Climatic Change

, Volume 111, Issue 2, pp 487–495

Increasing prevalence of extreme summer temperatures in the U.S.

A Letter


    • Lawrence Livermore National Laboratory
    • Climate Central, Inc.
  • C. Tebaldi
    • National for Atmospheric Research

DOI: 10.1007/s10584-012-0396-6

Cite this article as:
Duffy, P.B. & Tebaldi, C. Climatic Change (2012) 111: 487. doi:10.1007/s10584-012-0396-6


Human-caused climate change can affect weather and climate extremes, as well as mean climate properties. Analysis of observations and climate model results shows that previously rare (5th percentile) summertime average temperatures are presently occurring with greatly increased frequency in some regions of the 48 contiguous United States. Broad agreement between observations and a mean of results based upon 16 global climate models suggests that this result is more consistent with the consequences of increasing greenhouse gas concentrations than with the effects of natural climate variability. This conclusion is further supported by a statistical analysis based on resampling of observations and model output. The same climate models project that the prevalence of previously extreme summer temperatures will continue to increase, occurring in well over 50% of summers by mid-century.

1 Introduction

Climate models project that summertime-average temperatures that are historically unprecedented will become normal sometime during this century (Battisti and Naylor 2009; Diffenbaugh and Ashfaq 2010; Diffenbaugh and Scherer 2011; Anderson 2011a and b). Here we show that summertime temperatures that were historically rare already occur more frequently in some regions of the 48 contiguous United States. While we do not attempt to perform a rigorous detection and attribution study, we show how the patterns of temperature intensification that appear in observations are consistent with those that are obtained as multi-model averages in 20th century climate simulations downscaled from CMIP3 global climate simulations. The same patterns appear, further intensified, as the average patterns during the current and future part of the simulations. Since the average behavior of an ensemble of simulations like CMIP3 is interpretable as the forced component of the climate change signal, our analysis suggests that what we see in observations is consistent with the effects of enhanced greenhouse gas forcings, as simulated by the CMIP3 ensemble of global climate models.

2 Results

As an initial exercise to evaluate correspondence between model results and observations, we consider the period 1950–1999 and compare results based upon global climate models to two observation-based data sets (Maurer et al. 2002; PRISM 2007). The model results are based on simulations from 16 global climate models (GCMs) contributed to the World Climate Research Programme’s (WCRP’s) Coupled Model Intercomparison Project phase 3 (CMIP3) multi-model dataset (see Table 1 for a list of the GCMs used, which are all that are available under the chosen emission scenario). These simulations were bias corrected and downscaled to a grid spacing of 0.125° in latitude and longitude (Maurer et al. 2007). Briefly, the bias correction is achieved through quantile mapping between cumulative distribution functions of monthly temperatures in observed and modeled data. The spatial disaggregation from the native GCM grid to the finer resolution is achieved through an interpolation that uses observed fine-scale spatial patterns of temperature variations, month-specific, to account for terrain feature and other local effects. A key assumption behind this and related methods is that these fine-scale patterns, derived during a historical period, will also apply in the future. Each simulation spans the period 1950–2099, and assumes historical greenhouse gas and other climate forcings during 1950–1999, and the A2 emissions scenario thereafter. This scenario reaches concentrations of more than 800 ppm of CO2 by 2100 as a consequence of assuming a heterogeneous future world with continuously increasing global population and regionally oriented economic growth, relatively slower and more fragmented than other families of future emission scenarios (Nakicenovic et al. 2000).
Table 1

The 16 GCMs for which results for the SRES A2 scenario are available from the downscaled and bias corrected archive, and their country of origin






















South Korea











For the present purpose, bias-correction is useful because the method employed differentially adjusts values from the GCM such that the cumulative distribution function (CDF) of adjusted values during a historical reference period (1950–1999) matches the CDF of observed values. This in principle leads to improved representation of extreme values beyond the reference period.

For each model or observational data set, we first calculate at each location the 95th percentile value of the mean summer temperature (averaging June, July and August monthly means) during a reference period, 1950–1974. The choice of 95th percentile as a threshold is to a large extent arbitrary but is a common choice in defining extremes and modeling their behavior. We next determine the fraction of summers during the next 25 years (i.e. 1975–1999) when that 95th percentile JJA temperature value is exceeded. For the model-based results, we show an average frequency of exceedance based upon the 16 GCMs. Figure 1 shows broad agreement between the models and the two observational data sets in both the overall spatial pattern and the magnitude of these historical changes. The observation-based results have more fine-scale structure than the model-based results, presumably because taking the multi-model mean tends to “smooth” the model results; this difference complicates quantitative comparison between models and observations. Areas where the expected frequency of exceedance appears to have increased are the Southwest, the upper tier of the Midwest and the Atlantic coast, while the main portion of the Midwest, together with much of the Southeast and Northwest are characterized by observations and simulations that remain consistent with a stationary climate, i.e., where the exceedance frequency is close to 5%, the climatological percentile chosen as threshold. Statistical significance is confirmed for the general regional patterns of increased frequencies of exceedance through a bootstrapping procedure (see Materials and methods section and maps in Supplementary Material). Several studies (Pan et al. 2004; Knutson et al. 2006; Wang et al. 2009; Meehl et al. 2012) have documented the lack of a warming trend, especially in the summers, for these same regions broadly speaking. In particular, a stark contrast exists between seasonal trends in the Eastern and Western US (Portmann et al. 2009), which our analysis confirms along the same broad lines.
Fig. 1

Exceedance frequencies during 1975–1999 for summer-mean temperatures that were 95th percentile values during 1950–1974. Results are shown as percentage, for two observational datasets (top row) and a multimodel ensemble average of 16 GCMs that have been bias corrected and downscaled (bottom row). In a stationary climate we would not expect these values to be statistically significantly different from 5%. Figure S1 shows the results of a bootstrap procedure determining at which locations the results differ from 5% with high statistical significance

The strong increase in exceedances in the Southwest and Northeast are explained by strong historical and projected warming there, together with relatively weak interannual variability. On the other hand, the main portion of the Midwest has stronger interannual variability and less historical and projected warming, hence smaller increases in exceedances (see Supplementary Material for maps of the ratio between linear trends and interannual standard deviation from observational and modeled data).

One may ask if this correspondence between model-based results and observations could be an artifact imposed by the bias-correction process mentioned above. That process forces the year-to-year variability in the bias-corrected results to have some of the same statistical properties as observations when the entire period 1950–1999 is considered. However, it does not affect the likelihood of a favorable comparison between 1950–1974 and 1975–1999 (or any later period), because that depends on the sequencing of values, which is not affected by the bias correction. To confirm this, we recalculated the results shown in Fig. 1c based upon the same GCM results before bias correction and downscaling. The results (not shown) are very similar to those from the bias corrected and downscaled results.

In this study we do not perform a rigorous detection and attribution analysis. However, the results shown in Fig. 1 suggest that the observed increase in extreme summer temperatures is consistent with the forced signal rather than with low frequency natural climate variability. If the changes in the frequency of exceedance were due to natural variability, the model-based results should not agree with the observations except through chance. This is so because in the models the phasing of cycles of natural variability is random, and hence the effects of natural variability tend to disappear when results from multiple models are averaged together. We have also used a bootstrapping procedure (described in detail in the Materials and methods section) to confirm that the likelihood of this larger number of exceedances happening by chance through natural variability is extremely small. Thus, even if we do not formally attribute the behavior in the observations to the effects of increased radiative forcings from rising greenhouse gas concentrations we find it to be consistent with the forced signal from the CMIP3 ensemble, with or without bias correction. Note that recently several papers (Christidis et al. 2010; Stott et al. 2010; Zwiers et al. 2011) have documented anthropogenic influences on temperature extremes variously defined, at global and large, subcontinental regional scales, but no study has performed formal detection and attribution at finer geographical resolution.

Figure 1 shows that changes in the frequency of occurrence of extreme summer temperatures are apparent in broad regional patterns even when there is no time-gap between the two time intervals compared. It also shows that these models are simulating the observed historical behavior, replicating the large scale spatial differentiation between Southwest, Rockies and Atlantic coast on the one hand and Midwest, Pacific Northwest and Southeast on the other; this supports the use of these models to look at the same phenomena during the 21st century under increasing anthropogenic greenhouse gas concentrations. Note that we expect the results of a multimodel average to appear smoother and less “extreme” numerically than the observational fields, which are expected to behave more akin to individual simulations. Next, then, we analyze what the same simulations project for the beginning of this century and longer-term future threshold exceedances.

First, we use simulation results from 1995 to 2024 as representative of the present period. Using the same method as before, with 1950–1979 as reference period to compute the 95th percentile, we calculate average frequencies of exceedances in the present epoch (Fig. 2). As is evident, simulations project substantially increased probabilities of formerly rare summertime mean temperatures (happening with 5% chance or less during the reference period) everywhere in the 48 states. As noted above, the result is unlikely to be a consequence of natural fluctuations in summer temperatures, and is more consistent with the forced climate response emerging as the average behavior of the CMIP3 simulations, thus suggesting the effect of human-caused climate change. It is also interesting to note how the spatial pattern of change is similar for the two periods considered so far, and only the intensity is amplified in the later period.
Fig. 2

Exceedance frequencies during 1995–2024 for summer-mean temperatures that were 95th percentile values during 1950–1979, from the same ensemble of 16 models used in the bottom panel of Fig. 1. A bootstrap procedure applied to the individual simulations determined that these frequencies are statistically significantly different from 5% at every gridpoint, for each of the models

Finally, we use the same model-based results and approach to project forward to the middle of this century (2035–2064; Fig. 3). These results show the same general spatial pattern as for earlier periods, with the South and Southwest of the United States projected to experience the largest intensification on the frequency of hot summer by historical standards. If the spatial pattern is similar, the actual values of exceedance frequencies are greatly increased. For the mid-century period, summertime mean temperatures that occurred historically only 5% of the time are projected to occur at least 70% of the time everywhere in the 48-state region. Many studies (for example Meehl and Tebaldi 2004; Stott et al. 2010) have recognized the Southwest as a hot spot of future warming, and find similar patterns for the intensification of summer extremes.
Fig. 3

Same as Fig. 2, except considering a study period of 2035–2064 instead of 1995–2024

3 Discussion

We use two gridded observational datasets and a downscaled version of a subset of the CMIP3 simulations to study rare summer-average temperature exceedances in historic, present-day and future climate over the United States. A comparison of historical data and simulations confirms that the models skillfully represent the behavior found in observations for the latter part of the 20th century, showing increases in threshold exceedances (with the threshold set at the 95th percentile of climatological summer temperatures) that are already statistically significant and not consistent with the effect of natural variability alone. We then analyze exceedances of historically rare temperatures in the simulations for the current early-21st century climate and future mid-21st century climate, finding a steady increase in the frequencies of previously rare hot summers and robust geographical patterns of change across the US region.

This study does not perform a rigorous detection and attribution of this behavior, but shows how the observations are already more consistent with an estimate of the forced signal in CMIP3 (i.e., its ensemble average behavior) than with natural variability, as estimated through a bootstrap procedure. It also builds confidence in the use of simulations to project ahead in the future by showing the consistency of observations and model results both in terms of broad spatially differentiated behavior and intensities. The changes ahead appear of increasingly larger magnitude, consistent with a warming climate, with a spatially diverse behavior similar to what already appears in observations and historic model simulations. Even in those areas that are less intensely affected by warming, however, changes in the frequency of what was historically a one in twenty year event are so large that such events will be experienced with at least a 70% chance every year.

4 Materials and methods

To quantify the likelihood of the result shown being a chance consequence of natural climate variability, we perform two simple Monte Carlo-type assessments. With regard to the significance of the observed and historic simulated data, we use a randomization of the 50 years available (1950–1999) into two disjoint sets of 25 years, and repeat the analysis to evaluate changes in frequencies of exceedances between the two. This exercise is repeated 100 times, with the same individual shuffling of years applied to each grid cell in the dataset (observed and modeled). As in the original analysis, we do this for each of the 16 models individually and compute the model-mean result at each location. When the set of 100 simulated values is available we ask in what fraction of the 100 cases the exceedance values computed from the original data (shown in Fig. 1) is exceeded. When this happens in fewer than 5 cases out of 100 we deem the values in Fig. 1 statistically significant. Maps in the supplementary material where all non-significant values have been set to 5% show how the broad geographical areas where the exceedances are above 5% are indeed statistically significant in both observational datasets and for the multi-model mean (in the latter case we show areas where at least half of the 16 model simulations agree on the statistical significance, following the criteria proposed in Tebaldi et al. 2011). We perform the same type of bootstrap using the entire period (1950–2099) of the individual simulations, in this case selecting at random two disjoint sets of 30 years out of the available 150 years. The ensuing estimate of the likelihood of the results in Fig. 2 being due to chance ordering of years; i.e., natural climate variability turns out to be less than 1% at all 0.125º grid cells, thus we do not show corresponding maps in the Supplementary Material as they would be identical to Fig. 2.

One may argue that this procedure has limited validity because it ignores year-to-year autocorrelation among seasonal temperatures—although it is not clear in which direction this limitation would tend to push the result. As a second estimate, therefore, we repeat the Monte Carlo calculation, this time selecting at random not individual summer temperatures but 3-year temperature sequences. The results did not change.


Claudia Tebaldi acknowledges support from the US Department of Energy, Office of Biological and Environmental Research, grant DE-SC0004956 and thanks the Climate and Global Dynamics division of the National Center for Atmospheric Research, Climate Change Research section, for hosting her.

Supplementary material

10584_2012_396_MOESM1_ESM.pdf (816 kb)
Figure S1Like Fig. 1 but here we set to 5% all values that are not determined significantly different from 5% on the basis of the bootstrap procedure described in detail in the Materials and methods section. (PDF 816 kb)
10584_2012_396_MOESM2_ESM.pdf (268 kb)
Figure S2Ratio of the value of a linear trend fitted to the 50 year period 1950–1999 (in degrees Celsius per year) divided by the inter-annual standard deviation computed on the same 50 year period, for the two observational datasets top row and the ensemble of GCM simulations (presented here as the ensemble average ratio). These results confirm the different magnitude of this ratio in the different regions that the analysis of exceedance has highlighted. Note that observations in some regions show negative trends, while the ensemble average of the GCMs do not, consistent with the idea that negative trends are caused by internal variability that is not replicated consistently and simultaneously across the ensemble of models. (PDF 267 kb)

Copyright information

© Springer Science+Business Media B.V. 2012