Rapid and extensive warming following cessation of solarradiation management

Kelly E. McCusker*1, Kyle C. Armour2, Cecilia M. Bitz1, & David S. Battisti1

1Department of Atmospheric Sciences, University of Washington, Seattle, WA 98195

2Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technol-

ogy, Cambridge, MA 02139

Solar radiation management (SRM) has been proposed as a means to alleviate the climate

impacts of ongoing anthropogenic greenhouse gas (GHG) emissions. However, the efficacy of

this strategy depends on our ability to maintain SRM indefinitely, without interruption from

a variety of possible sources, such as technological failure, global cooperation breakdown,

or negative unintended consequences. Here, we consider the scenario in which SRM — via

stratospheric aerosol injection — is terminated abruptly following a multi-decadal period of

implementation during which anthropogenic GHG emissions have continued. We show that

upon cessation of SRM, an abrupt, spatially broad, and sustained warming over land occurs

that is well outside familiar 20th century bounds of climate variability. We further show

that the rate of warming from SRM cessation — of critical importance for ecological and

human systems — is principally controlled by the background GHG concentrations. Thus, a

risk of abrupt and dangerous warming is inherent to the large-scale implementation of SRM,

and this risk can be diminished only through concurrent strong reductions in anthropogenic

GHG emissions.

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Stratospheric aerosol injection has emerged as one of the most promising SRM techniques

because of its technological and economic feasibility and potential to swiftly avoid impending

climate emergencies1. Moreover, we know with high confidence that an enhanced stratospheric

aerosol layer will effectively act to limit global warming, given the observed cooling following

volcanic eruptions2 and numerical simulations of SRM within climate models3–9. Finally, since

stratospheric aerosol concentrations would return to natural levels within 1-2 years10 following

the cessation of aerosol injections, this form of SRM could be terminated quickly should harmful

unintended consequences be encountered.

In order to stabilize global climate near modern conditions, SRM would need to provide

a negative shortwave radiative forcing that is equivalent to the modern global energy imbalance,

which is currently on the order of 0.5-1 W/m2 11–14. As GHG emissions continue, the magnitude

of SRM forcing required to cool or stabilize global climate will correspondingly increase. If a

large-scale stratospheric aerosol layer were produced, any interruption to its continual maintenance

would cause it to decay quickly, in turn driving rapid global warming as the climate adjusts to the

full, unmasked GHG radiative forcing.

Evaluations of SRM termination in previous studies3, 8, 9, 15–18 have focused on the global and

annual mean climate response under ‘business-as-usual’ future GHG emissions scenarios. These

studies suggest that the rates of global warming following SRM cessation could reach 1◦C/decade

or greater, far exceeding warming rates had no SRM been implemented. Such a rapid tempera-

ture change would substantially affect human and ecological systems whose tolerance has been

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estimated to be on the order of 0.05-0.3◦C/decade19, 20, although there is no generally agreed-upon

threshold in the literature for what constitutes a “dangerous” rate of temperature change19.

Of critical importance for ecosystem adaptation and survival is the geographic structure of

warming and the rate of seasonal temperature change19. Crop yields, for example, are highly

sensitive to growing season (typically summertime) temperature, and have already declined in re-

sponse to 20th century warming21. Historically, threats to food security were alleviated by regional

food surpluses compensating for low yields in other regions, and local adaptation or migration by

farmers22; a spatially broader or more rapid warming could preclude such adaptation techniques.

Moreover, a high rate of environmental change reduces the mean fitness of an ecological

population23 implying that a strong, sustained warming trend could limit a population’s ability

to evolve to its optimum for that environment. At minimum, stress on an ecological population

yields a less diverse group of the “luckiest” species23, resulting in the loss of biodiversity. While

some species may be able to evolve rapidly, long-lived organisms already may not evolve quickly

enough to keep pace with the relatively slow rate of observed 20th century climate change24. For

those organisms that can migrate, survivability depends on the distance to their optimal climate and

their dispersion rate. Many such mammals are already at risk of losing pace with climate change25.

Widespread and rapid warming following SRM cessation could issue a one-two punch to human

and ecosystem adaptation.

The goal of our paper is to quantify spatial patterns and rates of seasonal temperature change

following SRM cessation, and compare the response to climate change of the 20th century. We

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quantify this response under SRM cessation scenarios that span a variety of climate sensitivities,

future GHG emissions, and SRM termination years.

To investigate the spatial temperature trends, we use the Community Climate System Model

4.0 (CCSM4)26: a state-of-the-art global climate model (GCM) with coupled land, ocean, atmo-

sphere, and sea ice modules, all near 1◦ resolution. SRM is simulated by prescribing a stratospheric

sulfate aerosol layer (see Methods) that reflects shortwave radiation, counteracting increased long-

wave radiation from greenhouse gases. The future warming scenario that we investigate is the

CMIP5 Representative Concentration Pathway 8.5 (RCP8.5), which is the emissions scenario rep-

resenting the highest levels of GHG emissions wherein the radiative forcing reaches about 8.5

W/m2 above preindustrial in 210027. We conduct a two-member ensemble of SRM simulations.

We first allow the world to warm under the RCP8.5 scenario until it is about 1◦C warmer than at

the end of the 20th century. At this time, in year 2035, the sulfate aerosols are introduced and

ramped in concentration until the globally averaged temperature is returned to near the late 20th

century average (1970-1999), after which sulfates are added at a rate such that the global average

temperature is nearly stabilized. In the year 2060, after 25 years of SRM, the aerosol layer is

abruptly terminated (the ‘Shutoff’ scenario in Figure 1).

Following SRM termination, the global average annual mean surface air temperature (SAT)

rapidly approaches the temperature had no SRM been implemented (Figure 1). Global mean SAT

increases by almost 4◦C over the first 30 years following SRM termination, in contrast to a SAT

increase of less than 2◦C in that same time period under the RCP8.5 scenario. The linear trend of

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global SAT from the 2-member ensemble is 1.16◦C/decade over the first 20 years of the Shutoff

scenario, consistent with previous findings3, 8, 9, 15–18. This trend is about six times larger than the

observed global warming trend since 1975 (0.2◦C/decade28) and sixteen times greater than the

observed trend over the entire 20th century (0.07◦C/decade28). Note that the 20-year linear trend

underestimates the absolute SAT change, which is approximately 3◦C (or 1.5◦C/decade), because

SAT increases nonlinearly over the first 20 years.

Of crucial importance for the terrestrial biosphere is the geographic pattern of land surface

warming following SRM cessation. We focus here on summer temperatures in each hemisphere

(June, July, August north of 0◦ latitude, and December, January, February south of 0◦ latitude)

because of the implications for agricultural productivity, but warming rates for the winter mean

and annual mean are consistent with those in summer (Figures S1 and S2). The ensemble land-

averaged 5-year summer SAT trend following SRM termination is 3.3◦C/decade, while local trends

are as high as 15◦C/decade (Figure 2a); over much of the northern high latitudes temperature trends

are near 8◦C/decade. The 20 year trends are more spatially homogeneous, with an average trend

of 1.25◦C/decade, and many regions near 2-2.5◦C/decade (Figure 2b).

A key question is, how do these regional land surface temperature trends compare to those

experienced within the climate of the last century? It is to the local climate variability that ecosys-

tems and human systems have become well-adapted, in their respective regions, over past centuries.

Regional climate trends are strongly influenced by natural climate variability29, 30, which is particu-

larly large over land, in the high latitudes, and over short timescales. Thus, to put the SRM Shutoff

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trends into context, we normalize the 5 and 20 year trends by the typical variation in local simu-

lated historical trends of the same time interval (Figures 2e,f). Specifically, we divide the 5 and 20

year trends (Figures 2a and 2b) by the standard deviation of historical 5 and 20 year trends at each

grid point, respectively, where the historical standard deviation is calculated from distributions of

5 and 20 year trends sampled from a six-member ensemble of 20th century (1900-2005) Historical

CCSM4 simulations (see Methods for further details).

While the 5-year warming trend following SRM termination is on average 1.3 standard de-

viations of 20th century variability over land, there is substantial spatial variation (Figure 2e); in

many food insecure regions, such as Sub-Saharan Africa and South Asia31, trends exceed 2 stan-

dard deviations. However, the land-average 20-year warming trend is 4.5 standard deviations of

20th century variability, and local trends exceed two standard deviations in the majority of regions

(Figure 2f). Twenty-year trends are drastically outside of 20th century bounds within the tropics,

where variability is relatively small (Figure 2b), and exceed 6 standard deviations within many

food insecure regions. Annual mean, land-averaged trends are 1.8 and 5.6 standard deviations for

5 and 20 year trends respectively (Table 1), and global averages (not shown) are further out of

bounds due to relatively low variability over the world’s oceans.

The 20-year warming trends following SRM cessation are substantially larger than those

experienced over the 20th century in most regions, while the 5-year warming trends are in most

regions within the bounds of 20th century variability. To further quantify this response, we cal-

culate the probability density distribution across all land grid cells in each ensemble member, for

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the normalized summer SAT trends following cessation, and show its cumulative density distribu-

tion (CDD; Figure 3). For comparison, we also calculate these respective quantities for the 5-year

trends within the ensemble of Historical simulations, and from a long pre-industrial control sim-

ulation (“Preindustrial”), representing natural climate variability (Figure S3). We note that even

when imposed forcing evolves slowly (as in Historical) or is held fixed (Preindustrial), there are

small chances of very large positive or negative local 5-year summer SAT trends (+/-20◦C/decade)

somewhere on land (Figure S3) due to natural variability.

Cessation of SRM increases the probability of a large 5-year summer warming trend occur-

ring over land (i.e., warming above the level typical of the 20th century; Figure 3). Moreover, it

greatly increases the probability of “extreme” (i.e., trends greater than 2 standard deviations of his-

torical trends; Figure 2c-d) 20-year warming trends over land (Figure 3). After SRM termination,

15% of 5-year summer land trends and 74% of 20-year summer land trends are extreme relative to

the 20th century. Nearly 20% of 20-year summer land trends following SRM cessation exceed 5

standard deviations of the Historical trends (Figure 3), and the most extreme trends tend to occur

in the already stressed, less resilient regions in the tropics (Figure 2f).

The above results show that temperature trends following cessation of SRM could far exceed

the familiar bounds of 20th century temperature trends, particularly over land within the low lati-

tudes. Twenty-year temperature trends in particular were found to be highly anomalous, with rates

of warming exceeding several degrees per decade, over a very broad region covering the low to

mid latitude land masses (Figure 2f). These results follow from only a few key aspects of climate:

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the rapid increase in radiative forcing that would occur upon SRM cessation; the rapid adjustment

timescales of the ‘fast’ components of the climate system, such as land32; and the relatively small

climate variability of the past century, particularly within the tropics. While these general results

will be robust across a range of SRM cessation scenarios, the details will depend, to some extent,

on the climate sensitivity of the GCM we have used, the background GHG emissions scenario we

have employed, and our assumptions about the timing of the SRM termination. We thus shift our

focus to an evaluation of the degree to which the global and annual mean climate response to SRM

cessation is sensitive to these assumptions.

We employ here a reduced climate model consisting of a one-dimensional energy-balance at-

mosphere coupled to an upwelling-diffusion ocean (UD-EBM)33. Such models have been widely

used to simulate the time evolution of climate at the global scale34, 35 (additional details in Meth-

ods).

While the climate sensitivity (CS) of CCSM4 is well known (3.2◦C 36), CS in nature is

uncertain, with current best estimates constraining its value to likely be between 2◦C and 4.5◦C

with 68% confidence and very likely greater than 1.5◦C with 90% confidence37. This range of

uncertainty in CS can be understood in terms of the uncertainty in the value of radiative forcing that

has given rise to the observed global warming over the past century38—i.e., historical temperature

trends are consistent with a variety of CS and radiative forcing pairs, wherein high (low) CS can be

balanced by a plausibly weak (strong) 20th century forcing35. We thus consider here a CS range of

1.5◦C-10◦C and the corresponding range of background anthropogenic forcing (see Methods for

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more details), on top of which we prescribe the SRM radiative forcing scenario.

The SRM scenarios we construct and apply to the UD-EBM maintain constant net radiative

forcing from the year 2000 to the time of abrupt SRM termination. We first consider the case

in which SRM is employed to mask the same ‘business-as-usual’ RCP8.5 emissions scenario as

was used in the CCSM4 experiments (Figures 1-3). When SRM is terminated following a 20-year

implementation period (year 2020 in Figure 4a), radiative forcing abruptly increases by about 1

W/m2, producing a small spike in the rate of temperature change that quickly decays to the rate

of the background RCP8.5 scenario. The 20-year temperature trends following SRM cessation

are 0.2-0.6◦C/decade, depending on CS, comparable to those trends that occur under the RCP8.5

scenario without any SRM (Figures 4a and 5c).

In contrast, when SRM is implemented for a period of 80 years before cessation (year 2080

in Figure 4b), there is an abrupt radiative forcing increase of 5-6 W/m2 due to the loss of the

large SRM radiative forcing that was required to mask the ongoing accumulation of GHGs in the

atmosphere. This spike in radiative forcing produces a rapid and substantial increase in global

averaged temperature: up to 10◦C/decade in the first few years (Figure 4b) and 20-year trends of

0.6-2◦C/decade (Figure 5c). Thus, under high future GHG emissions, the stabilization of climate

with SRM for a period of longer than about two decades creates the potential for sustained high

rates of warming when SRM is terminated, even for relatively low CS (Figure 5c).

We next consider the case where SRM is employed along with concurrent aggressive GHG

mitigation measures, as represented by the low-emissions RCP2.6 scenario wherein anthropogenic

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radiative forcing is about 2.6 W/m2 above preindustrial in 210027. Due to the limited accumulation

of GHGs in the atmosphere, the SRM radiative forcing required to stabilize climate is relatively

small (compared to the RCP8.5 case), and thus SRM termination results in an abrupt radiative

forcing increase of less than about 2 W/m2 regardless of its timing (Figures 4c,d). Following

SRM cessation, there are high rates of temperature change in the first few years (Figures 4c,d), but

20-year temperature trends remain below about 0.4◦C/decade—comparable to those trends that

occur under the RCP2.6 scenario without any SRM—over the full range of CS and timing of SRM

termination (Figure 5d).

Within each of the above scenarios, the initial rate of temperature change following SRM

cessation depends on CS only nominally (Figures 4a,c and 5a,b, and see supplementary note).

Climate sensitivity does become an important factor in setting longer-term temperature trends,

particularly under a large radiative forcing increase (compare the 5- and 20-year trends in Figure

5). However, Figure 5 shows that the principal control on the rate of temperature change following

SRM cessation is the size of the abrupt radiative forcing increase, which, in turn, is determined

jointly by the background GHG emissions scenario and the duration of time that SRM has been

deployed. For example, Figure 5a shows that over the full range of CS, the 5-year temperature

trend for a 20-year SRM deployment is about 0.7◦C/decade (range 0.5-1.0◦C/decade) but balloons

to 3.8◦C/decade (range 2.3-4.7◦C/decade) for an 80-year deployment. Critically, even for the low-

est plausible values of CS, decadal temperature trends would be extremely large in the event of

a late 21st century SRM termination under high (RCP8.5) future emissions; conversely, even for

the highest plausible values of CS, decadal temperature trends would remain relatively small in

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the event of SRM cessation, at any point in the 21st century, under low (RCP2.6) future emis-

sions. Thus, the only way to avoid creating the risk of substantial temperature trends through SRM

implementation is through concurrent strong reductions of GHG emissions.

While we have considered here only SRM cessation scenarios within the 21st century, these

findings have relevance for more distant scenarios as well. If SRM was used to stabilize global cli-

mate under high future GHG emissions, it would need to be maintained on timescales determined

by the turnover time of GHGs in the atmosphere, which in the case of carbon dioxide is multiple

millennia39. Indeed, the stabilization of global temperature with SRM would also preclude further

observations of the climate response to the ongoing GHG emissions15, on which many estimates

of global climate sensitivity are based. Thus, the large-scale use of SRM coupled with business-

as-usual GHG emissions will lead to the disconcerting situation wherein SRM must be maintained

for millennia, else risking a large and uncertain level of global warming upon its cessation.

Absolute temperatures and rates of temperature change are inextricably tied to future green-

house gas emissions. Our results highlight the risks associated with utilizing SRM as a replacement

for mitigation of greenhouse gases. Given unabated emissions, the spatial and temporal extent of

SAT trends caused by a cessation of SRM would be well beyond the bounds experienced in the last

century or due to natural variability, and would far exceed those considered safe for many ecolog-

ical systems19, 20. For the same reason that a heat wave is dangerous to humans due to persistent

high daily temperatures40, the sustained nature of these warming trends combined with the global

spatial scale of the trends would have strong negative impacts on agriculture and countless natural

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systems. It precludes the possibility that there will be isolated regions that may experience brief

periods of “relief” from high rates of warming; thus food production would be severely reduced

everywhere and simultaneously under a scenario of high GHG emissions and SRM termination.

Additionally, while there are multiple avenues to adaptation, for many species the adaptive options

reach their limits under standard projected climate changes, let alone the large and rapid changes

that could occur due to SRM cessation with continued high greenhouse gas emissions.

Alternative climate change mitigation measures could arguably become necessary should

climate change progress at a rate or to a degree deemed dangerous to ecological or human systems.

Such a scenario could arise if GHG emissions continue unabated, or if climate sensitivity is higher

than anticipated. While it has been argued that SRM would be particularly effective in curbing

future climate change under high emissions or high climate sensitivity41, our results show that the

warming following SRM cessation becomes most severe under these same conditions. We are thus

left with the troubling situation in which SRM is most useful precisely when its associated risks

are the greatest. Furthermore, SRM via stratospheric aerosols may introduce a host of additional

problems, among them changes in atmospheric and ocean circulation that act to destabilize the

West Antarctic ice sheet3 and stratospheric ozone depletion42. It has been suggested that SRM be

combined with mitigation with the aim of reducing warming in addition to ocean acidification43

(which SRM does not address). Our results emphasize that should SRM ever be implemented,

aggressive mitigation must occur simultaneously due to the climatic risks involved with abrupt

cessation of SRM.

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Methods

Global climate model and simulations To simulate the spatial response to an SRM termination,

we use the Community Climate System Model version 4 (CCSM426), a state-of-the-art global cli-

mate model (GCM) with a finite volume 0.9◦x1.25◦ resolution atmosphere coupled to a nominal 1◦

full-depth ocean, sea-ice, and land models. We obtained the following CCSM4 simulations from

the National Center for Atmospheric Research: Six 20th century (Historical; 1900-2005) simula-

tion ensemble members, a long pre-industrial control simulation (Preindustrial), and an RCP8.5

simulation. The RCP8.5 simulation is forced with greenhouse gas (GHG) and aerosol emissions

into the future, such that the radiative forcing reaches about 8.5 W/m2 above preindustrial lev-

els by 2100. The Historical simulations have slightly varied initial conditions and are identically

forced with historical GHG and aerosol emissions plus volcanic eruptions, and the Preindustrial

simulation is forced with constant 1850’s GHG concentrations.

To simulate SRM, we first allow the climate to warm under RCP8.5 emissions until it is

about 1◦C higher than the end of the 20th century (1970-1999 mean), at which time (in the year

2035) we begin to impose a stratospheric sulfate aerosol burden (as in ref. 3). The aerosol layer is

a monthly climatology with a spatial structure derived from a model study in which sulfur dioxide

was injected from 10◦N to 10◦S at a height of 25 kilometers in the previous version of CCSM, and

allowed to circulate and oxidize to sulfate7. Here we increase the prescribed (annual mean, global

total) sulfate burden from zero to 8 teragrams of sulfur equivalent (TgS) in 3 years to approximately

return to the end of the 20th century temperature, then increase the concentration to provide a

roughly equal and opposite radiative forcing to RCP8.5; a rate of 0.67 TgS/year. The sulfate burden

13

is zeroed in the year 2060 after 25 years of climate engineering to simulate an SRM termination.

We conduct an ensemble of two Shutoff simulations with slightly varied initial conditions at the

time of SRM termination.

We utilize the standard deviation (SD) of 5 and 20 year trends in the Historical ensemble to

normalize the respective length trends in the Shutoff ensemble at each grid point (Figures 2e,f).

The SD is calculated over a set of 5 and 20 year trends, respectively, which are sampled from the 6-

member Historical ensemble (years 1900-2005) as follows: Five year linear trends are calculated

starting every 2 years, and 20 year linear trends are calculated every 10 years. The resulting

sample sizes (N) at each grid point are N=306 and N=54 for 5 and 20 year trends, respectively.

Note that we deliberately do not de-trend the Historical simulations so that the Shutoff trends

are compared with “what humans have experienced” over the last century. We similarly sample

300 years of the long Preindustrial simulation, resulting in N=148 and N=28 for 5 and 20 year

trends, respectively. Probability density distributions (PDD) are generated by aggregating area-

weighted summer SAT trends (or normalized trends) in all land grid cells in each sampled time

period (or ensemble member in the case of Shutoff; N=2). A cumulative density distribution

(CDD) is computed by integrating the PDD (Figures 3 and S3).

Simple model and simulations In order to explore the extended parameter space of the range of

climate sensitivity, background emissions scenarios, and termination years, we utilize a simplified,

one-dimensional, climate model that has an energy balance atmosphere and upwelling-diffusion

ocean (UD-EBM)33, 34. We first tune the UD-EBM so that it captures the global mean response

of CCSM4, including its equilibrium climate sensitivity of 3.2◦C and transient climate response

14

of 1.7◦C36. When tuned to the climate sensitivity of CCSM4, the UD-EBM successfully repro-

duces annual and global mean SAT trends following SRM cessation when the radiative forcing

jump in the UD-EBM matches that in the CCSM4 Shutoff simulations (about 4-5W/m2; see black

symbols in Figures 5a,c). We then simulate combinations of GHG emissions scenarios and SRM

deployments by prescribing time-evolving radiative forcing. We simulate each scenario over a

distribution of climate sensitivities that is constrained by the uncertainty in tropospheric aerosol

radiative forcing, as described below.

The 90% confidence interval on historical radiative forcing (RF) due to tropospheric aerosols

spans the range from -0.5 to -2.2 W/m2 44, which is the primary uncertainty in total RF over the

last century. This uncertainty in total RF implies a spread in climate sensitivity because historical

surface temperature can be reproduced with a range of climate sensitivities, as long as they are

paired with an appropriate past RF within the range of observational constraints35. For example, a

large (negative) tropospheric aerosol RF — yielding a small total RF — paired with a high climate

sensitivity can produce the same temperature response as a small (negative) tropospheric aerosol

RF paired with a low climate sensitivity35. Thus, the first 100 years of the UD-EBM simulations

represents the ”historical” period, 1900-2000, wherein climate sensitivity and radiative forcing

pairs produce surface temperatures constrained to lie within a small range (Figure S4). The next

100 years represent future projections, from 2001-2100, of increased GHGs with and without SRM

and subsequent SRM shutoff (Figure 4).

We prescribe RF into the future for the RCP8.5 emissions scenario45, corresponding to the

GCM analysis, and for the RCP2.6 emissions scenario46 that incorporates strong GHG mitigation.

15

We simulate SRM in combination with these background emissions scenarios by maintaining RF at

year 2000 levels until the time of abrupt SRM termination, at which time the RF returns to the GHG

emissions scenario RF until 2100. Each of these simulations is executed for each climate sensitivity

in a 100 member distribution that spans the range and probability of climate sensitivities described

above. While very high sensitivities of 12◦C+ cannot be ruled out, their probability is small and we

limit our analysis to values of 1.5◦C to 10◦C, to coincide with CS values that reproduce historical

temperatures over the ”very likely” range of tropospheric aerosol RF44.

We reconcile uncertainty in year 2000 RF and prescribed future scenario RF (in year 2001)

by relaxing the year 2000 RF to the RCP scenario RF over the years 2001-2100 (Figure S4). This

can be interpreted as a reduction in RF uncertainty as tropospheric aerosols are cleaned up over the

next century. Note that we ignore any uncertainties in SRM RF since we define it to exactly cancel

the RF from increasing GHGs. This is a potentially important issue, but one that is separate to the

objectives of this study.

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1980 2000 2020 2040 2060 2080286

287

288

289

290

291

292

Time (years)

Annu

al m

ean

glob

al m

ean

surfa

ce a

ir te

mpe

ratu

re

1850rcp8.520thCquickramp shutoffquickramp shutoff 2quickramp ensemble spreadquickramp ensemble mean

Time (years)

SAT

(o C)

Preindustrial control

HistoricalRCP8.5SRM rampShutoff ensemble

19

18

17

16

15

14

13 1980 2000 2020 2040 2060 2080

Figure 1: Annual mean, global mean surface air temperature (SAT). Annual mean, global mean

SAT (◦C) for Historical (black), RCP8.5 (red), average of 4 SRM Ramp simulations (blue line) and

ensemble range (light blue shading), two Shutoff simulations (orange), and a Preindustrial control

(black) simulation.

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Acknowledgements This research was funded by the Tamaki Foundation and supported in part by the Na-

tional Science Foundation through TeraGrid resources provided by the Texas Advanced Computing Center

22

3 410 62 5

d)c)

0 4-4-8 8 0 1-1-3 3-2 2

f)

oC/dec oC/dec

Standard

deviations

Standard

deviations

e)

oC/dec

1 1.50.50 2

oC/dec

b)a)

3 410 62 5

4 620 8 10

Figure 2: Summer SAT trends following SRM cessation. (a) The ensemble average summer (JJA north

of 0◦ latitude and DJF south of 0◦ latitude) 5-year SAT trends (◦C/decade) for the period following SRM termination

in the Shutoff scenario. (c) The 5-year summer SAT trend (◦C/decade) representing two standard deviations (SD)

of Historical summer trends, calculated from the ensemble of Historical simulations. Local trends greater than this

magnitude represent the warmest ∼ 5% of historical trends. (e) The 5-year trends shown in (a), but each grid point is

normalized by the typical historical 5-year trend by dividing by the SD of Historical 5-year trends at each grid point.

Essentially, (e) equals (a) divided by (c)/2. (b), (d), and (f) are as (a), (c), and (e), but for 20-year trends.

23

Cu

mu

lative

fre

qu

en

cy

1

0.5

0-2 0 4 8 12

Standard deviations

!2 0 2 4 6 8 10 12 140

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

15 and 20 yr land Normalized SAT trend: cumulative density function

5-year

20-year

Figure 3: Cumulative density distribution of summer land SAT trends following SRM cessa-

tion. Cumulative density distributions (CDD) of 5-year (solid) and 20-year (dashed) normalized summer land SAT

trends in units of standard deviation for the Shutoff simulations. The CDDs consist of normalized trends for each

ensemble member for each land grid point, as described in Methods.

24

2000 2050 2100 2050 2100 2050 2100Time (yr)

2000 2050 2100 2050 2100 2050 2100Time (yr)

RF (Wm-2) ∆T (oC) d∆T/dt (oC/decade) RF (Wm-2) ∆T (oC) d∆T/dt (oC/decade)

Shutoff after 20 yrs

Shutoff after 80 yrs

a) b)

10

8

6

4

2

0

2000 2050 2100 2050 2100 2050 2100Time (yr)

2000 2050 2100 2050 2100 2050 2100Time (yr)

RF (Wm-2) ∆T (oC) RF (Wm-2) ∆T (oC)

Shutoff after 20 yrs

Shutoff after 80 yrs

4

3

2

1

0

c) d)d∆T/dt (oC/decade) d∆T/dt (oC/decade)

Figure 4: UD-EBM radiative forcing, temperature, rate of temperate change. (a) Evolution of

the net radiative forcing (RF ) due to GHGs and SRM, and including the uncertainty in net RF (left), temperature

response (4T , middle), and rate of temperature change (d4T/dt, right) for the high-background emissions scenario

(RCP8.5; dashed red curves) and an SRM scenario with termination after 20 years of temperature stabilization (solid

blue curves). Shading indicates the range in the response (4T and d4T/dt) due to the uncertainty in CS with (blue)

and without (red) SRM. The top curve in RF is the lowest CS and the bottom curve is the highest CS, and vice versa

for4T and d4T/dt. The dashed black line is the climate sensitivity of CCSM4 = 3.2◦C. The RCP scenario has thick,

dashed lines to distinguish it from the SRM scenario when curves overlap. The range in year 2000 SRM RF is due

to uncertainty in the net historical forcing (compared to preindustrial conditions) at the time of SRM deployment in

the year 2000 (as constrained by observations - see Methods for further details). (b) is as (a) but for SRM termination

after 80 years of stabilization. (c) and (d) are as (a), and (b) but for RCP2.6, the low background emissions scenario.25

5 y

ea

r tr

en

d (

oC

/de

ca

de

)RCP8.5 background emissions

Shutoff after 50 yrs

Shutoff after 80 yrs

Climate sensitivity (oC)

RCP2.6 background emissions

Shutoff after 50 yrs

Shutoff after 20, 80 yrs

likelyvery likely

Climate sensitivity (oC)

Shutoff after 20,50,80 yrs

Shutoff after 50 yrs

Shutoff after 20 yrs

Shutoff after 80 yrs

20

ye

ar

tre

nd

(oC

/de

ca

de

)

RCP8.5

a) b)

c) d)

Shutoff after 20 yrs

RCP2.6

RCP8.5

RCP2.6

5

4

3

2

1

0

5

4

3

2

1

0

2

1.6

1.2

0.8

0.4

0

2

1.6

1.2

0.8

0.4

0

1 3 5 7 9 1 3 5 7 9

1 3 5 7 9 1 3 5 7 9

Figure 5: UD-EBM temperature trends versus climate sensitivity. (a) Five year temperature trend fol-

lowing SRM termination — after 20, 50, and 80 years of SRM deployment that approximately stabilized temperature

— as a function of climate sensitivity for the RCP8.5 background emissions scenario (blue markers) and the maxi-

mum RCP8.5 trend as a function of climate sensitivity (red markers). (c) is as (a) but for twenty-year trends following

SRM termination. The dark gray and light gray regions indicate the IPCC “likely” (68%) and “very likely” (90%)

climate sensitivity ranges respectively. The vertical black line indicates the climate sensitivity of CCSM4 (3.2◦C), the

black triangles show CCSM4 5 and 20 year global mean, annual mean trends following SRM cessation (3.0◦C/decade,

and 1.16◦C/decade), and the black circles show the upwelling-diffusion energy balance model (UD-EBM) results for

SRM termination after 65 years of implementation (2.8◦C/decade and 1.0◦C/decade), when the radiative forcing jump

roughly matches the estimated jump in CCSM4 (about 4-5W/m2). The horizontal black lines in (a) and (c) indicate the

maximum global mean annual mean 5 and 20 year trends, respectively, sampled from the CCSM4 Historical ensemble

simulations. (b) and (d) are as (a) and (c) but for the RCP2.6 background emissions scenario. There are some nuances

in the relationship of termination year and trend magnitude with the RCP2.6 GHG scenario due to the fact that the

RCP2.6 emissions scenario does not monotonically increase (cf. Figures 4c,d).

26

5yr 20yr 5yr SD 20yr SD

Summer 3.3 1.3 1.3 4.5

Winter 4.2 1.4 1.0 3.3

ANN 3.6 1.4 1.8 5.6

Table 1: Summer and Winter land-averaged 5 and 20 year SAT Shutoff trends (◦C/decade), and

normalized trends in which the units are standard deviations (SD) of the Historical simulations.

Summer is defined as JJA north of 0◦ latitude, and DJF south of 0◦ latitude, while winter is DJF

north of 0◦ latitude and JJA south of 0◦ latitude.

under Grant TG-ATM090059

Author Contributions K.E.M. conceived of the study and performed the simulations and analysis. K.E.M.

and K.C.A. wrote the paper. C.M.B. and D.S.B. contributed to interpreting results and editing the text.

Competing Interests The authors declare that they have no competing financial interests.

Correspondence Correspondence and requests for materials should be addressed to K.E.M.

(email: kelly@atmos.washington.edu).

27

Rapid and extensive warming following cessation of solarradiation management

Kelly E. McCusker*1, Kyle C. Armour2, Cecilia M. Bitz1, & David S. Battisti1

1Department of Atmospheric Sciences, University of Washington, Seattle, WA 98195

2Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technol-

ogy, Cambridge, MA 02139

Supplementary Note

The relationship between climate sensitivity (CS) and the rate of temperature change is illustrated

by the simple climate model, CdT/dt = −T (t)/λ +4RF (1). Here C is the heat capacity, λ is

the climate sensitivity parameter, and4RF is the radiative forcing. Note that CS = λ4RF2xCO2 ,

where 4RF2xCO2 = 3.67 W/m2, and λ is the climate sensitivity parameter that we effectively

vary in the UD-EBM. For the application of a constant 4RF applied at t = 0, the analytical

solution of equation (1) is T = λ4RF (1 − e−(1/(Cλ))t) (2). Thus, the rate of temperature change

in response to a sudden imposition of forcing, 4RF (such as after SRM cessation), is: dT/dt =

4RF/C(e−(1/(Cλ))t) (3). In the limit of t → 0 in equation (3), dT/dt = 4RF/C and is not

dependent on CS. As time passes, dT/dt decays exponentially with a timescale that scales with

CS. If instead 4RF increases for t > 0, as is the case in our SRM cessation scenarios, dT/dt

decays more slowly.

1

c) d)

b)a)

3 410 62 5 3 410 62 5

0 1-2-3 3-1 20 2-4-8 6-2 4 8-6

Standard deviations

oC/dec

Standard deviations

oC/dec

Supplementary Figure 1: Winter SAT trends following SRM cessation. (a) The ensemble aver-

age winter (DJF north of 0◦ latitude and JJA south of 0◦ latitude) 5-year SAT trends (◦C/decade)

for the period following SRM termination in the Shutoff scenario. (c) The 5-year trends shown

in (a), but each grid point is normalized by the typical historical 5-year trend by dividing by the

standard deviation (SD) of Historical 5-year trends at each grid point. (b), (d) are as (a), (c) but for

20-year trends.

2

c) d)

b)a)

3 410 62 5

0 1-2-3 3-1 20 2-4-8 6-2 4 8-6

3 410 62 5Standard deviations

oC/dec

Standard deviations

oC/dec

Supplementary Figure 2: Annual SAT trends following SRM cessation. (a) The ensemble aver-

age annual mean 5-year SAT trends (◦C/decade) for the period following SRM termination in the

Shutoff scenario. (c) The 5-year trends shown in (a), but each grid point is normalized by the typi-

cal historical 5-year trend by dividing by the standard deviation (SD) of Historical 5-year trends at

each grid point. (b), (d) are as (a), (c) but for 20-year trends.

3

5 year SAT trend (oC/dec)

Fre

quency

3

2

0

1

!10 !5 0 5 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

15 yr land SAT trend: cumulative density function

b40.20th.track1.1deg.ens MAX: 29, MIN: !26, b40.1850.track1.1deg.006 MAX: 25, MIN: !23-10 0 10-5 5-10 0 10-5 5

Cum

ula

tive fre

quency

1

0

.5

Historical

Preindustriala) b)

(-26, 29)

(-23, 25)

Supplementary Figure 3: Control probability and cumulative density distributions of land-

averaged Summer 5 year SAT trends. (a) Probability density distributions of 5 year summer

SAT trends (◦C/decade) on land for the Historical (black) and Preindustrial (blue) simulations.

The distributions are generated by aggregating area-weighted 5-year trends in all GCM land grid

cells sampled from all ensemble members, as described in Methods. (b) Cumulative density dis-

tributions (CDD) of (a). The parenthetical numbers are the minimum and maximum values of the

CDD, which has been truncated for clarity, for Historical (black) and Preindustrial (blue) distri-

butions. The distributions of Historical and Preindustrial trends are remarkably similar, indicating

that Historical 5 year trends are largely due to natural variability.

4

Supplementary Figure 4: UD-EBM radiative forcing and temperature response for RCP8.5.

Left) Historical (1900-2000) and RCP8.5 (2001-2100) radiative forcing (W/m2) and right) sim-

ulated temperature response to the radiative forcing scenario. This demonstrates how a range of

radiative forcings, when paired with an appropriate climate sensitivity, will reproduce historical

temperature over the 20th century. The range of CS causes for a spread in future temperatures.

The range in year 2000 RF is due to uncertainty in the net historical forcing (compared to prein-

dustrial conditions) at the time of commencement of the future projection in the year 2000 (as

constrained by observations - see Methods for further details).

5