a positive radiative forcing) and
FS<0 (SRM is used to lower the radiative forcing). As explained above, pT>0 and
pC<pS<0. Therefore, if SRM were employed such as to cancel the global
mean temperature change (FS=-FC-Fother, hence T=0),
the slow responses stemming from temperature change would cancel and the
fast response to CO2 would dominate, reducing P.
We use P as a proxy for residual climate change,
i.e. for all effects which remain even if global mean temperature changes are cancelled by SRM.
The damage function and SRM costs
As in DICE , the gross domestic product (GDP) Y‾ is diminished by climate-related damage
and by expenditures for climate policy (CO2 abatement and SRM implementation).
Including these losses, we retain for the net output
Y=Ω11+DΛY‾-λSIS.
Here, Ω describes damage due to tipping
points (see Sect. ). If tipping has occurred,
then Ω=0.9 (reducing the economic output), otherwise Ω=1
(output not reduced). D≥0 describes non-tipping damage (discussed below).
Λ is a factor describing the abatement costs (Λ<1
in case of abatement and Λ=1 in case of no abatement) taken over
from DICE-2013 :
8aΛ(μ)=1-Λ0(t)μλ0,8bΛ0(t)=λ1σ(t)λ2[λ2-1+exp(-λ3t)],
where σ(t) is the carbon intensity (amount of carbon released per dollar production, in
absence of abatement) and λi are constants.
Since CO2 emission is proportional to Y‾, so are
abatement costs (the more economic output, the more CO2 emissions
and hence the higher the costs of eliminating a fraction, μ, of these emissions).
λSIS is the implementation cost of SRM, which
we assume to be linear in the injection rate IS and independent
of Y‾. Two studies
suggest that the costs for lifting gases to 20 km height are of the
order of USD 2–10 billion per megatonne of injected gas. Taking an intermediate
value of USD 7 billion per megatonne, and assuming that the gas used is
SO2 (which has twice the molecular weight of elementary S),
this amounts to USD 14 billion per megatonne of sulfur. Note that H2S
would have a lower weight per mole of S, which might reduce transportation costs. However,
H2S is also more poisonous and thus potentially difficult to handle. To be
conservative, we assumed the costlier solution.
Graphical representation of the damage
function. The thin black arrows represent contributions to the damage
function, while grey arrows depict how the climate variables influence
each other (+ and - stand for increasing and decreasing effects, respectively,
see Eqs. and ).
The percentages for C, T, and P are based on the contributions
of these variables for the standard case of 2.5 K warming in equilibrium
and in absence of SRM. In this standard case, our damage equals that
of the DSICE model . The sulfur injections that
would be needed to offset 2.5 K warming cause a direct damage of 20 % of the
standard damage function.
While the original DICE model assumes that climate-induced damage
D scales with the square of temperature change T2
(i.e. D(T)=ψ0T2
with constant ψ0), we keep the quadratic structure but split
the damage function into three climate-related contributions and one
contribution representing the damage inflicted by sulfate SRM (see
Fig. ):
D(T,P,C,IS)=ψTT2+ψPP2+ψCC2+ψSIS2,
where T, P, and C are the changes (w.r.t. pre-industrial levels) in
global mean temperature, global mean precipitation, and atmospheric
CO2 concentration, respectively, and IS the sulfur
injection rate in megatonnes of sulfur per year (Mt(S) yr-1). Note that while SRM counteracts the effect of
CO2 on both temperature and precipitation, the relative influence of the
forcing agents on both variables differs, so that it is not possible to compensate the
warming and precipitation change at the same time.
Both positive and negative precipitation changes, P,
are considered damaging because both require ecosystems and humanity to adapt.
An increase in atmospheric CO2 may not be damaging in itself, or may even
benefit plant growth , but we consider C as a (rough) proxy for ocean acidification,
which we do not model explicitly.
The coefficients ψ (for values see Table )
are chosen such that for the standard case of 2.5 K warming in equilibrium without
SRM, our total damage equals that of the original DICE model, and the contributions
by T, P, and C are 60 %, 30 %, and 10 %, respectively.
The standard case was determined by running the climate module of GeoDICE
to equilibrium with constant greenhouse-gas concentrations, such as to obtain T=2.5 K.
Following , and approximately in agreement
with RCP (representative concentration pathway) scenarios, it was assumed that other forcing agents (other
greenhouse gases and aerosols constituting Fother) contribute
14 % to the total radiative forcing. These other forcing agents are not assumed
to cause direct damage.
The damages associated with the annual sulfur injections needed to offset
a warming of 2.5 K are assumed to equal 20 % of the standard case damage.
Previous studies likewise split
the damage function, but without including residual climate
change (P).
assume oceanic and atmospheric CO2 to
cause 10 % of the total damage each (20 % in total). However, atmospheric
CO2 is not known to cause substantial direct damage
and may even be beneficial to plant growth , while oceanic CO2
leads to ocean acidification.
As mentioned, we do not explicitly compute oceanic CO2 but reduce total
CO2-related damage to 10 % because half of the total damage in
seems in fact small.
The splitting between T and P is somewhat arbitrary, but is based
on the rough assumption that, although precipitation changes can have a substantial
impact, much of the damage is either determined by temperature (especially
sea level rise, a major contributor) or at least strongly
influenced by it (e.g. hurricanes), hence ψT>ψP. The damage related to SRM
depends on the injection rate, not on the percentage of compensated
greenhouse-gas forcing as was (somewhat unrealistically) assumed in earlier studies .
The choice of ψS is again somewhat arbitrary as virtually
no data on the economic damage of SRM is available. However, our main conclusions
are unaffected by the exact choice of the parameters ψ (see Sect. ).
Tipping points and SRM failure
Climate change may not only lead to smooth and predictable damages
but also induce low-probability, high-impact, and irreversible events
such as a collapse of ice sheets . The chance
of such tipping behaviour is thought to increase with temperature. We
take tipping into account in a stylised way, assuming that
there is one tipping event that, once activated, reduces GDP by 10 %
for all subsequent time steps (i.e. Ω=0.9 in Eq. ).
The likelihood of tipping obeys
Ltipp=0T<Ttipp,(T-Ttipp)×κtippT>Ttipp,
i.e. it is zero if the global mean temperature change T<Ttipp=2 K
but increases linearly with warming above 2 K.
While in the real climate system a sharp threshold might not exist, this choice reflects
political reality in which policy makers set thresholds for dangerous climate change to be avoided.
The constant κtipp is chosen such that in a scenario
where the policy maker uses only abatement and remains unaware of possible
tipping behaviour, the probability of tipping within 400 years is 50 %. This
order of magnitude of the likelihood and damage of tipping is consistent
with earlier studies .
We also take into account the possibility that SRM has to be abolished.
While possible reasons remain speculative at this point, it is not inconceivable that SRM
has an unexpected destructive side effect, such as a massive deterioration of the ozone layer.
We model this by assuming that each year, there is a probability κfail that
SRM may not be applied anymore in the future. The cumulative probability
of SRM failure over 400 years is 20 %.
Failure is assumed irrevocable; once failed, SRM remains unavailable forever.
In the basic scenarios (see Sect. ),
we include no economic damage related to SRM failure, because humanity is
optimistically assumed to realise such dangers and abandon SRM in time (see
the realistic storyline scenario in Sect. and the high SRM failure
damage scenario in Sect. ).
Finally, in the albedo tipping scenario (see Sect. ), we replace the
damage tipping point described above by a tipping point which causes an additional radiative
forcing (thought of as being due to temperature-driven albedo changes),
loosely following . The forcing obeys
Falb=αalbmax(T-Talb,0),
i.e. a positive temperature-dependent forcing occurs if the tipping point is activated and if
T exceeds the threshold Talb=1.5 K. The tipping probability obeys Eq. ()
except that the threshold Ttipp is replaced by Talb. Note that this tipping point is reversible in the
sense that Falb can decrease again if T decreases.
Optimisation and performance measures
As in DICE, we assume that all decisions are made by a single policy maker who
aims to optimise the welfare of the (homogeneous) world population.
As in DICE, welfare depends entirely on consumption.
The economic output is spent on investment,
I=rY, and global consumption, Lc=Y-I, where r is the saving
rate and L and c are the world population and per capita consumption,
respectively. We assume a fixed saving rate of r=22%. The utility u
(which can be thought of as the current happiness of the world population)
depends on c: u=L(c1-γ-1)/(1-γ) with γ=2
and the quantity to be maximised is the expectation value E(W)
of the welfare W (the time-integrated discounted utility):
W=∑tu(t)e-ρt,
where t is (discrete) time and ρ the rate of pure time preference.
The greater ρ, the less the far-future count towards W. The
morally correct value of ρ has been fiercely discussed
. Here, we will not join the
ethical debate on the correct value, but use the standard value of 1.5 %
and perform a sensitivity study with ρ=0.5 (see Sect. ).
The decision variables are the amount of CO2
abatement μ (the fraction of CO2 avoided)
and the sulfur injection rate IS.
The model is integrated in yearly time steps, but the decision variables
μ and IS are changed only once a decade to save computational effort. The
policy (sequence of values for μ and IS) is optimised such as to maximise
the expected welfare, E(W), over a time horizon until 2400, though
the far future is heavily discounted. The optimisation is performed
using dynamic programming (see Appendix).
Once an optimal policy is found, it is evaluated by running an ensemble
of 5000 members with this policy and Monte Carlo realisations of the
stochastic elements (climate tipping and SRM failure).
The best policy is the one yielding the highest expected welfare E(W).
For easier comparison, we define a performance measure based on the
improvement of W under policy π with respect to a no-action policy
(μ=0,IS=0):
ζ(π)=100%×Wπ-W0WAD-W0,
where Wπ, W0, and WAD are the expectation values
over the Monte Carlo ensemble of the welfare
associated with policy π, the no-action case, and the optimal policy for the
deterministic abatement-only case (the policy that would be optimal if the decision
maker may only use abatement and no climate tipping occurs), respectively.
By construction, the relative performance is 100% for abatement-only scenario
in the deterministic case.
Although the objective for the optimisation is the expectation value of the welfare,
it is also interesting to investigate the range of possible welfare outcomes, especially
the worst-case (or at least relatively bad) scenario.
Hence we present two additional performance measures based on the 10th and 90th
percentiles of the welfare Wπ.
Similar to Eq. () we define ζX(π), the X-percentile
relative performance of a policy π as
ζX(π)=100%×Wπ,X-W0WAD-W0,
where Wπ,X is the Xth percentile of the welfare (discounted
cumulated utility) for policy π.
Note that WAD and W0 are still the mean (i.e. not percentiles)
welfare associated with the optimal policy for the
deterministic abatement-only case, and the no-action case, respectively.
Scenarios
In Sect. – we first consider
three stylised policy scenarios. The first is the abatement-only scenario
in which the decision maker is allowed to use CO2 abatement
but no SRM. The second is SRM-only scenario in which the decision maker uses
only SRM until an SRM failure occurs, after which
only abatement may be used. This scenario represents a society which
does not reduce CO2 emissions but relies entirely on SRM (until
it fails). The third is abatement+SRM scenario where the decision maker
can use both abatement and SRM, unless SRM fails, after which only
abatement is used. A no-policy scenario with neither abatement nor SRM serves
as benchmark for performance comparison (see Eqs. and ).
These three standard scenarios are first discussed in a deterministic setting
(Sect. ), i.e. in absence of climate tipping and SRM failure,
before addressing them in the full model with uncertainty
(Sect. ).
While the previous stylised scenarios serve to isolate specific effects,
we also present the realistic storyline (see Sect. ),
which allows for the fact that
it may take time to develop SRM technology, generate a legal framework and public
support, and evaluate associated risks. Also, all these processes may fail or the effectiveness
of SRM might be found to be too low.
Therefore we assume that SRM will become possible only in 2055
and only at 30 % probability.
To be precise, at each time step until 2055, there is an equal probability that
humanity discovers that SRM is impracticable.
In the first decade where SRM is allowed,
there is a 20 % probability of SRM failure, 10 % in the second decade, 5 % in the third decade, and 1 % per decade after that, i.e. after some
decades of testing, failure becomes less likely.
In this scenario, we also investigate the effect of damage in case of SRM failure
(“termination shock”): SRM failure is accompanied
by a one-time reduction of the GDP by a factor 1-ψfailIS, where IS is the
injection rate in megatonnes of sulfur per year (Mt(S) yr-1) and ψfail is given in Table .
Optimal policy and climate model results for the three
stylised scenarios in the deterministic setting. (a) Abatement (fraction of CO2
emissions avoided), (b) SRM (Mt(S) yr-1), (c) atmospheric CO2
concentration (ppmv), and (d) global mean temperature above pre-industrial temperature (K). The dashed blue line represents the abatement-only scenario,
dashed-dotted orange line represents SRM-only scenario, solid green line represents abatement+SRM scenario, and dotted red line
(only panel c and d) represents no climate action (i.e. neither abatement nor
SRM).
Comparison of policies in the deterministic setting
(no tipping, no SRM failure).
abatement-only scenario means that no SRM is used, SRM-only scenario means that no abatement
is used (unless SRM fails see text), and in abatement+SRM scenario both are used.
The performance ζ (see Eq. ) is a measure
of the increase in expected cumulated discounted utility w.r.t. the no-action scenario,
and is normalised such as to yield 100 % for abatement-only scenario.
The column “Peak SRM” contains the highest SRM values (in Mt(S) yr-1) over all time steps.
“Ab 50 %” and “Ab 99 %” show the year in which the abatement reaches
50 % and 99 %, respectively. SCC is the social cost of carbon in the first time step
(measured in USD (in 2005) per tonne of carbon).
* SRM does not peak but keeps increasing until the upper limit of 100 Mt(S) yr-1.
n/a means not applicable.
ResultsThe deterministic case
As a reference, we first consider the deterministic case, i.e. without
SRM failure and tipping points, in the three stylised scenarios (see
Fig. and Table ).
Allowing SRM in addition to abatement delays abatement by 2–3 decades,
but does not replace it (Fig. a).
CO2 concentrations in abatement+SRM scenario (Fig. c)
peak slightly later than in abatement-only scenario and reach higher values (875 ppmv instead
of 741 ppmv). SRM helps to reduce global warming considerably: the
global mean temperature change T peaks at 1.6 K for abatement+SRM scenario
but at 3.1 K for abatement-only scenario (Fig. d).
SRM slightly decreases towards the end of the simulation, when CO2
concentration also goes down. This illustrates the potential use of SRM as a transition
technology, especially under ambitious abatement: SRM can be used for a limited time
in modest strength to cut off a warming overshoot.
In SRM-only scenario, CO2 concentrations reach 2000 ppmv in
2260 and continue to increase (Fig. c). Note
that currently known fossil fuel reserves are insufficient to generate this much carbon,
but it is not impossible that fracking and newly discovered coal deposits will lead to
sufficient fuel resources .
The temperature increase T continues to rise, reaching 5.4 K in 2400
(Fig. d), although it is lower than in the no-action
case (neither SRM nor abatement). Due to the sub-linear increase in the radiative
forcing with SRM, very high SO2 injection rates would be needed to stabilise
T with SRM-only scenario so that the damage related to sulfate injection
outweighs the climate damages. Compared to SRM-only scenario, considerably
less SRM is needed in abatement+SRM scenario, namely ≈35 Mt(S) yr-1
(Fig. b; 3-4 Pinatubo eruptions per year),
yet T remains much lower. This suggests that abatement is required
in order to achieve long-term temperature stabilisation.
The relative performance ζ(π) for SRM-only and abatement+SRM scenarios
becomes 186 % and 238 %, respectively (see Table ).
(By construction, ζ=100% for abatement-only scenario in the deterministic setting.)
The reason for the better performance of SRM-only scenario compared to abatement-only scenario
is that SRM-only scenario yields lower temperatures and a higher utility in
the first two centuries, which contribute most to the cumulative
utility due to discounting. In addition, postponing damage is beneficial
as it allows more time for accumulating capital.
The effect of uncertainties
Comparison of policies in the stochastic setting, i.e.
including climate tipping and SRM failure.
No-action case means that neither abatement nor SRM are used; other scenarios are explained in
Sect. .
The performance measures ζ, ζ10, and ζ90 are given in
Eqs. () and ().
The columns “SRM fail” and “Tipping” show the probability that SRM failure or climate
tipping occurs before 2415. The column “Peak SRM” contains the highest
SRM value (in Mt(S) yr-1) over all time steps and over all
ensemble members. This corresponds to members in which no SRM failure
or climate tipping occurred, at least before the time of the SRM peak.
“Ab 50 %” and “Ab 99 %”
show the year in which the abatement reaches 50 % and 99 %, respectively.
SCC is the social cost of carbon in the first time step (measured in USD (in 2005) per tonne of carbon).
1 SRM does not peak but keeps increasing until the upper limit of 100 Mt(S) yr-1.
2 Tipping can occur but the policy maker ignores this and chooses
the policy which would be optimal in the deterministic (det.) case.
n/a means not applicable.
Tipping risk and policy in the stochastic
setting (i.e. with tipping point and SRM failure). (a) cumulative probability
of tipping for abatement-only scenario (blue dashed line), SRM-only scenario (yellow
dash-dotted) and abatement+SRM scenario (green solid).
(b–l) policy and climate response for the same scenarios (zoomed in on years 2015–2300 to
enhance readability), namely abatement-only
(d, g, j), SRM-only (b, e, h, k), and
abatement+SRM (c, f, i, l) scenarios.
Variables shown are
SRM deployed (b, c); note the different y-axis scale),
abatement fraction (d, e, f),
atmospheric CO2 content in ppmv (g, h, i),
and global mean temperature change (j, k, l); note the different y-axis scale).
The thin blue lines represent a sample of individual ensemble members,
the thick red line the ensemble mean, and the blue shaded area indicates the
range of possible values in the whole ensemble. The dashed blue line
depicts the results from the deterministic case (Fig. )
for reference.
Next we include the stochastic elements, temperature-induced
tipping, and SRM failure, and determine again the optimal policies for each scenario,
prior to evaluating the optimal policy by means of a Monte Carlo ensemble
(see Sect. ).
In Fig. b–l, we plot the policy (abatement and SRM), carbon
concentration, and temperature for the three stylised scenarios.
The plots depict some sample paths of individual
Monte Carlo runs (thin blue lines), the range of possible outcomes (shading) and the
ensemble mean (red line). For comparison, the results from the deterministic case
(compare Fig. ) are also plotted (dashed blue lines).
In the abatement-only scenario, the danger of tipping initially leads
to higher abatement (Fig. d) than in the
deterministic case, although
the temperature is not kept below the 2 K threshold (see Fig. j).
If tipping occurs, the abatement decreases again as there is no further
tipping point to be avoided.
(This effect is caused by having a single tipping point which, once activated, does not
react to system changes. Compare the Albedo tipping point in Sect. .)
The relative performance is 105 %
(see Table , row 3), i.e. it slightly improves when
the decision maker takes tipping into account (compare
Table , row 2). Recall that the reference scenario for
WAD uses the policy that would be optimal in absence of tipping, i.e. the policy
maker ignores climate tipping.
In the abatement+SRM case, the optimal policy closely resembles the deterministic
one if no SRM failure occurs (Fig. c, f). Without
SRM failure, T stays below 2 K (Fig. l)
and hence no tipping occurs.
In case of an SRM failure, the temperature suddenly increases
and abatement suddenly increases, as the decision maker now
tries to limit the warming (and tipping risk) with only abatement.
Note that such a sudden increase in abatement may not be feasible
in reality. If climate tipping occurs, abatement is reduced again.
Compared to abatement-only scenario, the abatement is delayed by 3–4 decades.
In the SRM-only scenario, the policy again resembles the deterministic
case provided no SRM failure occurs and T is below 2 K (Fig. b).
When T=2 K is reached, SRM increases sharply to reduce the tipping risk.
As before, abatement strongly increases after SRM failure, but is
reduced slightly if tipping occurs (Fig. e). SRM-only scenario has a
performance of 181 %, much higher than abatement-only scenario. However, the chance
of climate tipping by the year 2415 is considerably higher for SRM-only scenario (61.0 %
vs. 37.8 % for abatement-only scenario, see Table ). As in the deterministic
setting, the reason is that initially SRM can control the global warming
more effectively than abatement, while abatement is a long-term measure. Hence
damage is postponed to the far future which is heavily discounted.
The cumulative probability of tipping is lower for SRM-only scenario than for
abatement-only scenario until 2350, when the situation reverses
(Fig. a).
Compared to the deterministic cases,
including uncertainty slightly reduces the difference in
relative performance between abatement-only scenario and the scenarios using
SRM (compare Table vs. Table ).
There are two competing effects: the danger of tipping might
favour using SRM, which reduces the tipping probability
in the near future, while the possibility of SRM failure reduces the
performance of SRM-based scenarios.
In abatement-only scenario, there is a high spread between the relative performance measures
ζ, ζ10, and ζ90 compared to SRM-only and abatement+SRM scenarios.
This is due to the fact that in most (>90%) of the ensemble members, SRM
keeps global warming below 2 K at least until ≈2200. Hence SRM
postpones climate tipping into the far future (except in the few ensemble
members with early SRM failure); for abatement-only scenario, tipping can occur
as early as 2080. Early tipping greatly reduces the performance because it reduces the
GDP for a long period of time and because it is less heavily discounted.
For abatement+SRM scenario, only 6.2 % (i.e. <10%) of the ensemble members show climate tipping,
but they strongly affect the mean performance. This explains why, for this scenario,
ζ<ζ10.
Although DICE is too limited to give reliable absolute values of the
social cost of carbon (SCC) , comparing
scenarios gives qualitative insight into how SRM affects the SCC
(Table and Table ).
For abatement-only scenario, the SCC in 2015 is USD 35 per tonne of carbon (in 2005 USD)
in the deterministic case and USD 41 per tonne of carbon when including tipping
points. For abatement+SRM scenario, the SCC is USD 20 per tonne of carbon (both deterministic
and stochastic): SRM lowers the SCC by partially compensating the
damage caused by CO2 emissions. For SRM-only scenario, the
SCC is only slightly higher, namely USD 21 per tonne of carbon (deterministic) and
USD 23 per tonne of carbon (stochastic) because SRM suppresses most climate
damage in the near future, which is discounted least.
Realistic storyline
The previous scenarios were very stylised, in order to isolate the impact of SRM
and stochastic elements. However, the actual situation is more complex: presently
SRM is not available and we do not know whether it ever will be; yet we might want to
decide now whether to pursue (research and development of) SRM.
To address this question, we consider a “realistic storyline” scenario in which we
assume that SRM will become possible only in 2055, and only at 30 % probability
(in the decades before 2055, there is a certain probability each time step that
SRM is declared infeasible, e.g. because scientists identify unacceptable environmental risks).
We also assume that after 2055, the probability of SRM failure decreases in time, i.e. with
ongoing testing, and allow for damage associated with a termination shock
in case of SRM failure (see Sect. ). Unlike (irreversible) climate tipping,
the termination shock is a short-lived phenomenon and is stronger for extensive SRM.
In those ensemble members where SRM becomes available in 2055, it is used sparingly in
the first time step because the probability of failure is still high and the decision maker wants
to limit the termination shock. In later time steps, SRM is used only slightly less than in the
abatement+SRM scenario, peaking at 31.4 % rather than 35 %. This difference mainly arises
because the decision maker wants to reduce the termination shock: if the termination shock
damage is omitted from the realistic storyline, SRM peaks at 34.7 %.
Optimal policy and climate development for the
realistic storyline scenario. (a) Abatement fraction, (b) SRM
in 100 Mt(S) yr-1, (c) atmospheric carbon concentration in ppmv, (d) global mean temperature change w.r.t. pre-industrial temperature.
The thin blue lines represent a sample of individual ensemble members,
the thick red line the ensemble mean, and the blue shaded area indicates the
range of possible values in the whole ensemble. The dashed blue line
depicts the results from a deterministic reference case in which SRM becomes
available in 2055 certainly and neither SRM failure nor climate tipping occur.
In the first time step (2015), when the decision maker assumes that SRM will become available
with 30 % probability only, the abatement μ(2015)=0.17, only slightly less than in the
abatement-only scenario where μ(2015)=0.18. For comparison, in a deterministic reference
case in which SRM will be available from 2055 certainly, and no SRM failure or tipping occurs,
μ(2015)=0.14 (see Fig. ). As time progresses until 2055,
the ensemble members diverge: if SRM is already banned, abatement increases, but if a time
step has passed without a ban, the decision maker becomes more optimistic that SRM will
become feasible and abatement becomes less ambitious. In ensemble members where SRM
becomes available, 50 % abatement is reached 45 years later than in cases where SRM
remains impossible. For current policy, however, the most important point is that in 2015
(“now”), a 30 % chance of SRM becoming available does not lead to significant reduction in
optimal abatement.
On the other hand, the performance, ζ, of this scenario is 125 %
(Table ), significantly higher than for abatement-only scenario.
The lowest 10th percentile performance, ζ10, is very similar to the
abatement-only scenario. In the realistic storyline, the low-performance members
are those in which SRM never becomes available, and the policy (i.e. trajectory
of abatement) in these runs is very similar to abatement-only scenario.
However, ζ90 is much higher for the realistic storyline than
for abatement-only scenario. This measure is dominated by those members in which SRM
becomes available.
The total climate tipping risk for the realistic storyline is 30.1 % compared to 37.8 % in
the abatement-only scenario. The SCC for the realistic storyline is USD 37 per tonne of carbon,
12 % lower than for abatement-only scenario.
These comparisons between the realistic storyline and abatement-only scenario indicate that the
former performs better.
This is because in those cases where SRM does become available, the welfare gain
of climate policy is twice as high as in the abatement-only case.
Therefore, a policy maker in 2015 should not dismiss SRM
prematurely, but keep the option open (by encouraging research and development).
If we are lucky and SRM works well, it can greatly enhance future welfare,
whereas if it never becomes feasible we are not worse off than with abatement-only scenario.
(Note, however, that we did not include the possibility of a large-scale SRM test with huge
unexpected damage, but assumed careful well-designed research.)
However, the prospect of possible future SRM should not lead to a significant reduction in
abatement efforts at the current stage.
SRM as “climate insurance”
In the previous scenarios, SRM was used in a continuous way
as a complement for abatement in order to further reduce global warming,
especially when the warming was highest. Here we investigate under which circumstances
it can be advisable to use SRM as an insurance, i.e. suddenly increase its use
or even voluntarily delay using it at all.
First, we consider a situation in which SRM is very dangerous, and thus unattractive to
use unless climate change is also very dangerous. This is achieved by
assigning a very high, but one-time only, damage to SRM failure, namely reducing capital
by a factor ΩK=IS/(IS+IS0) in case of SRM failure. Here IS is the injection rate
in megatonnes of sulfur per year (Mt(S) yr-1) and IS0=5 Mt(S) yr-1. This means that already at modest injection rates, SRM failure
is assumed to cause substantial capital losses. In addition, we increase
the likelihood of tipping failure by a factor of 4.
Apart from these changes, the scenario is the same as the abatement+SRM
scenario in Sect. .
This scenario is not necessarily considered the most likely but serves as a proof of concept.
The result is that SRM is not started until the tipping threshold T=2 K threatens to be reached
(see Fig. a–c). When the threshold is reached, SRM is started and
somewhat more SRM is applied than strictly necessary to keep below T+2 K.
This is because in our parameterisation, damage levels off somewhat with increasing
injection rate, i.e. if SRM is used at all, then a little extra does not make failure costs that much worse.
The temperature increase is kept below T=2 K throughout, unless SRM fails. Compared to the standard
abatement+SRM case, peak SRM is reduced to 27.6 Mt(S) yr-1, i.e. by about 21 %, and
50 % abatement is reached in 2127, i.e. 12 years earlier.
This experiment shows that the possibility of SRM causing high damage can cause a delay
in its use until climate change also becomes very dangerous (tipping threshold reached).
Policy and temperature for the “SRM as insurance”
scenarios (see Sect. ). The top row shows the scenario with high
damage in case of SRM failure, while the bottom row shows the scenario with an albedo tipping point.
The left column (a, d) show abatement, the middle one (b, e) SRM, and the right (c, f) warming.
The thin blue lines represent a sample of individual ensemble members,
the thick red line the ensemble mean, and the blue shaded area indicates the
range of possible values in the whole ensemble.
Second, we replace the standard tipping point in abatement+SRM scenario
by the “albedo” tipping point (see Sect. ).
It is found that if the policy maker can use SRM freely, they do not employ it to such a degree as
to stay below T=Talb=1.5 K but take the (small) chance of crossing the threshold. If this happens,
they do increase SRM to counteract the albedo feedback (the bump after 2200 in Fig. e).
Although the time step for determining policies is 10 years, the albedo feedback is weak enough that
no runaway global warming occurs since, with SRM, T-Talb and hence Falb is small. This is
why a modest increase suffices to suppress this effect.
However, if SRM has failed, temperature is much higher than Talb, increasing both
the probability of albedo tipping and the radiative forcing strength if tipping occurs.
As in the standard abatement+SRM scenario, the policy maker increases abatement in case
of SRM failure to avoid the tipping point. However, if the albedo tipping occurs after SRM failure,
the policy maker increases abatement yet again in order to limit the positive temperature feedback.
Nonetheless, the albedo tipping can cause additional warming of more than 2 K.
A positive climate feedback tipping point can thus lead to enhanced climate policy – SRM or abatement
or both – after being triggered, in order to reduce its consequences.
Sensitivity analysis
Policy metrics of the sensitivity runs.
“Abate 50%” is the year in which abatement reaches 50 % (μ=0.5).
“Peak SRM” (in Mt(S) yr-1) is the highest SRM value of the ensemble (over all
times and all members) and corresponds to those ensemble members without early
SRM failure or climate tipping. “SCC” is the social cost of carbon in USD(2005) per tonne of carbon.
All simulations were preformed in the stochastic settings and are either abatement-only scenario or abatement+SRM scenario (abbreviated here as Ab.+SRM).
The first two cases, labelled “standard”, are repeated from Table
for convenience. The sensitivity runs correspond to those discussed in Sect. . n/a means not applicable.
ScenarioAbate 50%Peak SRMSCCAbatement-only scenario, standard2095n/a41Ab.+SRM, standard213935.020Abatement-only scenario, low rate of pure time preference (ρ=0.5%)2068n/a70Ab.+SRM scenario, low rate of pure time preference (ρ=0.5%)211631.130Faster decline abatement cost (λ2→2;λ3→0.015)211229.021Ab.+SRM scenario, less temp. damage, more precip.damage (ψT→ψT/2, ψP→ψP×2)214332.617Ab.+SRM scenario, lower tipping threshold (Ttipp=2K→1K)213935.621Ab.+SRM scenario, double damage from tipping (Ω=0.8)213634.820Ab.+SRM scenario, double climate tipping probability (κtipp→κtipp×2)213734.920Ab.+SRM scenario, quadrupled SRM failure probability (κfail→κfail×4)212134.323Ab.+SRM scenario, double damage from SRM (ψS→ψS×2)213326.822Ab.+SRM scenario, half damage from SRM (ψS→ψS/2)214343.620
The results of our model substantially depend on the rate of time preference
ρ (see Sect. ).
In abatement-only scenario, reducing ρ from the standard value of 1.5% to a lower
value of 0.5% will lead to stronger abatement: 50 % abatement is reached
27 years earlier (see Table ). This is expected as a lower rate of
time preference means that the decision maker gives more weight to the welfare of future
generations and is more willing to sacrifice present consumption to reduce climate
change. The SCC rises from USD 41 to USD 70 per tonne of carbon. Interestingly,
abatement also increases in the abatement+SRM scenario (50 % abatement
is reached 23 years earlier) when reducing ρ to 0.5%, while the peak
SRM (definition: see Table ) decreases by about 11 %.
In other words, a decision maker who
cares strongly about the future will choose to reduce CO2
emissions rather than forcing future generations to rely on SRM, which
causes damages and might fail. The SCC rises from USD 20 to
USD 30 per tonne of carbon.
A potentially important limitation of DICE is that abatement costs are exogenous, whereas in reality
one would expect costs to decline with growing employment (learning by doing). While fully exploring
learning by doing is outside the scope of this study, we estimate the sensitivity to abatement costs in a simulation
wherein abatement costs decrease more quickly in time and reach a lower value for t→∞.
This is done by putting λ2=1.5 and λ3=0.015 in Eq. (), which lowers abatement cost by
a factor of about 0.6 after 70 years compared to the standard scenario. The resulting policy shows a
faster abatement by about 30 years, leading to a lower peak in atmospheric carbon (745 ppm instead of 870 ppm).
Peak SRM is reduced to 29 Mt(S) yr-1, as less SRM is needed if carbon concentrations are lower. Thus the development
of abatement cost can significantly affect the need for SRM.
The distribution of the damages between the two major contributors, namely warming and
residual climate change, was chosen rather arbitrarily. However, halving ψT
(warming contribution) and doubling ψP (residual contribution) does not qualitatively affect
our results. A 50 % abatement is reached 4 years later in the abatement+SRM scenario, and
SRM peaks at 32.6 Mt(S) yr-1 instead of 35.0 Mt(S) yr-1,
i.e. the optimal policy still combines a similar abatement with modest SRM.
The SCC drops from USD 20 to USD 17 per tonne of carbon.
Lowering the tipping threshold from 2 to 1 K leads to a 2 % increase in peak SRM,
while not affecting abatement.
Doubling the damages associated with climate tipping (Ω=0.9→Ω=0.8) only
accelerates 50 % abatement by 3 years in the abatement+SRM case and the SCC
remains at USD 20 per tonne of carbon.
Doubling the likelihood of climate tipping (κtipp)
accelerates 50 % abatement by 2 years and likewise does not affect SCC.
Increasing the failure probability of SRM (κfail) by a factor of 4, i.e. such
that SRM failure occurs in 80 % of the ensemble members rather than 20 %,
increases the SCC only by 15 % in the abatement+SRM scenario, i.e. from
USD 20 to USD 23 per tonne of carbon. The reason is that the likelihood of SRM failure
in the first decades, which are least discounted, is still fairly
small. The peak SRM is reduced only by 2 %: as long as SRM is
available, it is used despite high failure probability. A 50 % abatement is reached in
2121, rather than 2138, in the ensemble mean.
Doubling the damage associated with SRM (i.e. doubling ψS) accelerates 50 %
abatement by 6 years and the SCC rises from USD 20 to USD 22 per tonne of carbon. The peak
SRM is reduced by about 23 %, to 26.8 Mt(S) yr-1.
Likewise, halving ψS increases peak abatement by 25 %.
Hence even if SRM is twice (or half) as damaging as assumed in the standard case, the optimal
policy still employs modest SRM as a complement to abatement.
To summarise, changes in the damage function and/or likelihood of stochastic events
do not qualitatively affect the optimal policy in the abatement+SRM scenario,
which consists of a combination of reasonably high abatement (delayed by a few
decades w.r.t. abatement-only scenario in the standard settings) and modest SRM.
Summary and discussion
In this paper, we present the first cost–benefit analysis of SRM under uncertainty
performed with a rigorous optimisation approach (dynamic programming).
From our analysis we draw two conclusions. First, sulfate SRM has
the potential to greatly enhance future welfare and should therefore
be taken seriously as a possible policy option. Second, even if successful, SRM does
not replace CO2 abatement, but complements it.
In particular, a policy maker who puts great value on the welfare of future generations
(i.e. uses a low rate of pure time preference) will accelerate abatement efforts, which
have a long-term benefit rather than forcing later generations to rely on SRM.
Apart from smoothly reducing peak warming, SRM might also have a role to play as
emergency measure, e.g. in case of emerging positive warming feedbacks or unforeseen strong
climate-induced damages. However, this might be a risky approach if SRM itself is potentially
associated with strong damages.
Compared to previous studies ,
our results are more optimistic about SRM, which seems partly due
to the improved methodology we adopted. For instance, demonstrating
that welfare is severely impacted if the decision maker makes wrong assumptions
on the SRM-related damages
is not a consistent cost–benefit analysis.
The analysis by only considers a full replacement
of abatement by SRM rather than a complementary approach. Compared
to , we find a much stronger reduction
in the SCC. However, as discussed previously, their model and optimisation method
differ in some crucial points from ours.
In particular, assume that the implementation cost and damage
associated with SRM depend on the fraction of CO2-induced radiative forcing that is balanced by SRM –
no matter how high the CO2 concentration is – rather than letting costs and damage depend
on the amount of sulfur injected. Therefore at high (low) CO2 concentrations,
they obtain a much higher (lower) radiative forcing effect from SRM for the same price, which makes
SRM more (less) attractive. In their deterministic simulation, they compensate 50 % of the peak CO2-induced
radiative forcing of 6 W m-2, which in our model settings would require an injection rate of 27 Mt(S) yr-1 –
about 80 % of our peak injection rate of 35 Mt(S) yr-1 in the deterministic abatement+SRM scenario.
However, for the first century, use considerably less SRM because
they overestimate the price by ignoring that much lower injection rates are needed while CO2
concentrations are low. So overall they use too little SRM and therefore end up with higher temperatures
(about 2.5 K peak warming) and a higher SCC.
Our results should not be interpreted as precise policy recommendations
to set, for example, exact values of the SCC, as our
model is too limited to offer more than a qualitative
exploration and comparison of simple scenarios. For example, uncertainty
in the climate system is limited to one tipping point, while uncertainty
in the climate sensitivity is ignored. Our climate model is based on linear
response theory and although this approach captures many climate feedbacks
adequately, it does not capture the possible dependence of the response on the
background state, e.g. a saturation of carbon sinks .
A controversial component in integrated assessment models such as DICE
is the quantification of climate damages ,
which is highly aggregated and based on very limited data. We introduced additional
parameters to the damage function by making a plausible, but rather ad hoc, attribution
of climate damages to temperature, global precipitation (“residual
climate change”), and CO2 concentrations. Also,
little is known about the size of ecological, let alone economic,
damages associated with SRM. Gaining a better understanding of these
damages, and those related to climate change, is essential for conducting
a meaningful cost–benefit analysis and ultimately determining a climate policy,
hence it should be given a high priority.
The abatement sector of DICE also has important limitations.
First, technological improvement is exogenous (abatement costs decrease in time
at a prescribed rate) rather than including learning by doing (costs decrease with
technology employment). This means that in DICE it is advantageous to wait for the
later cost reduction, rather than starting early to bring abatement price down through learning.
In addition, DICE assumes that abatement is always costly, whereas in fact the energy
transition might rather be a big investment: once the infrastructure is installed, green energy
might be cost-competitive with fossil fuels. Both effects likely bias our results
against early abatement.
A faster (still exogenous) decrease in abatement costs was found to lead to faster abatement
and reduced peak SRM.
Our model does not include negative emission techniques, which might provide
an important alternative to SRM. Neither does it include active adaptation. The trade-off
between negative emissions, adaptation, and SRM would be interesting to study with a
more detailed model.
Finally, DICE assumes a homogenous economy and a single decision maker. In reality, the
damages and benefits of SRM are likely unevenly distributed, with potential for solitary
actions and conflict, which was not studied here.
Despite the large scientific and political uncertainties which need
to be overcome, we believe that one cannot afford to dismiss SRM at
the current stage as it has the potential to greatly reduce climate
risk and enhance future welfare. However, the scientific uncertainties,
especially concerning efficiency and damages of SRM, and the extent
to which SRM can mitigate damages inflicted by global warming must be better quantified.
For the time being, the uncertain prospect of SRM becoming available should not tempt
us to reduce abatement.
Data availability
The code used (described in the Methods section) is available upon request from the corresponding author.
Solving the GeoDICE modelTerminal function
Unrealistic behaviour occurs in the last time steps of an optimisation
problem because the decisions made do not influence the future anymore
(as the future is not simulated). To avoid this problem, we follow
and run the optimisation
over 600 years, only considering the first 400 as actual simulation and
the final 200 years as “terminal function”. During termination, tipping can still
occur and SRM can be freely chosen, while abatement is set to 1.
Due to discounting, the trajectory after 600 years has little relevance
for the optimal policy during the first 400 years. Indeed, prolonging
the runs to 800 years had a negligible effect on policies during the
first 400 years.
Optimisation method
The social planner problem aims at finding the policy that maximises
the expected cumulative discounted utility. To solve this problem
in the stochastic setting, we apply dynamic programming .
This methodology relies on the concept of the value function to obtain
the optimal policy via backward reduction. As our state space is continuous
and no analytic solution is available, we are forced to adopt some
approximation scheme to represent the value function at each time
step. Following , we use a Chebyshev
approximation, which is well suited for parallelisation. The Chebyshev
polynomial is obtained by solving a small optimisation problem at
each of a finite number of regularly spaced Chebyshev approximation
nodes. We used a fourth-degree Chebyshev polynomial with five approximation
nodes per continuous dimension. In combination with the binary state
variables for the tipping point and SRM failure, this results in 312 500
approximation nodes per time step. This method is developed and discussed
extensively in the work by and .
For a complete overview we refer the reader to these papers and the
references therein. Here we outline the methodological choices specific
to the present application: the boundaries used for the domain of
the Chebyshev polynomial and adjustments to the value function approximation
to accommodate the asymmetry and non-smoothness of the true value
function. Additionally, we examine the accuracy of this methodology
when applied in the current setting.
Boundaries
In order to define the Chebyshev approximation nodes, we must first
set the boundaries of the region of state space in which we are interested.
To do this, we calculate three trajectories in the deterministic model:
first the optimal trajectory (obtained by optimising the whole system in all
decision variables with standard deterministic optimisation software);
second a “high-emission”
trajectory calculated by setting mitigation and SRM to zero for the
whole run; and third a “low-emission”
trajectory calculated by setting mitigation to one and SRM to zero
for the whole run. We subsequently take as domain boundaries for each
variable the minimum and maximum over these three trajectories, with
an additional margin of minus and plus 30 % of these values.
For all experiments, we check that all the sample paths in the ensemble
remained well within the boundaries of the domain. For approximation
nodes close to the boundaries, it will still be possible to select
actions that may bring the system outside the boundaries in the next
step. Since a Chebyshev polynomial cannot be extrapolated outside
its domain, we first project the state onto the region of interest
before evaluating the approximate value function.
Value function smoothing
In the current setting, directly using a Chebyshev polynomial to approximate
the value function gives poor results because the value function exhibits
an asymmetry and a non-smoothness that a low-degree Chebyshev polynomial
cannot capture.
The discontinuity is caused by the fact that in states with positive
temperatures, SRM is available to reduce them, while in states with
negative temperatures this is impossible; therefore, positive temperature
deviations are preferred over negative temperature deviations of equal
magnitude. This problem is resolved by allowing reverse
SRM, which generates a radiative forcing of the same magnitude but
opposite sign as regular SRM. Allowing such actions changes the value
of certain states, thus removing the asymmetry. This is a purely mathematical
construct (we do not assume such reverse SRM is actually possible):
the states with modified values are never reached in actual trajectories,
and are only considered in the first place because the domain of the
Chebyshev approximation must be a hypercube.
The non-smoothness results from the fact that the tipping point can
only be crossed after a certain threshold is reached: this generates
a discontinuity in the first derivative of the value function. This
is resolved by fitting two separate Chebyshev polynomials to the two
parts of the value function.
Accuracy
We test the accuracy of our optimisation by comparing the resulting
policy in a deterministic setting to the policy obtained by regular
non-linear optimisation. The difference in action and trajectory is
<3 %, while the difference in the SCC is <2 %. For the scenario
in which only abatement is allowed, errors are lower (0.1 %–1 %
for actions and SCC, 0.01 %–0.1 % for trajectories), which
is in line with the accuracy reported by .
Good accuracy in the deterministic setting may not generalise to the
stochastic setting when the stochasticity itself introduces issues.
To guard against this problem we ensure that the value function approximation
fits well to the actual value function samples obtained at each time
step.
Author contributions
All authors conceived the research. CEW and KGH designed the model
and scenarios and interpreted results. KGH performed simulations.
All authors contributed to writing the paper.
Competing interests
The authors declare that they have no conflict of interest.
Financial support
Claudia E. Wieners is supported by the
Complexity Lab Utrecht (CLUe) of the Centre for Complex Systems
Studies at Utrecht University. Henk A. Dijkstra acknowledges
support by the Netherlands Earth System Science Centre (NESSC),
financially supported by the Ministry of Education, Culture and Science
(OCW) (grant no. 024.002.001).
Review statement
This paper was edited by Ben Kravitz and reviewed by Michael MacCracken and one anonymous referee.
References
Ackerman, F.: Debating Climate Economics: The
Stern Review vs. Its Critics, Report to Friends of the Earth-UK, 1–25,
2007.Aengenheyster, M., Feng, Q. Y., van der Ploeg, F., and Dijkstra, H. A.: The point of no return for climate action: effects of climate uncertainty and risk tolerance, Earth Syst. Dynam., 9, 1085–1095, 10.5194/esd-9-1085-2018, 2018.Ahlm, L., Jones, A., Stjern, C. W., Muri, H., Kravitz, B., and Kristjánsson, J. E.: Marine cloud brightening – as effective without clouds, Atmos. Chem. Phys., 17, 13071–13087, 10.5194/acp-17-13071-2017, 2017.Andrews, T., Forster, P. M., Boucher, O.,
Bellouin, N., and Jones A.: Precipitation, radiative forcing and global
temperature change, Geophys. Res. Lett., 37, L14701, 10.1029/2010GL043991, 2010.Auffhammer, M.:
Quantifying Economic Damages from Climate Change, J. Econ. Persp.,
32, 33–52, 10.1257/jep.32.4.33, 2018.Bahn, O., Chesney, M., Gheyssens, J., Knutti,
R., and Pana, A. C.: Is there room for geoengineering in the optimal
climate policy mix?, Environ. Sci. Policy, 48, 67–76,
10.1016/j.envsci.2014.12.014, 2015.
Bellman, R.: Dynamical Programming, Princeton
University Press, Princeton, NJ, USA, 1957.Brovkin, V., Petoukhov, V., Claussen, M., Bauer,
E., Archer, D., and Jaeger, C.: Geoengineering climate by stratospheric
sulfur injections: Earth system vulnerability to technological failure,
Climatic Change, 92, 243–259, 10.1007/s10584-008-9490-1, 2009.
Cai, Y.: Dynamic Programming and its Application
in Economics and Finance, PhD Thesis, Stanford University, 2009.Cai, Y., Judd, K. L., and Lontzek, T. S.: DSICE: A Dynamic Stochastic Integrated Model of Climate and Economy, RDCEP Working Paper No. 12-02, SSRN, 10.2139/ssrn.1992674, 2012.Cai, Y., Judd, K. L., and Lontzek, T. S.: Continuous-Time
Methods for Integrated Assessment Models, Working Paper 18365, National
Bureau of Economic Research, available at:
http://www.nber.org/papers/w18365, last access: May 2012.Cai, Y., Judd, K. L., Lenton, T. M., Lontzek, T. S.,
and Narita, D.: Environmental tipping points significantly affect the
cost-benefit assessment of climate policies, P. Natl. Acad. Sci. USA, 112, 4606–4611,
10.1073/pnas.1503890112, 2015.Cai, Y., Lenton, T. M., and Lontzek, T. S.: Risk of
multiple interacting tipping points should encourage rapid CO2
emission reduction, Nat. Clim. Change, 6, 520–525, 10.1038/nclimate2964, 2016.
Cassedy, E. S. and
Grossmann, P. Z.: Introduction to Energy – Resources, Technology, and Society, Third edition,
Cambdrige University Press, Cambridge, UK, 2017.
Ciais, P., Sabine, C., Bala, G., Bopp, L., Brovkin, V.,
Canadell, J., Chhabra, A., DeFries, R., Galloway, J., Heimann, M., Jones, C.,
Le Quéré, C., Myneni, R. B., Piao, S., and Thornton, P.: Carbon and
Other Biogeochemical Cycles, in: Climate Change 2013: The Physical
Science Basis, Contribution of Working Group I to the Fifth Assessment
Report of the Intergovernmental Panel on Climate Change, edited by: Stocker,
T. F., Qin, D., Plattner, G.-K., Tignor, M., Allen, S. K., Boschung, J.,
Nauels, A., Xia, Y., Bex, V., and Midgley, P. M., Cambridge University
Press, Cambridge, United Kingdom and New York, NY, USA, 2013.Crutzen, P. J.: Albedo enhancement by stratospheric
sulfur injections: A contribution to resolve a policy dilemma?, Climatic
Change, 77, 211–219, 10.1007/s10584-006-9101-y, 2006.Effiong, U. and Neitzel, R. L.: Assessing the
direct occupational and public health impacts of solar radiation management
with stratospheric aerosols, Environ. Health, 15, 1–9,
10.1186/s12940-016-0089-0, 2016.Gabriel, C. J., Robock, A., Xia, L., Zambri, B., and Kravitz, B.: The G4Foam Experiment: global climate impacts of regional ocean albedo modification, Atmos. Chem. Phys., 17, 595–613, 10.5194/acp-17-595-2017, 2017.Goes, M., Tuana, N., and Keller, K.: The economics
(or lack thereof) of aerosol geoengineering, Climatic Change, 109,
719–744, 10.1007/s10584-010-9961-z, 2011.Heutel, G., Moreno-Cruz, J., and Shayegh, S.: Climate
tipping points and solar geoengineering, J. Econ. Behav.
Organ., 132, 19–45, 10.1016/j.jebo.2016.07.002, 2016.Heutel, G., Moreno-Cruz, J., and Shayegh, S.: Solar
Geoengineering, Uncertainty, and the Price of Carbon, J. Environ.
Econ. Manag., 87, 24–41, 10.1016/j.jeem.2017.11.002, 2018.Howard, P.: Omitted Damages: What's missing from
the Social Cost of Carbon, available at: https://costofcarbon.org/files/Omitted_Damages_Whats_Missing_From_the_Social_Cost_of_Carbon.pdf (last access: 27 November 2017), 2014.
IPCC, 2014: Climate Change 2014:
Impacts, Adaptation, and Vulnerability, Part A: Global and Sectoral Aspects,
Contribution of Working Group II to the Fifth Assessment Report of the
Intergovernmental Panel on Climate Change, 2014.Irvine, P. J., Kravitz, B., Lawrence, M. G., Gerten, D.,
Caminade, C., Gosling, S. N., Hendy, E. J., Kassie, B. T., Kissling, W. D., Muri, H., Oschlies, A., and Smith, S. J.:
Towards a comprehensive climate impacts assessment of solar geoengineering, Earth's
Future, 5, 93–106, 10.1002/2016EF000389, 2017.Joos, F., Roth, R., Fuglestvedt, J. S., Peters, G. P., Enting, I. G., von Bloh, W., Brovkin, V., Burke, E. J., Eby, M., Edwards, N. R., Friedrich, T., Frölicher, T. L., Halloran, P. R., Holden, P. B., Jones, C., Kleinen, T., Mackenzie, F. T., Matsumoto, K., Meinshausen, M., Plattner, G.-K., Reisinger, A., Segschneider, J., Shaffer, G., Steinacher, M., Strassmann, K., Tanaka, K., Timmermann, A., and Weaver, A. J.: Carbon dioxide and climate impulse response functions for the computation of greenhouse gas metrics: a multi-model analysis, Atmos. Chem. Phys., 13, 2793–2825, 10.5194/acp-13-2793-2013, 2013.Keller, D. P., Feng, E. Y., and Oschlies, A.: Potential
climate engineering effectiveness and side effects during a high carbon
dioxide-emission scenario, Nat. Commun., 5, 3304, 10.1038/ncomms4304, 2014.Kleinschmitt, C., Boucher, O., and Platt, U.: Sensitivity of the radiative forcing by stratospheric sulfur geoengineering to the amount and strategy of the SO2injection studied with the LMDZ-S3A model, Atmos. Chem. Phys., 18, 2769–2786, 10.5194/acp-18-2769-2018, 2018.Kravitz, B., Caldeira, K., Boucher, O., Robock, A., Rasch, P. J., Alteskjær, K.,
Bou Karam, D., Cole, J. M. S., Curry, C. L., Haywood, J. M., Irvine, P. J., Ji, D., Jones, A., Kristjánsson, J. E., Lunt, D. J., Moore, J. C.,
Niemeier, U., Schmidt, H., Schulz, M., Singh, B., Tilmes, S., Watanabe, S., Yang, S., and Yoon, J.-H.: Climate model response from
the Geoengineering Model Intercomparison Project (GeoMIP), J. Geophys.
Res.-Atmos. 118, 8320–8332, 10.1002/jgrd.50646, 2013.Kravitz, B., MacMartin, D. G., Rasch, P. J.,
and Jarvis, A. J.: A new method of comparing forcing agents in climate
models, J. Climate, 28, 8203–8218, 10.1175/JCLI-D-14-00663.1, 2015.Latham, J., Rasch, P., Chen, C.-C., Kettles, L., Gadian, A., Gettelman, A.,
Morrison, H., Bower, K., and Chourlaton, T.: Global temperature stabilization
via controlled albedo enhancement of low-level maritime clouds, Philos.
T. R. Soc. A, 366, 3969–3987, 10.1098/rsta.2008.0137, 2008.
Lemoine, D. and Traeger, C., Watch Your Step: Optimal Policy in a
Tipping Climate, Am. Econ. J.-Econ. Polic., 6, 137–166, 2014.Le Quéré, C., Andrew, R. M., Friedlingstein, P., Sitch, S., Pongratz, J., Manning, A. C., Korsbakken, J. I., Peters, G. P., Canadell, J. G., Jackson, R. B., Boden, T. A., Tans, P. P., Andrews, O. D., Arora, V. K., Bakker, D. C. E., Barbero, L., Becker, M., Betts, R. A., Bopp, L., Chevallier, F., Chini, L. P., Ciais, P., Cosca, C. E., Cross, J., Currie, K., Gasser, T., Harris, I., Hauck, J., Haverd, V., Houghton, R. A., Hunt, C. W., Hurtt, G., Ilyina, T., Jain, A. K., Kato, E., Kautz, M., Keeling, R. F., Klein Goldewijk, K., Körtzinger, A., Landschützer, P., Lefèvre, N., Lenton, A., Lienert, S., Lima, I., Lombardozzi, D., Metzl, N., Millero, F., Monteiro, P. M. S., Munro, D. R., Nabel, J. E. M. S., Nakaoka, S.-I., Nojiri, Y., Padin, X. A., Peregon, A., Pfeil, B., Pierrot, D., Poulter, B., Rehder, G., Reimer, J., Rödenbeck, C., Schwinger, J., Séférian, R., Skjelvan, I., Stocker, B. D., Tian, H., Tilbrook, B., Tubiello, F. N., van der Laan-Luijkx, I. T., van der Werf, G. R., van Heuven, S., Viovy, N., Vuichard, N., Walker, A. P., Watson, A. J., Wiltshire, A. J., Zaehle, S., and Zhu, D.: Global Carbon Budget 2017, Earth Syst. Sci. Data, 10, 405–448, 10.5194/essd-10-405-2018, 2018.
Lilley, P.: The Failings of the Stern Review
of the Economics of Climate Change, The Global Warming Policy Foundation
(GWPF) Report 92012, 2012.MacMartin, D. G. and Kravitz, B.: Dynamic climate emulators for solar geoengineering, Atmos. Chem. Phys., 16, 15789–15799, 10.5194/acp-16-15789-2016, 2016.Matthews, H. D. and Caldeira, K.: Transient
climate-carbon simulations of planetary geoengineering, P. Natl.
Acad. Sci. USA, 104, 9949–9954, 10.1073/pnas.0700419104, 2007.McClellan, J., Keith, D., and Apt, J.: Cost
analysis of stratospheric albedo modification delivery systems, Environ.
Res. Lett., 7, 034019, 10.1088/1748-9326/7/3/034019, 2010.Moreno-Cruz, J. B. and Keith, D. W.: Climate
policy under uncertainty: A case for solar geoengineering, Climatic
Change, 121, 431–444, 10.1007/s10584-012-0487-4, 2013.Moriyama, R., Sugiyama, M., Kurosawa, A., Masuda, K.,
Tsuzuki, K., and Ishimoto, Y.: The cost of stratospheric climate engineering revisited, Mitig.
Adapt. Strateg. Glob. Change, 22, 1207, 10.1007/s11027-016-9723-y, 2017.
Myhre, G., Shindell, D., Bréon, F.-M., Collins, W., Fuglestvedt, J., Huang, J., Koch, D., Lamarque, J.-F., Lee, D., Mendoza, B., Nakajima, T., Robock, A., Stephens, G., Takemura, T., and Zhang, H: Anthropogenic and Natural Radiative Forcing, in: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, edited by: Stocker, T. F., Qin, D., Plattner, G.-K., Tignor, M., Allen, S. K., Boschung, J., Nauels, A., Xia, Y., Bex, V., and Midgley, P. M., Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 2013.Niemeier, U. and Timmreck, C.: What is the limit of climate engineering by stratospheric injection of SO2?, Atmos. Chem. Phys., 15, 9129–9141, 10.5194/acp-15-9129-2015, 2015.Niemeier,
Niemeier, U. and Schmidt, H.: Changing transport processes in the stratosphere by radiative heating of sulfate aerosols, Atmos. Chem. Phys., 17, 14871–14886, 10.5194/acp-17-14871-2017, 2017.
Nordhaus, W. D.:
The “DICE”
Model: Background and Structure of a Dynamic Integrated Climate–Economy
Model of the Economics of Global Warming, Cowles Foundation Discussion
Paper No. 1009, Cowles Foundation for Research in Economics: New Haven,
CT, 1992.
Nordhaus, W. D. and Boyer, J.:, Warming the World
– Economic models of Global Warming, The MIT Press, 2000.Nordhaus, W. D.:
Evolution of Modeling of the Economics of Global Warming:
Changes in the DICE model, 1992–2017,
Climate Change, 148, 623–40, 10.1007/s10584-018-2218-y, 2018.Pindyck, R. S.: The Use and Misuse of
Models for Climate Policy, Rev. Env. Econ. Policy, 11, 100–114,
10.1093/reep/rew012, 2017.Pitari, G., Aqula, V., Kravitz, B., Robock, A.,
Watanabe, S., Cionni, I., De Luca, N., Di Genova, G., Mancini, E., and Tilmes, S.: Stratospheric ozone response
to sulphate geoengineering: Results from the Geoengineering Model
Intercomparison Project (GeoMIP), J. Geophys. Res.-Atmos., 119, 2629–2653,
10.1002/2013JD020566, 2014.Robock, A.: Volcanic eruptions and climate, Rev.
Geophys., 38, 191–219, 10.1029/1998RG000054, 2000.Robock, A., Marquardt, A., Kravitz, B., and Stenchikov,
G.: Benefits, risks, and costs of stratospheric geoengineering, Geophys.
Res. Lett., 36, L19703, 10.1029/2009GL039209, 2009.Seneviratne, S. I., Phipps, S. J., Pitman, A. J., Hirsch, A. L.,
Davin, E. L., Donat, M. G., Hirschi, M., Lenton, A., Wilhelm, M., and Kravitz, B.: Land radiative
management as contributor to regional-scale climate adaptation and
mitigation, Nat. Geosci., 11, 88–96, 10.1038/s41561-017-0057-5, 2018.Stenchikov, G. L., Kirchner, I., Graf, H.-F., Antuña, J. C.,
Grainger, R. G., Lambert, A., and Thomason, H: Radiative forcing
from the 1991 Mount Pinatubo volcanic eruption, J. Geophys. Res.,
103, 13837–13857, 10.1029/98JD00693, 1998.
Stern, V., Peters, S., Bakhshi, V., Bowen, A., Cameron, C., Catovsky, S., Crane, D., Cruickshank, S., Dietz, S., Edmondson, N., Garbett, S.-L., Hamid, L., Hoffman, G., Ingram, D., Jones, B., Patmore, N., Radcliffe, H., Sathiyarajah, R., Stock, M., Taylor, C., Vernon, T., Wanjie, H., and Zenghelis, D.: The Stern Review, Government
Equalities Office, Home Office, 2007.Stowe, L. L., Carey, R. M., and Pellegrino, P. P.: Monitoring
the Mt. Pinatubo aerosol layer with NOAA/11 AVRHH DATA, Geophys. Res.
Lett. 19, 159–162, 10.1029/91GL02958, 1992.Thompson, W. J., Wallace, J. M., Jones,
P. D., and Kennedy, J. J.: Identifying Signatures of Natural Climate
Variability in Time Series of Global-Mean Surface Temperature: Methodology
and Insights, J. Climate, 22, 6120–6141, 10.1175/2009JCLI3089.1, 2009.Tilmes, S., Richter, J., Kravitz, B., MacMartin, D. G.,
Mills, M. J., Simpson, I. R., Glanville, A. S., Fasullo, J. T., Phillips, A. S., Lamarque, J.-F.,
Tribbia, J., Edwards, J., Mickelson, S., and Ghosh, S.: CESM1(WACCM) Stratospheric
Aerosol Geoengineering Large Ensemble (GLENS) project, B. Am.
Meteorol. Soc., 99, 2361–2371, 10.1175/BAMS-D-17-0267.1, 2018.
Tjiputra, J. F., Grini, A., and Lee, H.: Impact
of idealized future stratospheric aerosol injection on the large-scale
ocean and land carbon cycles, J. Geophys. Res.-Biogeo., 121, 2–27,
10.1002/2015JG003045, 2016.Trisos, C. H., Amatulli, G., Gurevitsh, J., Robock, A.,
Xia, L., and Zambri, B.: Potentially dangerous
consequences for biodiversity of solar geoengineering implementation
and termination, Nat. Ecol. Evol. 2, 475–482,
10.1038/s41559-017-0431-0, 2018.
UNFCCC: Adoption of the Paris Agreement,
United Nations Framework Convention on Climate Change, United Nations
Office, Geneva, Switzerland, 2015.van den Bergh, J. C. J. M. and Botzen, W. J. W.:
Monetary valuation of the social cost of CO2 emissions: a critical
survey, Ecol. Econ., 114, 33–46, 10.1016/j.ecolecon.2015.03.015, 2015.Visioni, D., Pitari, G., and Aquila, V.: Sulfate geoengineering: a review of the factors controlling the needed injection of sulfur dioxide, Atmos. Chem. Phys., 17, 3879–3889, 10.5194/acp-17-3879-2017, 2017.Ward, P. L.: Sulphur dioxide initiates global climate
change in four ways, Thin Solid Films, 517, 3188–3203,
10.1016/j.tsf.2009.01.005, 2009.World Bank: available at: https://data.worldbank.org/indicator/NY.GDP.MKTP.KD (last access: 5 July 2019), 2017.