Historically hottest summers projected to be the norm for more than half of the world's population within 20 years

We use detection and attribution analysis (e.g. Allen and Stott 2003, Ribes et al 2013) to assess whether climate model simulations of summer temperatures are consistent with observations. We first average land-surface temperatures over three summer months and over the regions outlined in figure 1(A). We then estimate the factors by which the model simulated response to anthropogenic and natural forcing (ALL) should be scaled to best match the observations. These scaling factors are obtained by regressing observations onto the expected climate responses to external forcings, i.e. the signals represented by the multi-model ensemble mean of climate simulations under the respective forcings. We use the standard total least square based optimal detection method (Allen and Stott 2003) for the detection and attribution analysis. This method takes noise in the model-simulated climate response that arises from internal climate variability into account. This requires estimates of the climates internal variability, which we obtain following the Ribes et al (2013) approach that uses a regularized estimates of the covariance matrix estimator in place of standard sample covariance matrices as regularization improves the covariance matrix estimates (see discussion in Ribes et al 2013) and obviates the need for adhoc regularization, such as through the EOF truncation approach that has often been used in the past.

The goodness of fit of the regression models is tested using a residual consistency check (Allen and Tett 1999, Ribes et al 2013). Figure 1(B) illustrates the best-estimate and the 5th and 95th percentile of the resulting ALL scaling factors for three selected regions. The signal is detected in the observations if the 90% confidence interval lies above zero. If the confidence intervals for the scaling factors include unity, the magnitudes of model-simulated and observed changes are comparable. If the scaling factors are larger than unity, the model simulated response is underestimated, and if they are smaller than unity, overestimated. We also perform a detection analysis using the climate response to natural (NAT) forcing alone, as well as to anthropogenic (ANT, obtained from ALL-NAT) and NAT forcing simultaneously (see figure D1 for all regions).

The best estimate of climate response to external (ALL) forcing in the observations is obtained by multiplying the model simulated response by the scaling factors. This is removed from the observations, and the residual is taken to represent natural variation of the climate without the influence of external forcings (see figure 1(C)).

We also use the ALL scaling factors to adjust the signals from historical ALL and future representative concentration pathway (RCP) simulations (figure 1(D)). The 380 samples of noise from pre-industrial simulations are added to these observational-constrained signals to produce multiple realizations of reconstructed and projected future temperature changes. Christidis et al (2012, 2015b) used a similar method, but with a single scaling factor obtained from a global space–time temperature pattern that was regionally resolved. By using scaling factors obtained for individual regions, we constrain signals only with information from the respective regions, which allows closer adjustment to regional differences between observed changes and signals, but also means that the uncertainty in the scaling factors is larger due to the averaging over smaller regions.

The proportion of reconstructed time series with temperature anomalies greater than the observed hottest temperature anomaly is referred to as the probability of exceedance (P₁, see figure 1(D)), or as the probability of a hot summer. A similar probability (P₀) is computed for the 380 pieces of control simulations. The fraction of attributable risk

$$\begin{eqnarray}&&\mathrm{FAR}=\displaystyle \frac{{P}_{1}-{P}_{0}}{{P}_{1}}\end{eqnarray} \tag{ 1 }$$

is then computed for each region. The FAR lies between −Inf and 1. A negative value indicates that an event becomes rarer due to anthropogenic forcing, while a positive value indicates that the event becomes more frequent.

Lastly, we define the year after which the probabilities of a hot summer P₁ are continuously larger than 50% and 90%. Each year, the population of the region for which this is the case is summed up to obtain time series of population exposure to hot summers.

The observational data are the University of East Anglia Climatic Research Unit gridded global land-surface temperature anomalies (CRU version 3.21, Mitchell and Jones 2005). Climate model simulations were obtained from the Coupled Model Intercomparison Project phase 5 (CMIP5) multi model ensemble (Taylor et al 2012) and are listed in tables A.1 and A.2. We consider historic simulations under ALL and NAT forcings. For future projections, we include simulations from two emission scenarios—RCP4.5 and RCP8.5. The RCP8.5 assumes radiative forcing to be 8.5 W m⁻² by 2100 (Riahi et al 2011, van Vuuren et al 2011). The reduction in emissions necessary to limit the forcing to this level is supposed to be reached with air quality legislation but without a strict climate policy. The RCP4.5 has a target radiative forcing of 4.5 W m⁻² and requires, for example, a decline in overall energy and fossil fuel use and a substantial increase in renewable energy forms (Thomson et al 2011). The increase in the global mean temperature is estimated to be 4.9 and 2.4 K above pre-industrial levels by 2100 under the RCP8.5 and RCP4.5 scenarios, respectively (Rogelj et al 2012).

Our ensemble consists of 54 ALL simulations, 45 NAT simulations, and 15 RCP4.5 and RCP8.5 simulations. When constructing time series over the past and future, we selected only model members from ALL simulations that also produced RCP runs (indicated with ALL_rec in table A.1). We conduct the detection and attribution analyzes based on the period 1950–2012 (63 years) and provide future projections for the period 2013–2069 (57 years). Fifty-one multi-year control simulations from various models are also used for the estimation of internal variability. Overall, these control simulations provide 380 chunks of data which are of the same length as the historical data (63 years).

We interpolate all data onto a 5 × 5° grid and mask the historical and control simulations to mimic availability of the CRU data. We then compute the summer mean temperatures by averaging monthly values of the three summer months (June–August for the northern hemisphere and December–February for the southern hemisphere). For the observations and ALL and NAT simulations, anomalies are calculated relative to the individual simulations' average over 1950–1984; anomalies are similarly calculated relative to the year 0–34 average in the case of the control simulations. The anomalies for each RCP simulation are calculated relative to the respective historical ALL simulation (1950–1984). Finally, we average the anomalies over large regions (see figure 1(A)) with the same region boundaries as used in the Special Report on Extremes (IPCC SREX report, Seneviratne et al 2012). The detection and attribution analysis is performed on 3 year mean series.

Projections of gridded population data for the years 2000–2100 are obtained from the GGI Scenario Database developed at the International Institute for Applied System Analysis (IIASA, Riahi and Nakicenovic 2007, scenario A2, available at http://iiasa.ac.at/Research/GGI/DB/). The original data is available at a time-step of 10 years. We obtain annual values by linearly interpolating the decadal values.

For time series of global-averaged summer temperatures, the responses to ALL and NAT forcing are detected in the observations. In all 26 regions except for North Australia, the responses to ALL forcing are detected, while the response to natural forcing alone is only detected in 11 out of 26 regions (figure D1).

Not detecting the responses to ALL forcing in observed changes—as is the case in North Australia—indicates that the ensemble mean of the simulations under ALL forcing does not match observations well. In North Australia, observed summer temperatures show only a very small increasing trend (figure D2). For the sub-period of 1979–2010, Li et al (2013) even report a cooling trend over the region and suggest that the cooling is due to the increase in North Australian summer rainfall and surface evaporation. The reason for the positive trend in precipitation is still unclear, although Li et al (2013) suggest that it is linked to an anomalous Gill-type cyclone response to increasing sea surface temperatures in the tropical Western Pacific. While such variability is present in observations and thus mask the response to ALL forcing, ensemble averaging would have largely removed the influence of internal variability in the ensemble mean of ALL simulations, leaving essentially only the forced response. Thus a discrepancy between observations and the ALL signal in a region strongly affected by low frequency variability is not implausible despite strong evidence of the ALL influence at the global scale and in most other regions.

The confidence intervals for the ALL scaling factors include unity in most cases, indicating a good match between models and observations in general. The residual consistency checks indicate no evidence of too little model variability. In 21 regions, the model-simulated variability is consistent with the regression residuals. In the remaining 5 regions, the simulated variability is too large. Larger variability in model simulations increases the width of the confidence interval for the scaling factor, making the detection results more conservative. We therefore include all regions in the subsequent analyzes.

Column 2 in table B.1 lists the historically hottest summers for each region. By multiplying these years' model simulated response under ALL forcing with the ALL scaling factor (see figure 1(C)) for each region, we obtain the temperature anomaly attributable to external forcing (figure 2). The attributable temperature anomalies have a mean of 0.59 K with an interquartile range of 0.33–0.73 K across the regions. The highest attributable temperature anomalies of 1.59, 1.29 and 1.43 K appear in the Mediterranean, North Africa and the Middle East, respectively (regions 13, 14, 19, figure 2 and table B.1). Their temperature anomalies relative to the 1950–1984 mean in the absence of external influences are estimated to be 0.47, 0.34 and 0.47 K, respectively. These three regions are also among the regions with the largest observed summer temperature increases over the past few decades (figure D2).

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In all regions except North Australia, the influence of external forcing on summer temperatures has become obvious over the last 30 years (figure D2). This has resulted in an increase in the occurrence probability of hot summers (supplementary figure S1), presented as the FAR in table B.1 and figure 2. Table B.1 also presents estimates of the uncertainty in the FAR (for explanations, see appendix B). The FAR for the historically hottest summer is over 0.9 in many regions, i.e. the occurrence frequency for a hot summer has increased by a factor of 10 due to the anthropogenic influence on the climate (figure 2). The FAR is lower in South America, Indonesia, North Australia and western North America. Christidis et al (2015b) showed that in 83% of global land regions, anthropogenic influence has at least doubled the odds of hot temperature events during June–August. This is consistent with generally large FAR values that we find here. Our results are also comparable to Jones et al (2008) who estimated that a past 1 in 10 year hot summer in the Northern Hemisphere has already become a 4 in 10 year event, equivalent to a FAR of 0.75. Zwiers et al (2011), investigating the return period of extreme annual maximum daily maximum temperature, found a FAR of roughly 0.25 for several Northern Hemispheric regions. Although we only present results for the FAR for the temperature anomaly during the historically hottest summer, it can be estimated for any temperature anomaly by the reader using our data (appendix C).

The year beyond which a region is projected to regularly experience hot summers is shown in figure 3. The timing represents the year after which the probability of a hot summer is higher than 50% (top) and 90% (bottom), respectively, in every subsequent year (for probability time series, see figure S1). This is synonymous with an occurrence frequency of 1 in 2 and 9 in 10 years, respectively, which we will also refer to as 'the norm' and 'most years', respectively (see table 1). As our analyzes extend only to the year 2069, 'every subsequent year' strictly means up to the end of our data record. The possibility that the probability for a hot summer after 2069 is below the thresholds cannot be ruled out completely, but is highly unlikely under the RCP4.5 and RCP8.5 pathways given that the projected warming is essentially irreversible on human time scales (Solomon et al 2009) . Note that we show results for both RCP4.5 and RCP8.5, but only discuss those for RCP4.5 in detail .

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Many northern hemispheric regions are projected to experience hot summers in 1 out of 2 years within a decade, and 9 out of 10 summers by 2040 (figure 3). Climate change has already impacted these regions in the past (Jones et al 2008, Christidis et al 2015b). Our analysis suggests that the Sahara region is the first to experience higher than historic summer temperature maxima—in 9 out of 10 summers within 15 years. The region exhibits a very strong warming trend and relatively small natural variability (figure D2). In Eastern Asia (region 22), we find that 1 out of 2 summers is projected to be hot by around 2020, comparable to the results from Sun et al (2014) for Eastern China (2025). Other areas for which hot summers are projected to soon become the norm are the Mediterranean region (around 2025), large parts of Asia (before 2025) and the Western US/Canada (2030, figure 3). These early dates are consistent with the strong summer temperature responses to climate change in these regions as documented in the IPCC 4th assessment report (AR4). The report shows that the median temperature response in the Sahara and the 'Southern Europe and Mediterranean' region are among the largest for the summer months (IPCC 2007 and table D.1). Jones et al (2008) also find a large increase in the occurrence probabilities in the Sahara and the Mediterranean regions in response to anthropogenic forcing, with a 1 in 10 year-event to become a 6 in 10 year and 7 in 10 year- event (or a FAR value of 0.83 and 0.86), respectively.

Our temperature threshold for hot summers in the Mediterranean is higher than the June–August average of the heat-wave summer of 2003. Such temperature extremes are projected to become the norm by 2025, and very few summers will be colder than that after 2035. The likelihood of hot summers in Europe has been studied extensively. Schar et al (2004) for example analyzed the temperature at the end of the twenty-first century simulated by a regional climate model and found that 1 in 2 summers would be as warm or warmer than the 2003 summer. Stott et al (2004) report a hundredfold increase in the expected frequency of 2003-type summers by the mid-twenty-first century, and Christidis et al (2015a) suggest that the human influence on this frequency has been underestimated.

The percentage of regions and population living in regions where summers are projected to be hot in 1 out of 2 (full lines) and 9 out of 10 years (dashed lines) are illustrated in figure 4. The timeseries are based on probabilities calculated from the observationally constrained projections. We ask the question: When are hot summers projected to be so widespread that half of the population regularly experiences summers (i.e. 1 in 2) that are hotter than any summer of the past? Under the moderate emission scenario RCP4.5, more than half of the world's population is projected to experience a hot summer in 1 out of 2 years within 20 years. If greenhouse gas emissions continue to rise throughout the 21st century (RCP8.5), this is projected to occur in just over a decade. The time at which half the world's regions are projected to be affected occurs only slightly later, which indicates that regions affected first have a somewhat smaller proportion of the global population. Just after 2050, nearly the entire population and over 70% of all regions are projected to be exposed to hot summers in 1 out of 2 years under RCP4.5.

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The timing of half of the regions being affected (2035 under RCP4.5 and 2030 under RCP8.5) is earlier than the timing reported in Mora et al (2013) for half of the grid cells being outside the historical range (around 2069 under RCP4.5 and 2047 under RCP8.5). The dates should, however, not be compared, as the definition of the timing in the two studies differ given the two entirely different approaches. Results in Mora et al (2013) are based on model simulations only. The timing is the median of the years at which each of the 37 models considered simulate temperatures higher than the maximum of the respective simulation's past temperature. Our probabilistic approach combines information from observation and model output and accounts for uncertainties from internal climate variability. The timing represents the year after which 50% of the set of 380 observationally constrained reconstructions of temperature timeseries are above the observed historical maximum. Nevertheless, it is worth mentioning that earlier timing in our study could also be explained by differences in the foci: while the quoted years of 2069 and 2047 from Mora et al (2013) are results for annual values, we analyze summer temperatures. Summer temperatures are less variable than annual mean values, which can lead to earlier occurrence dates. Furthermore, while Mora et al (2013) consider the grid cell scale (roughly 100 km), we average over large regions, which further reduces variability. Our analyzes are also restricted to land areas—the area most relevant for human exposure to heat—whereas Mora et al (2013) analyze values over ocean and land.

Due to the adjustment of simulated RCP time-series with the scaling factors obtained by comparing model simulations with observations, we should improve our estimates of probabilities of hot future summers as compared to using the raw time series. In our analysis, 21 out of the 26 regions show a best estimate of the scaling factor below unity, i.e. model simulations overestimate the historic temperature increase. By adjusting raw model output with these scaling factors, we reduce temperature change relative to that in the raw model output, which leads to more gradual increase in the population affected by hot summers and a later timing of exceeding historically maxima temperatures.

We re-sample the 380 chunks of the control simulations 1000 times with replace to obtain 1000 times 380 bootstrap samples . We use each bootstrap sample of control chunks to estimate P₀ directly from the re-sampled control chunks and P₁ from reconstructions produced with the sample of control chunks. We thus calculate

$$\begin{eqnarray}&&\mathrm{FAR}=1-\displaystyle \frac{{P}_{0}}{{P}_{1}}\end{eqnarray} \tag{ 2 }$$

1000 times. We then calculate the interquartile range (25th and 75th percentiles) and the median of these 1000 realizations of the FAR to estimate it is uncertainty. Note that the medians (table B.1) are very close to the single FAR estimate using the original set of control simulations (column 'FAR').

We additionally include the uncertainty of the scaling factor by re-sampling the scaling factor 1000 times. We do not know the distribution of the scaling factor obtained from the total least square method (see Ribes et al 2013). However, to roughly approximate the shape of the distribution, we assume a shifted log-normal distribution. The scaling factor (x₅₀) and its 5th (x₀₅) and 95th-percentiles (x₉₅) are obtained from the ROF. If x₀₅ is below zero, we do not calculate the FAR (region 25). If the 5th and 95th-percentile values indicate a right shifted distribution, i.e. $| {x}_{95}-{x}_{50}| \lt | {x}_{50}-{x}_{05}|$, we first mirror x₀₅ and ${x}_{95}$ to obtain a left shifted distribution, using the formula ${x}_{95}^{\prime }={x}_{50}-({x}_{95}-{x}_{50})$ and ${x}_{05}^{\prime }={x}_{50}+({x}_{50}-{x}_{05})$. We then calculate the parameters σ (scale parameter) and γ (shift parameter) to minimize the function

$$\begin{eqnarray}&&y=1/2+1/2\ast \mathrm{erf}\displaystyle \frac{\mathrm{ln}(x-\gamma )-\mu }{\sqrt{2}\sigma }\end{eqnarray} \tag{ 3 }$$

with $\mu =\mathrm{ln}({x}_{50})$ and with the arbitrary choices of initial values $\sigma =0.5$ and $\gamma =\mathrm{min}(\mu ,{x}_{05},{x}_{95})-0.001$. With the resulting σ and γ values, we generate scaling factors β by selecting values x at random from the uniform distribution on the interval $\left[{x}_{05}-\tfrac{{x}_{95}-{x}_{05}}{10},{x}_{95}+\tfrac{{x}_{95}-{x}_{05}}{10}\right]$ and then applying the probability integral transform

$$\begin{eqnarray}&&\beta =\displaystyle \frac{1}{(x-\gamma )\sigma \sqrt{2\pi }}\ast {{\rm{e}}}^{-}\displaystyle \frac{{(\mathrm{ln}(x-\gamma )-\mu )}^{2}}{2{\sigma }^{2}}\end{eqnarray} \tag{ 4 }$$

in order to sample from the shifted log-normal distribution. We then re-transform the resulting values if the original distribution was right shifted. Lastly, we reconstruct P₀ and P₁ similar to above, but with drawing a different scaling factor for each reconstruction. We calculate 1000 simulations of the FAR with equation (1) and calculate the 25th, 50th and 75th-percentile of the FAR. Table B.1 shows that the interquartile range of the FAR is larger when the uncertainty of the scaling factor is included, as expected.