Climatic Change
DOI 10.1007/s10584-016-1616-2

Future risk of record-breaking summer temperaturesand its mitigation
Flavio Lehner 1 & Clara Deser 1 & Benjamin M. Sanderson 1

Received: 9 September 2015 / Accepted: 24 January 2016
# The Author(s) 2016. This article is published with open access at Springerlink.com

Abstract The probability that summer temperatures in the future will exceed the hottest on
record during 1920–2014 is projected to increase at all land locations with global warming.
Within the BRACE project framework we investigate the sensitivity of this projected change
in probability to the choice of emissions scenario using two large ensembles of simulations
with the Community Earth System Model. The large ensemble size allows for a robust
assessment of the probability of record-breaking temperatures. Globally, the probability thatany summer during the period 2061–2081 will be warmer than the hottest on record is 80 %for RCP 8.5 and 41 % for RCP 4.5. Hence, mitigation can reduce the risk of record-breaking
temperatures by 39 %. The potential for risk reduction is greatest for some of the mostpopulated regions of the globe. In Europe, for example, a potential risk reduction of over
50 % is projected. Model biases and future changes in temperature variance have only minor
effects on the results, as their contribution stays well below 10 % for almost all locations.

1 Introduction
The frequency and intensity of heat waves or extremely warm summers is expected to increase
as anthropogenically-driven global warming progresses (Coumou et al. 2013; Russo et al.
2014). Potential impacts of such high temperature events range from health effects (Anderson
et al. 2015, accepted; Marsha et al. 2015, submitted) to drought occurrence (Towler et al. 2015,
submitted) and agricultural losses (Battisti and Naylor 2009; Levis et al. 2015, submitted). In
particular, projected changes in growing season temperature may result in potential hazards forfood security, as they can offset mitigation benefits resulting from irrigation or technologicalThis article is part of a Special Issue on BBenefits of Reduced Anthropogenic Climate ChangE (BRACE)^ edited
by Brian O’Neill and Andrew Gettelman.
Electronic supplementary material The online version of this article (doi:10.1007/s10584-016-1616-2)
contains supplementary material, which is available to authorized users.

* Flavio Lehner
flehner@ucar.edu

1

Climate and Global Dynamics, National Center for Atmospheric Research, Boulder, CO, USA

Climatic Change

advancements (Lobell et al. 2011). Motivated by the notion that present-day society andagricultural systems are vulnerable to record-breaking summer temperatures, Battisti andNaylor (2009) examined the probability that summers at the end of the 21st century will bewarmer than the record to date. They showed that by the end of the 21st century under ascenario of continued rise in greenhouse gas (GHG) concentrations, the probability of exceeding the historical summer temperature record is >50 % for almost the entire land surface. Recent
examples of fatal heat waves and food crises linked to record-breaking summer temperatures
can therefore serve as case studies for a potential future norm. Here, we revisit this issue, using a
new generation of climate model simulations and focusing on potential benefits from climate
mitigation in light of different emission scenarios.
A common approach to exploring the range of potential future climate outcomes is to consider
different GHG emissions scenarios. Contrasting those scenarios and highlighting their relative
costs and benefits has become a standard practice for the depiction of policy-relevant climate
science (IPCC 2013). In preparation for the latest Assessment Report of the Intergovernmental
Panel on Climate Change, a subset of four scenarios, the so-called Representative Concentration
Pathways (RCPs; van Vuuren et al. 2011), have been adopted for climate model simulations:these are RCP 2.6, RCP 4.5, RCP 6.0, and RCP 8.5, with the numbers indicating the estimatedglobal radiative forcing at the end of the 21st century due to human activities. Underlying the
RCPs are different socio-economic storylines: deployment of aggressive mitigation strategies andnet negative GHG emissions in the case of RCP 2.6, or business-as-usual use of resources in RCP
8.5. The remaining scenarios, RCP 4.5 and RCP 6.0, describe moderate mitigation pathways.
Besides the scenario uncertainty described above, uncertainty in climate projections also
arises from structural differences between models, as well as irreducible uncertainty from
intrinsic variability of the climate system on multi-decadal time scales (Hawkins and Sutton2009). Communicating these different types of uncertainty associated with climate change
projections has become increasingly important (Deser et al. 2012a) and requires probabilistic
risk assessments (Field et al. 2014). The National Center for Atmospheric Research’s projecton Benefits of Reducing Anthropogenic Climate changE (BRACE; O’Neill and Gettelman
2015, in preparation) offers an opportunity to tackle some of these challenges by providing twolarge ensembles of simulations with the Community Earth System Model (CESM), underscenarios RCP 4.5 and RCP 8.5 (Kay et al. 2015; Sanderson et al. 2015).
The aim of this study is to quantify the probability that summers in the future (2061–2080)
will be warmer than any experienced in the past roughly 100 years and to investigate how thisrisk differs for RCP 4.5 versus RCP 8.5. The large ensemble sizes (15 members for eachscenario) allow us to calculate this probability in a robust manner within the physicallyconsistent framework of one specific model. Thus, we account for the effects of intrinsic
climate variability in the presence of forced climate change without confounding uncertainties
due to model differences. Most models in the Coupled Model Intercomparison Porject (CMIP)
archive do not provide enough ensemble members to tackle this issue in a robust manner andaggregation across different models prohibits a straightforward physical interpretation of theresults (Battisti and Naylor 2009). Hence, we interpret risk in our study as a probability,
conditional on the model physics being representative of reality. We also address the influenceof model bias in simulating present-day temperature variability as well as the role of futurechanges in temperature variability (Schär et al. 2004; Huntingford et al. 2013) on the results. In
these respects, our study expands on that of Battisti and Naylor (2009), who considered only
one emissions scenario, folded in model structural uncertainties by using a multi-model
approach, and did not consider that temperature variance may change with climate change.

Climatic Change

The paper is structured as follow. A description of the model and experimental setup ispresented in Section 2. In Section 3 we investigate the changing risk of record-breaking
summer temperatures in the future, its dependence on emissions scenario, as well as its effects
on population. In addition, Section 3 examines the importance of changes in temperature
variance and model bias on the results. A summary follows in Section 4.

2 Data and methods
Similar to most studies in this special issue, we make use of two ensembles of simulations with
the National Center for Atmospheric Research Community Earth System Model version 1(hereafter CESM) at about 1° horizontal resolution (Hurrell et al. 2013). One ensemble
consists of 30 members for the period 1920 to 2100 under historical forcing until 2005 and
RCP 8.5 thereafter (Kay et al. 2015). The individual ensemble members differ only by roundoff errors in their initial atmospheric temperatures (10−14 °C), and hence provide an ideal setup
to characterize the role of internal variability. The second ensemble consists of branches fromthe first 15 members of the RCP 8.5 ensemble at the year 2006 using RCP 4.5 forcing from2006 to 2080 (Sanderson et al. 2015). We focus on the period 1920–2080 common to both
ensembles. In addition, we make use of a 1800-year control simulation with the same modelversion under perpetual preindustrial (1850) radiative conditions.
In this study we define Bsummer^ at each location as the climatologically warmest 3-monthseason based on the reference period 1920–2014, the period common to both observations andmodel simulations. We do this separately for observations and the model, using quadraticallydetrended data. For observations we use monthly means from the Berkeley Earth Surface
Temperature (BEST) data set at 1° spatial resolution (Rohde et al. 2013). Similar results wereobtained with other data sets (not shown). The similarity of the BEST and model grids allows
us to bilinearly regrid the observations to the model grid with minimal error. The model shows
good agreement with observations on the definition of summer at most locations; areas ofdisagreement occur mainly in the tropics, where the amplitude of the seasonal cycle is modest(Fig. S1). We define the warmest summer during 1920–2014 as the Bhistorical record^,
considering the first 15 members of each ensemble: that is, the record occuring over 1425
summers (95 years × 15 ensemble members). We then calculate the probability that a summer
in a given 20-year period in the future, i.e., post-2014, is warmer than the historical record bycounting the number of summers exceeding the historical record and dividing by the total
number of summers (300: 20 years × 15 ensemble members). For most locations, the warmest
3-month period does not change in the future (Fig. S1). Therefore, we use the same months todefine summer in the future as derived from the historical period. Throughout this study theword Bprobability^ is used in the sense of a relative likelihood based on a single climate model,
rather than the strictly statistical use of the word that does not allow for model errors.

3 Resultsa) Evolution of record-breaking temperatures
Validating the model’s ability to produce realistic extreme summer temperatures similar toobservations is inherently difficult, as the limited duration of the observational record prohibits

Climatic Change

60(a) Global
Control Simulation
RCP 8.5
RCP 4.5
Observations

40

20
Max. control simulation

Land fraction seeing new record [%]8080(b) Europe

60

40

20

0
1920 1940 1960 1980 2000 2020 2040 2060 2080

01920 1940 1960 1980 2000 2020 2040 2060 2080

Time [Years]

Time [Years]

80(c) USA

60

40

20

Land fraction seeing new record [%]Land fraction seeing new record [%]Land fraction seeing new record [%]robust estimates of extreme values (even for seasonal means). During the European heat wave
in 2003, for example, summer temperatures exceeded its 1920-2014 climatological values byfour standard deviations (not shown). Such extreme temperatures have a one in 15,787 chanceof occurrence under a stable, normally distributed climate. The model equivalent of theobserved period 1920 to 2014 represents only 1425 summers (95 years × 15 ensemble
members = 1425 summers) and hence might still be too short to capture such outliers. Indeed,in this model ensemble, as well as in the 1800-year long control simulation, no extreme
summer in Europe comparable to the one observed in 2003 occurs.
Another way of comparing the occurrence of extreme summer temperatures in observations
and the model is to calculate the fraction of land area over which a new temperature record is set
within a given summer. We use the time period 1920 to 2014 from observations (BEST) and1920 to 2080 from the two model ensembles. In the first summer (1920), by definition a record is
set for the entire land area (100 %). In the second summer (1921), only the land fraction thatbreaks the current record (summer 1920) is counted, and so forth. The land area fraction for eachyear is then normalized by 1/n × total land area, with n being the number of years considered, sothat for the first year the 100 % are normalized to 1 %. Hence, in a stable climate the theoretically
expected land area fraction will be 1 % for each year (following Bador et al. 2015). We do thisseparately for the entire land surface as well as for Europe, the US, and South-East Asia (Fig. 1).
For the model ensembles, the range across the ensemble members is shown. For the control

80(d) South-East Asia

60

40

20

0
1920 1940 1960 1980 2000 2020 2040 2060 2080

01920 1940 1960 1980 2000 2020 2040 2060 2080

Time [Years]

Time [Years]

Fig. 1 Observed (black curve) and simulated (shading) land area fraction that sees record-breaking summer
temperatures for a global, b Europe, c the contiguous US, d South-East Asia. Time series are normalized by 1/n ×
total land area with n being number of summers considered. Shading gives minimum and maximum values
across the 15 members from RCP 8.5 (red) and RCP 4.5 (blue) ensembles. The range across the control
simulation (gray shading), illustrating uncertainty due to internal variability, is constructed from ten nonoverlapping 160-year long segments. Overlap between the shadings is visible due to transparency. Dashed blacklines give maximum value from control simulation. Maps show respective domain

Climatic Change

simulation, the range across non-overlapping 160-year segments is shown. These ranges provide
estimates against which the null-hypothesis of a stable climate can be tested.
The period 1920 to about 1980 is indistinguishable from natural variability as suggested by
the control simulation in both observations and the model ensembles. After that, and certainlyin the early 21st century, the observed and simulated record-breaking global land area fraction
significantly exceeds the range of the control simulation, implying a non-stationary climate(Fig. 1a). The land area fraction also increases for Europe, the contiguous US, and South-East
Asia, even though for these regions most observed values are still within the uncertainty range
estimated from the control simulation (Fig. 1b–d). Globally and in South-East Asia, the year
1998, which was marked by a strong El Niño event, stands out as having the highest land
fraction (>20 %) over which records were broken. To put this event into perspective, no year
from the entire control simulation ever exceeds 10 % globally. In Europe, the 2003 summer
broke records on >40 % of the land area, while the control simulation produces records over up
to 26 % of the land area. While model biases in El Niño magnitude might influence suchrecord-breaking statistics (Coumou et al. 2013), we note that the CESM Large Ensemble
simulates the amplitude (and frequency) of ENSO quite well (the standard deviation of the
Nino3.4 Index is 1.15 °C compared to 1.0 °C in ERSSTv3b; see Deser et al. 2012b for more
information).
Moving further into the 21st century, both scenarios are characterized by consistently larger
record-breaking land area fractions globally than would be expected from a stable climate(Fig. 1a). In the year 2080, at least 10 %, and up to >40 % of the land area might see a newtemperature record. The scenarios RCP 8.5 and RCP 4.5 start to separate eventually
and RCP 8.5 sees a consistently higher land area fraction than RCP 4.5, which seems
to stabilize. However, that stabilization occurs around an ensemble mean value ofabout 15 %, indicative of continued global-scale warming (see also Fig. 1 in
Sanderson et al. 2015). In the subdomains Europe, contiguous US, and South-East
Asia, the signal is noisier and the two scenarios largely overlap, with new records onanywhere between 1 and >80 % of the land area by 2080 (Fig. 1b–d). This is evident
also when the land fraction is scaled by the global average temperature of the respective
scenario (not shown).
b) Risk of future exceedance of historical record temperatures
As described in Section 2, we now examine the probability that summer temperaturesduring 2061–2080 will exceed the historical record. Under RCP 8.5, large parts of North andSouth America, central Europe, Asia and Africa are subject to probabilities of over 90 %,indicating that nearly every summer will be warmer than the warmest during the historicalperiod (Fig. 2a). Some regions with probabilities <50 %, such as Alaska, the central US,
Scandinavia, Siberia, and continental Australia, are subject to large interannual variability, andhence a tendency towards small signal-to-noise ratios (Mahlstein and Knutti 2011). Under
RCP 4.5, mainly tropical regions see a probability >90 %, while most other regions remain<50 %.
By 2061–2080 in RCP 8.5, the probability that the global land area is warmer than thehistorical record is on average about 80 %, excluding Antarctica (Fig. 2a). By the same time in
RCP 4.5, the probability that the global land area will be warmer than the historical record
from 1920 to 2014 is only 41 % (Fig. 2b). Globally, this results in an average 39 % reductionin probability of record exceedance under RCP 4.5 instead of RCP 8.5 (Fig. 2c).

Climatic Change(a) RCP 8.5 2061-2080(b) RCP 4.5 2061-2080[%]
Probability of exceeding historical record summer temperature(c) RCP 8.5 − RCP 4.5 2061-2080[%]
Difference in probability

Fig. 2 Probability that a given summer during 2061–2080 will be warmer than the warmest on record during thehistorical period 1920–2014, determined from the CESM ensembles under a RCP 8.5 and b RCP 4.5. c The
difference between RCP 8.5 and RCP 4.5, i.e., how much higher the probability is for RCP 8.5 as compared to
RCP 4.5. The globally averaged value of each map, excluding Antarctica, is given in the bottom left corner. The
stippling in c indicates areas that see a risk of >90 % already under RCP 4.5

However, the scenario dependency of this metric is not spatially uniform. In other words,
some regions appear to benefit more than others from RCP 4.5 as compared to RCP 8.5. In
parts of Brazil, central Europe, and Eastern China, for example, the probability of exceeding
the historical record temperature is more than 50 % larger in RCP 8.5 than in RCP 4.5(Fig. 2c). The US East coast, Northeastern Africa, Indonesia and parts of China in contrast,show no significant difference in probability, since these regions already see a high probabilityof exceedance under RCP 4.5 (Fig. 2b, indicated by stippling). This also applies to large partsof the tropics, which—due to their small interannual variability—tend to have a large signalto-noise ratio with global warming (Mahlstein and Knutti 2011). That is, the absence of abenefit from mitigation in these areas is due to saturation of our metric and, while physicallyinteresting, is therefore not necessarily meaningful in a mitigation context (Fig. 2c). Yetanother example is Eastern Australia, where there exists a low probability of exceedance inboth RCP 4.5 and RCP 8.5 and only about 20 % difference in probability between the two
scenarios.
To further illustrate these issues, Fig. 3 shows the distribution of summer temperatures fromthe historical (1920–2014) and future (2061–2080) time periods for the two scenarios at three
representative locations: Cairo, Egypt (30.0 °N, 31.2 °E), Paris, France (48.9 °S, 2.4 °E),
Canberra, Australia (35.3 °S, 149.1 °E). We also show the observed distribution for thehistorical period. The observed and simulated historical record summer temperatures aremarked by triangles for reference. By 2061–2080, Cairo sees a mean warming of 3.2 °C forClimatic Change(a) Cairo, Egypt(b) Paris, France

0.15
0.1
0.05

0.2

0.25
!
!

Observations record 1920-2014
Model record 1920-2014
Median RCP 4.5 2061-2080
Median RCP 8.5 2061-2080

Frequency [%]

0.2

0
−5

(c) Canberra, Australia

0.25

Frequency [%]Frequency [%]

0.25

0.15
0.1
0.05

!

!
0
5
Temperature anomaly [°C]

10

0
−5

0.2

Observations 1920-2014 (n = 95)
Model 1920-2014 (n = 1425)
RCP 4.5 2061-2080 (n = 300)
RCP 8.5 2061-2080 (n = 300)

0.15
0.1
0.05

!!
0
5
Temperature anomaly [°C]

10

0
−5

!
!
0
5
Temperature anomaly [°C]10Fig. 3 Kernel fit to the histograms of summer temperature in a Cairo, b Paris, c Canberra, given as anomalies
relative to the mean over the historical period 1920–2014. The observed and simulated record,
respectively, from the historical period 1920–2014 are given by the black and gray triangles; theblue and red triangles indicate the median of the RCP 4.5 and RCP 8.5, respectively. The number ofsummers considered are given in the legend of panel c

RCP 4.5 and 5.2 °C for RCP 8.5. Due to the small interannual variability in Cairo, mostsummers in 2061–2080 under RCP 4.5 are already warmer than the warmest of the historicalperiod, so that there is little apparent benefit from mitigation. Paris is projected to warm asimilar amount as Cairo (3.0 °C for RCP 4.5 and 5.0 °C for RCP 8.5); however, due to thelarger interannual variability, the distributions show greater overlap than for Cairo, and theprobability of exceeding the historical record does not saturate in RCP 4.5, but increases
monotonically from RCP 4.5 to RCP 8.5. Finally, Canberra warms less than the previous
examples (2.1 °C for RCP 4.5 and 3.3 °C for RCP 8.5), while it has similar interannual
variability as Paris. The probability of exceeding the record therefore stays below 50 % underboth emissions scenarios. For all of these examples the model shows no significant bias in σcompared to observations.
c) Land fraction and population exposure
As with many impact-relevant quantities, an issue of interest is the number of people whowill be affected. To address this, we show the probability of exceeding the historical record as afunction of time, land surface fraction, and population fraction, using population fixed at 2010
values from Jones et al. (2015) (Fig. 4). Using transient population scenarios instead of Joneset al. (2015) does not alter the results significantly (not shown). Under RCP 8.5 by 2070,
100 % of the world population is subject to >10 % probability of exceeding of their local
historical temperature record as defined up until 2014 (Fig. 4a). Under RCP 4.5, 90 % of theworld population experiences >10 % probability; in other words, this result is largely independent of the emissions scenario (Fig. 4b). The results start to differ when higher probability
categories are considered. Under RCP 8.5 by 2070, 87 % of the world population is subject to>50 % probability of exceeding of their historical temperature record (Fig. 4a). This means
that, on average, every second summer will be as warm or warmer than the hottest summer
ever experienced by the population during 1920–2014. Under RCP 4.5 by 2070, this willaffect only 45 % of people. An even larger disparity arises for >90 % probability of record
exceedance: >60 % of the population under RCP 8.5, while only 10 % of the population is
subject to this same level of probability under RCP 4.5.
In this global perspective, the land fraction exposed to a certain probability is very similar tothe corresponding population fraction exposed; however, there are some interesting differences. Under RCP 4.5 by 2070, the population fraction seeing >70 % and >90 % probability of

(a) RCP 8.5(b) RCP 4.5

90%

70%
50%

%

10

Probability to exceed
for population fraction
Probability to exceed
for land fraction

Probability of exceeding historical (1920−2014)
summer temperature record [%]Climatic Change(c) 2061-2080
100
RCP 8.5

80

60
RCP 4.540

20
Land
Population

0
0

20
40
60
80
Land/Population fraction [%]

100

[%]
Probability to exceed historical record summer temperature

Fig. 4 Probability of exceeding the historical summer temperature record as a function of time and land surface/
population fraction for a RCP 8.5 and b RCP 4.5. Probability is calculated from 20-year moving windows andplotted at the central date. Population data are from Jones et al. (2015) and kept constant at 2010 values. cTimeslice of a and b for the period 2061–2080

record exceedance is roughly 4 % smaller than the corresponding land fraction (Fig. 4c). Under
RCP 8.5 this is reversed, indicating that densely populated regions preferentially shift to ahigher probability category. In other words, in terms of human exposure to record temperature
exceedance, the benefits would be disproportionately larger for RCP 4.5 as compared to RCP
8.5, although by only about 9 %.
d) Changes in variability
The interannual variability of summer temperature might change with warming due to shifts
in regional hydroclimate or as a consequence of feedbacks (Seneviratne et al. 2006;
Huntingford et al. 2013). Such changes could influence the probability of record temperature
exceedance. In both ensembles, there are indeed regions where significant changes in σ occur
towards the end of the 21st century (Fig. 5a and b). There is a well-understood decrease intemperature variability at Northern Hemisphere high-latitudes due to the diminished Arctic sea
ice cover at the end of the century (Screen and Simmonds 2010). Robust increases invariability occur in the Eastern Sahel region, the Amazon, Central North America, and Eastern
Europe (Fig. 5). While the σ changes in the Sahel region are likely related to a shift of the Inter
Tropical Convergence Zone, σ changes in the other regions might be due to soil moisture
feedbacks as suggested by, e.g., Seneviratne et al. (2006). To put the σ changes in CESM into alarger perspective, we have examined σ changes in 26 models participating in the fifth
Coupled Model Intercomparison Project (CMIP5) using the period 2061–2080 from the
RCP8.5 simulations compared to the historical period 1920–2014. Many of the regions witha statistically significant σ change in the CESM Large Ensemble (e.g., the Amazon, central
Europe, and Sahel) show the same sign σ change in more than 75 % of the CMIP5 models(not shown).
To investigate how the changes in variability impact our metric of record temperature
exceedance, we substitute the simulated future temperature distribution with a syntheticallygenerated temperature distribution using the simulated future mean, but using the simulated σfrom the historical period 1920–2014 (Fig. 5c and d). Hence, any potential narrowing or
widening of the temperature distribution with future warming is omitted. The syntheticallyClimatic Change(a) RCP 8.5 2061-2080 − 1920-2014(b) RCP 4.5 2061-2080 − 1920-2014

[σ]
-0.4

-0.2
0
0.2
Change in σ(c) RCP 8.5 2061-2080:
model σ − model historical σ

0.4(d) RCP 4.5 2061-2080:
model σ − model historical σ[%]

Difference in probability
Fig. 5 a–b Changes in interannual summer temperature standard deviation (σ) for 2061–2080 minus 1920–2014
in a RCP 8.5 and b RCP 4.5. Only significant changes are shaded, according to a F-test on the variance with
95 % confidence level. c–d Difference in probability of exceeding the historical temperature record between thesimulated temperature distribution in 2061–2080 according to c RCP 8.5 and d RCP 4.5 (see Fig. 2) and atemperature distribution with same mean but σ from the simulated historical period 1920–2014. Positive(negative) values indicate simulated change in σ leads to larger (smaller) probability

generated temperature distributions have the same sample size as the simulated ones
(20 years × 15 ensemble members = 300 summers). We stress that in this, as well as in otherapproaches (Battisti and Naylor 2009; De Vries et al. 2012; Gao et al. 2015), the generation ofsynthetic temperature distributions, although well grounded in physical understanding, is apurely statistical approach.
As shown in Fig. 5c and d, potential future changes in temperature σ have a very minor
effect (<2.5 %) on the probability of record exceedance in most locations. Certain regions,such as Eastern Europe or Siberia are subject to opposite signals for RCP 4.5 and RCP 8.5,
because with a strong warming (RCP 8.5) and a widening of the temperature distribution, theprobability of exceeding the record can become smaller than when the temperature distribution
stays at its historical width (see also Section 3e for further discussion of this effect). For otherregions the results are robust for both emissions scenarios. For example, along the US East
coast or in Western France, the probability of exceeding the historical record increases by 1–
7 % due to changes in σ.
e) Influence of model bias
Earlier studies raised concern regarding the capabilities of climate models to correctly
simulate interannual temperature variability (Battisti and Naylor 2009). Here, we investigate

Climatic Change

CESM biases in temperature variability and how they influence our results. Unlike in previous
sections, where we used the station-based BEST data set, we here use the European
Reanalysis-Interim (ERAi; Dee et al. 2011) product. Topography influences the estimate of
temperature variability at higher elevation, as higher elevations tend to have smaller interannual variability than surrounding lowlands. ERAi allows for a more appropriate comparison
with the model with regard to variability, as it applies a similar topographic smoothing. We
tested two other reanalysis (NCEP/NCAR, Twentieth Century Reanalysis), as well as two
station-based data sets (BEST, HadCRUT4) to confirm that reanalyses tend to have higher
variability than station-based datasets (not shown).
During the historical period 1979–2014, the model is in good agreement with observations
over most of the land areas, as measured by the ratio of simulated and observed interannual
summer temperature σ (quadratically detrended time series of 1979–2014 summer temperatures; Fig. 6a). The model tends to overestimate summer temperature variability in parts ofIndia and South East Asia, likely related to biases in the representation of the Indian monsoon.
A closer look at a grid point near New Delhi, India (28.6 °N, 77.2 °E), illustrates anoverestimation bias (Fig. 6b). Further, New Delhi serves as an example of non-linear warmingwith forcing scenario, a topic not touched upon in this study. There are other places, such as the
US East coast or central Africa, where variability is underestimated. In Africa, the biased(b) New Delhi, India(a) 1979-2014: model bias in σ

0.25
Frequency [%]

!

0.2
0.15
0.1

Model record 1920-2014
Median RCP 4.5 2061-2080
Median RCP 8.5 2061-2080
Observations
Model
RCP 4.5
RCP 8.5

0.05
0−5
Simulated σ / observed σ

!
0
5
10
Temperature anomaly [°C](c) RCP 8.5 2061-2080: model historical σ − observed σ (d) RCP 4.5 2061-2080: model historical σ − observed σ[%]Difference in probability

Fig. 6 a Model bias in interannual summer temperature standard deviation (σ), expressed as simulated σ divided
by observed σ over the period 1920–2014. Stippling indicates significant difference in variance of the two
samples, applying an F-test at the 95 % level. b Grid point example of a significant model bias; legends as inFig. 2. The bottom row (c–d) shows the difference in probability of exceeding the historical temperature record
using two different 2061–2080 temperature distributions: (i) a temperature distribution with the same mean as thesimulated temperature (see Fig. 2), but σ from the simulated historical period 1979–2014 σ, and (ii) same as (i)but using the σ from the observed historical period 1979–2014 (ERAi). Positive (negative) values indicate model
bias leads to overestimated (underestimated) probability. c (i)–(ii) for RCP8.5 and d (i)–(ii) for RCP 4.5

Climatic Change

location of the Intertropical Convergence Zone leads to an underestimate of precipitation
variability with associated effects on temperature variance (Siongco et al. 2014).
To examine how these biases influence our metric of record exceedance probability, we
repeat the analysis of Fig. 2, but using two different futures: (i) one in which we generate anormal distribution with the simulated future mean temperature, but using the simulated σfrom the period 1979–2014 and (ii) one in which we generate a normal distribution with thesimulated future mean temperature, but using the observed σ from the period 1979–2014.
Neglecting, for now, potential changes of σ itself with warming, this approach isolates theinfluence of model bias in variability on our metric.
Figure 6c–d contrasts the future temperature distribution with simulated σ with the one withobserved σ. From a global average perspective, the influence of model bias in temperature
variance is very small: −0.6 % under RCP 8.5 and 1.2 % under RCP 4.5 by 2061–2080. Theseseemingly contradictory tendencies are a result of the combination of model bias and our
metric. For example, in South-East Europe the model tends to overestimate summer temperature variability (Fig. 6a); in other words, the simulated historical σ is comparably large andthe observed one is comparably small. Adding the same moderate warming (RCP 4.5) to bothof these σ, enables the larger σ to exceed the historical record more easily, hence for RCP 4.5
the probability of exceeding for South-East Europe is overestimated. In contrast, once one adds
a large warming (RCP 8.5) to both of these σ the smaller σ tends to exceed the historical
record more often, as now the mean warming is as large or larger than the historical record.
Most of the biases in probability of exceeding the historical record are within ±10 % andtherefore do not affect the conclusions from Fig. 2, where the range ±10 % is not shaded.
However, such biases may need to be taken into account for certain applications.

4 SummaryThis study investigates the probability that summers in the future will be as warm or warmer
than the hottest on record during 1920–2014, based on large ensembles of simulations with
CESM under RCP 4.5 and RCP 8.5 emissions scenarios. The aim was to depict the benefits ofclimate mitigation by contrasting the two emission scenarios, as well as to illustrate theinfluence of model bias and changes in temperature variability on the results. While model
biases and changes in variability can be important locally, they are generally <10 % and thus
do not alter the large scale picture presented here. On a global basis, we find that theprobability of exceeding the historical record temperature increases from less than 10 % atpresent day to over 80 % at 2070 with projected warming under the business-as-usual scenario(RCP 8.5). This increase can be reduced to nearly half by moderate climate mitigation (RCP
4.5). A number of regions such as Brazil, Europe, or Eastern China benefit especially frommitigation by seeing risk reductions of over 50 %. Since these regions are densely populated,
this results in global population benefiting disproportionately from climate mitigation whencompared to just the land surface, as any mitigated warming in RCP 4.5 prevents those regions
from shifting into a higher risk category (see also Lehner and Stocker 2015). Some regions
show little risk reduction with climate mitigation, either due to small changes relative tointerannual variability, or because for those regions the projected summer temperatures willrobustly exceed the historical record temperatures already under RCP 4.5. Caution is therefore
warranted when interpreting the results, as the relative weights of benefits and limitations ofclimate mitigation depend strongly on the metric considered. Besides human exposure toClimatic Change

extreme heat, potential risk reductions from mitigation as shown here are also crucial for thesustainability of agriculture, which increasingly seeks to insure its yield for potential losses
from recurring heat waves and other severe weather. Note that crop-specific sensitivities toregional climate change and technological advancements, both not addressed here, cancomplicate the attribution of yield changes to climate change (Lobell and Asner 2003). In
conclusion, from the perspective of heat exposure of human and natural systems, there areclear and robust benefits associated with climate mitigation.
Acknowledgments We are very grateful to Bryan Jones for providing the population data and to Claudia
Tebaldi, Angeline Pendergrass, Laurent Terray, Brian O’Neill, and Andrew Gettelman for discussion and/or
constructive comments. We thank the three anonymous reviewers for their constructive comments and suggestions that helped to improve the paper. The National Center for Atmospheric Research is sponsored by the
National Science Foundation. F. L. is supported by an Early Postdoc Mobility fellowship from the Swiss National
Science Foundation.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International
License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide alink to the Creative Commons license, and indicate if changes were made.

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