US daily temperature records past, present, and futureGerald A. Meehla,1, Claudia Tebaldia, and Dennis Adams-Smithb

aNational Center for Atmospheric Research, Boulder, CO, 80301; and bClimate Central, Princeton, NJ 08542

Edited by Kerry A. Emanuel, Massachusetts Institute of Technology, Cambridge, MA, and approved October 13, 2016 (received for review April 15, 2016)

Observed temperature extremes over the continental United Statescan be represented by the ratio of daily record high temperatures todaily record low minimum temperatures, and this ratio has in-creased to a value of about 2 to 1, averaged over the first decade ofthe 21st century, albeit with large interannual variability. Two dif-ferent versions of a global coupled climate model (CCSM4), as wellas 23 other coupled model intercomparison project phase 5 (CMIP5)models, show larger values of this ratio than observations, mainlyas a result of greater numbers of record highs since the 1980s com-pared with observations. This is partly because of the “warm 1930s”in the observations, which made it more difficult to set record highslater in the century, and partly because of a trend toward less rain-fall and reduced evapotranspiration in themodel versions comparedwith observations. We compute future projections of this ratio onthe basis of its estimated dependence on mean temperature in-crease, which we find robustly at play in both observations andsimulations. The use of this relation also has the advantage of re-moving dependence of a projection on a specific scenario. An em-pirical projection of the ratio of record highs to record lows isobtained from the nonlinear relationship in observations from1930 to 2015, thus correcting downward the likely biased futureprojections of the model. For example, for a 3 °C warming in UStemperatures, the ratio of record highs to lows is projected to be∼15 ± 8 compared to the present average ratio of just over 2.

temperature extremes | temperature records | global warming |large ensemble

An analysis of observed continental US record high maximumand record low minimum daily temperatures in a quality-con-

trolled dataset of daily station data from 1950 to 2006 showed thatthe value of the ratio of record highs to record lows has been in-creasing over the United States since the late 1970s (1). Althoughthere is considerable interannual variability in the ratio, which is to beexpected when it is based on temperature time series with large in-terannual variability (2), averages of this ratio over the first decade ofthe 21st century had a value of about 2–1. This was a reflection of theincrease of mean temperature and a shift of its distribution, affectingthe tail behavior, such that, on average, for every one daily record lowminimum, there were roughly two record high maxima. This resultwas subsequently reproduced (3) and was also shown for Europe (4).A similar ratio of about 2–1 for monthly temperature records overAustralia was shown for roughly this same period (5). As noted inother studies (6), there are geographic and seasonal characteristics tothese records that depend on the variance of the temperature timeseries (7). Possible future increases to this ratio over the UnitedStates were shown for one future emission scenario (1).Several questions were raised in these studies that we address

here. First, the previous analysis (1) started in 1950 because of thedesire to use the more abundant and higher-quality postwar dailytemperature data. However, the 1930s are known as an extraor-dinarily warm period in the United States, introducing the questionof how the results would change if the “warm 1930s” were includedin the analysis. The same analysis also showed that the ratio ofrecord highs to record lows was greater in model simulations thanwas observed for the latter part of the 20th century, with the recordhighs in particular being more numerous in the models comparedwith the observations (1, 8). What can we say of the reasons for thisbias, and how can we use this knowledge to assess the credibility offuture projections of this ratio? In addition, can we quantify and

generalize the relationship between warming of mean US tem-peratures and temperature extremes represented by the ratio ofrecord highs to record lows for the 20th and 21st centuries, so thatfuture changes are not tied to a specific scenario?

ResultsAs described in previous studies (1), probability theory states that,in the case of a sequence of independent random variables iden-tically distributed, the expected number of records decrease as 1/n,where n is the number of realizations of the independent variableaccumulating as it is observed. In our application, n is the year forwhich the values of a calendar day maximum and minimum tem-perature are observed since the beginning of the observational re-cord considered. Each day of each year, values are compared withthe standing record highs and lows for the specific calendar day. Asyears (and records) accumulate, it becomes increasingly difficult fora stationary process to break a record, asymptotically as difficult asan event with probability 1/n (9). Thus, the number of years astation has been operating is an important factor in accounting forthe expected number of records.Analysis of observed station data for the continental United

States has shown that starting a 1/n calculation by taking all stationsavailable in the mid-20th century produced a credible accountingof records with distinct seasonal and geographical features up tothe more recent decades (since about 1980), when observed be-havior begins departing from expected (6). The same analysis alsoshowed that two factors influence changes in the numbers of re-cords that deviate from the theoretical 1/n relationship, involvingdifferent natural variability translating into a wider or narrowervariance of the climatologic distribution of temperature coupledwith changes in the mean of the distribution over time (i.e., thepresence of temperature trends). Following from the same the-ory, under stationarity, the ratio of daily record high maximumtemperatures to daily record low minimum temperatures should benear one, as the decay of the number of record highs and lowsfollows the 1/n time evolution for both. Any systematic and

Significance

Future changes in temperature extremes over the continentalUnited States are represented by the ratio of daily record highmaximum temperatures to daily record low minimum tempera-tures and computed as a function of mean temperature increasethat does not depend on scenario. A nonlinear empirical fit of therelation between this ratio and average temperature, using ob-servations from 1930 to 2015, is extended to 2100 and comparedwith the climate model projections. The projections of the ratioare somewhat higher than the empirical projection from obser-vations, continuing a positively biased trend in daily record hightemperatures in the 20th century in the models, which we link toless-than-observed summer precipitation and evapotranspiration.

Author contributions: G.A.M. designed research; G.A.M. and C.T. performed research; G.A.M.,C.T., and D.A.-S. analyzed data; D.A.-S. provided observed temperature and precipitation data;and G.A.M. and C.T. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence should be addressed. Email: meehl@ucar.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1606117113/-/DCSupplemental.

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prolonged change from a ratio of one indicates a change from theexpected numbers of record highs, record lows, or both.In Fig. 1, we compare the annual values of the ratio between the

total number of record highs and the total number of record lowsover the continental United States from 1930 to 2015 for observa-tions (black dots) and all values (gray dots) from the simulations bytwo CCSM4 model versions we consider here. These include a 1°resolution version, run with a large ensemble (termed “LE”) of 30initial condition ensemble members (Fig. 1A), and a more compu-tationally expensive half-degree version (hereafter “Hdeg”), run withfour initial condition ensemble members (Fig. 1B). The annualmedian values across the ensemble of individual model simulationsare shown as red dots in both panels in Fig. 1. There is considerableinterannual variability, indicated by the vertical spread of the dots(e.g., the observed value of the ratio in 2012 was around six, whereasit was less than one in 2013), and it is evident that the ratio in modelsand observations has been increasing, such that there are morevalues above one since about 1980, as was shown previously for ashorter record (1). In addition, the observations (black dots) liebelow the red dots (median model values) for most of the time se-ries, indicating a systematic overestimation of the ratio in the models.By extending this ratio into the future in the two models, followingrepresentative concentration pathway 8.5 (RCP8.5) (10) (Fig. 1 Cand D), the nonlinear nature of the increasing ratio is evident (4).The other notable, if expected, feature of Fig. 1 C and D for pro-jected future climate is that the variance of the ratio of record highsto lows gets larger with higher mean temperatures. This is becausethe denominator in the ratio (the number of record low minima)becomes increasingly small as record lows become less frequent andthe ratio becomes more variable. Note that using a different scenariowould produce a different projection. Thus there is a desire togeneralize the future changes of the ratio as a function of meantemperature change over the United States that does not involve aspecific scenario, following an approach that has been used to ad-vantage in other applications of future projections (11).To examine reasons for the different characteristics between

models and data, Fig. 2 shows the actual number of daily recordhighs and record lows for observations and model simulations,with the same plotting convention as in Fig. 1. There is a closecorrespondence between both models’ median values and the ob-servations for the record low minimum temperatures, with bothfollowing the expected 1/n time evolution until moving below 1/n

after about 1980, thus indicating a significant reduction in recordlow minima (Fig. 2 C andD) compared with their expected number.However, for record highs in Fig. 2 A and B, the models’ medianvalues track the 1/n line until about 1980, when the red dots moveabove the 1/n line, indicating a significant increase of record highsabove the expected number. This behavior is the mirror image ofthe record-low behavior and reflects the shift of the mean values ofthe temperature distributions. Meanwhile, the observations, startingin the late 1930s, actually track below the 1/n line, indicating lower-than-expected record highs, and then remain there until about 1980,when a few values finally move above the 1/n line, but are still belowthe median model values.To assess the effects of the warm 1930s on how records accu-

mulate, Fig. 3 shows the same analysis, using different start dates(pushing the start date even farther back in time before 1930 is notfeasible because of the lack of data with sufficient coverage torepresent conditions over the continental United States). If there isa very warm period at the beginning of the tabulation of records at astation, it will be difficult to set daily high maximum temperaturerecords later in the century, when daily maximum temperaturescooled somewhat before warming again at the end of the 20th andbeginning of the 21st century (Fig. 4). Fig. 3A shows the effects of astart year in 1930, 1950 (Fig. 3B), and 1970 (Fig. 3C), with annualvalues from observations as black dots and the green line being an11-y running mean. As the record compilation starts with succes-sively cooler initial decades, the dots move progressively closer tothe expected 1/n line (moving from left to right in the figure), butnote that they still have a tendency to remain below the expected 1/nlevel. Thus, the warm 1930s has an effect on where the observeddaily high maximum records lie in relation to the 1/n line, but itappears that something else has contributed to relatively lownumbers of record highs compared with the modeled values, evenwhen taking a less extreme starting date (1950).Given that the daily low temperatures have recovered recently to

values above the 1930s (Fig. 4), the behavior seen for record highs(i.e., the dependence on the starting date) should not affect asstrongly the compilation of record lows. Indeed, moving to succes-sively more recent start dates for compilation of record lows doesnot have nearly as much influence as for record highs, with therecord lows falling well below the 1/n line after about 1980 for allstart dates (Fig. 3).It has been noted that the warm 1930s were mostly a result of

natural internal decadal variability associated with tropical Pacificsea surface temperatures (SSTs) (12), but notably, when consid-ering the ability of models to replicate such an event, the warm

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Fig. 2. (A) Time series of record highs starting in 1930 for large ensemble. Graydots are values from individual ensemblemembers, red dots aremedian values foreach year, and black dots are observations; blue line is theoretical expected valuesfrom 1/n relationship noted in text. (B) Same as A, except for half-degree model.(C) Same as A, except for record lows. (D) Same as B, except for record lows.

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anomalies were intensified by disastrous land use practices over largeparts of the central United States (13). Consistent with these expla-nations of the observed warm anomalies, the models’ ensemble re-sponse (represented by the median values in Figs. 1 and 2) could notbe expected to capture the observed behavior of record highs. Noneof the 30 individual ensemble members, however, shows a behavior ofmaximum temperatures similar to the observed, either, confirmingthe importance of land use change effects and feedbacks that the landmodel in CCSM4 could not have replicated. A similar analysis ofrecord high behavior across the available daily output from a CMIP5ensemble of 24 models confirms that none of them shows a similarbehavior to the observed. All of them, in lesser or larger measure,simulated the increase in record highs from the expected 1/n sta-tionary behavior, starting in the early 1980s (Figs. S1 and S2). Asmentioned earlier, even with a start date in the relatively cooler yearof 1970 (Fig. 3C), the observed record high maxima still lie mostlynear the 1/n line, whereas in Fig. 2 A and B, the model median valueslie mostly above the 1/n line after about 1980, indicating that theextraordinary 1930s are not the only culprit for the different char-acteristics of the model or models.An additional factor that has been shown to have a preferential

influence on daily maximum temperatures compared with dailyminimum temperatures is evaporation from the land surface, withdrier soils and reduced latent heat flux (and thus reduced evapo-transpiration) contributing to higher daytimemaxima preferentially inthe warm seasons (14). Indeed, a version of Fig. 3A for the June–July–August (JJA) season shows a preference for the record highs tobe below the 1/n estimate compared with December–January–Feb-ruary for the post-1980 period (Fig. S3). Pinning down a connectionbetween record highs (which can be represented by daily high tem-peratures, as in Fig. 4) and evapotranspiration in observations issomewhat problematic, as a time series of observed evapotranspira-tion over the continental United States from 1930 to the present doesnot exist. However, a number of factors that contribute to evapo-transpiration can be studied in the models, with the goal of using awell-observed quantity as a proxy.Evapotranspiration depends on a number of interrelated pro-

cesses, starting with precipitation that is intercepted by vegetationand bare soil. Bare soil evaporation is dependent on top soil layer

moisture (which is a function of evaporation, infiltration, and thesoil moisture profile below it), the specific humidity gradientthrough the surface layer into the lower atmospheric boundarylayer, the reference height wind speed, the surface roughness, andthe atmospheric stability of the lower boundary layer. Vegetatedfluxes that contribute to evapotranspiration also depend on thosesame factors and are complicated by within-canopy turbulenttransfers and by water availability in the canopy and root zones(Materials and Methods).Soil moisture effects on temperature extremes are manifested both

by sensible heat flux and latent heat flux through evapotranspiration(15), with the latter playing a major role in daytime high temperatures(hereafter “Tmax”) during summer (16, 17). Although there are soilmoisture products that aim to represent observed quantities, theycan involve satellite-observed measures of skin wetness that maynot represent total moisture available for evapotranspiration froman upper layer of soil (18) or model-derived soil moisture metrics(19), and span relatively abbreviated periods. A well-observedquantity covering the same period as the temperature observationsnoted earlier, which relates directly to evapotranspiration and canbe compared with the model output, is precipitation. It has beenshown to be a credible proxy to represent soil moisture, and con-sequent evapotranspiration properties, during the summer season(16, 17).A distribution of precipitation trends for JJA is shown for ob-

servations and the two model simulations (Fig. 3D). The observa-tions show a distribution shifted toward a preponderance ofrelatively large positive precipitation trends (Fig. 3D, Upper) com-pared with smaller values and less substantial asymmetric behaviorin the distributions of JJA precipitation trends in the two modelsimulations (Fig. 3D, Lower). This discrepancy would be consistentwith an increase in warm season evapotranspiration since 1930 inthe observations compared with what the models would experience.The connection between JJA daily Tmax and precipitation trends isshown in Fig. S4, where there is a shift in the observed distributionof Tmax to negative trend values (Fig. S4B) compared with a shiftto positive values of precipitation trends (Fig. 3D, Upper, and Fig.S4D). Most of the observed negative trends in Tmax occur in thecentral United States, corresponding to positive precipitation trends

Fig. 3. (A) Same as Fig. 2 except for observations only with 1930 start date to compile record highs (Upper) and lows (Lower) and a best-fit line (green line).(B) Same as A, except for 1950 start date. (C) Same as A, except for 1970 start date. (D) Histogram of JJA precipitation trends for observations, 1930–2015(Upper), for large ensemble (Middle), and for half degree (Lower).

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in that same region (Fig. S4 A and C). This is reflected in negativecorrelations between Tmax and precipitation there in the observa-tions (Fig. S5A), and is illustrated with an example from the LEmodel results (Fig. S5B). This relationship does not change in thefuture climate in the model and, if anything, is stronger and moregeographically widespread (Fig. S5C).To connect Tmax and precipitation to evapotranspiration (using

the LE model as an illustrative example, the Hdeg model showssimilar results), Fig. S6 shows that JJA trends in Tmax (Fig. S6A) arenegatively correlated with comparable trends in evapotranspiration(i.e., higher Tmax associated with lower evapotranspiration, Fig. S6C:the pattern correlation of−0.5 is significant at the 5% level, as long aswe can assume that at least 12 of the grid-point locations in thesefields are independent of each other, which should be the case, evengiven the spatial correlation characteristics of these fields). Thelargest negative associations occur in the Western United States andGreat Plains. Meanwhile, JJA trends in precipitation (Fig. S6B) arepositively correlated with trends in evapotranspiration (Fig. S6C), ascould be expected from the discussion earlier (i.e., more precipitationassociated with greater evapotranspiration; positive pattern correla-tion of +0.4, significant at the 5% level if at least 15 independentlocations can be assumed). The largest positive associations are insimilar areas as the negative connections between precipitation andTmax noted earlier. Given these linkages in the model simulations,the large areas of negative precipitation trends in the observations

associated with comparable negative trends in Tmax would then likelybe associated with increased evapotranspiration that would contributeto the negative Tmax trends and fewer daily record high temperaturesin the observations compared with the models.This relationship in the model simulations between Tmax, pre-

cipitation, and evapotranspiration, if not directly tested for lack oflong records, can be inferred here for the observations and is con-sistent with physical process understanding. Such connections areconsistent with previous studies (14, 16, 17), particularly in the centralpart of the United States (20), and help us understand the modeltendencies of producing greater numbers of daily record high maxi-mum temperatures compared with observations (Fig. 2).With regard to the future and whether these relationships could

change in some way, Fig. S7 shows there is still a negative link be-tween JJA Tmax (Fig. S7A) and precipitation (Fig. S7B) for trendsin the LE model from 2006 to 2100 (pattern correlation of −0.5),and a positive connection between JJA precipitation trends (Fig.S7B) and evapotranspiration (Fig. S7C, pattern correlation of +0.6,significant at the 5% level if at least seven independent locations canbe assumed), both consistent with the 1930–2015 trends in Fig. S6.Another factor that could be producing lower daytime maxima

in observations compared with models is the rise of irrigation overcertain regions of the United States. Evidence from some areasshows that irrigation produces lower daytime temperatures in sum-mertime, but does not have an effect on nighttime temperatures (21,

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Fig. 4. (A) Time series from 1930 to 2015 of observed annual mean (solid line) and smoothed (green line) surface air temperatures over the continental United States,and the annual ratio of record highs to record lows (dots). (B) Same asA, except for daily maximum temperatures. (C) Same asA, except for daily minimum temperatures.

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22). Because the models do not include the effects of irrigation, thiscould be another contributing factor to the models simulating greaterdaytime maxima compared with observations.This assessment of possible biases in the simulation of record highs

vs. lows in the models brings us to the idea of trying to relate thebehavior of the record ratio with mean temperature changes, knownto be better simulated by climate models. We first quantify thenonlinear time evolution of the ratio of record highs to record lowsseen in Fig. 1 for the observations as a function of mean temperature(across the same set of stations) by fitting the log of the ratio of re-cord highs to record lows to US mean annual temperature (Fig. 5A).The fit has an R2 value of 0.50 and a slope of 0.66 (SD, 0.07). Similarplots for the two model versions, in which we use all ensemblemembers individually (i.e., without computing the ensemble mean,but using ensemble members as replicates) are shown in the rest ofFig. 5, with black dots plotted for the values from 1930 to 2015, andred dots for the rest of the time series, using RCP8.5 to 2100. Thenonlinear fit has a large R2 of 0.93 in both cases, with slopes of 1.16(SD, 0.004) for the LE and 1.05 (SD, 0.01) for the Hdeg. The re-lationship is therefore similar between the two model resolutions,with a steeper slope for the 20th century compared with observationsbecause of the issues noted earlier regarding the effects of the warm1930s and the differences inferred for precipitation trends, and likelythe implied evapotranspiration trends. Note that if we fit individuallog-linear relationships to the single ensemble members, we still ob-tain relationships showing a substantial positive bias in all cases (see

Fig. S8, where we plot histograms of the log-linear coefficients fromthe individual ensemble members and compare them with the ob-served values for the three starting dates used in our analysis of 1930,1950, and 1970).As mean temperatures increase in the 21st century, the nonlinear

relationship holds strongly for both model versions, but we proposecomparing the model projections with a projection made from theobserved relation and accounting for its uncertainty. As alreadymentioned, for the observations starting in 1930, the slope is 0.66 witha SD of 0.07. For a start date in 1950, the coefficient is 0.90 with thesame SD, and for a 1970 start date, the slope is 0.89 with the sameSD. To estimate a value for the future slope that factors in both theuncertainty relating to the starting date and the uncertainty in the fit,we use the lowest and highest values from the three observation-based fits (0.66 and 0.90) and add and subtract two times their SDs(2 × 0.08), obtaining a range for the future slope of 0.50–1.06. Notethat even by using this wide range based on observed behavior, onethat includes a period (starting from 1970) when models and obser-vations are in better agreement, our proposed future slopes are onlybarely overlapping with the model-based slopes (values of 1.05 and1.16). This procedure therefore notes a likely positive bias in themodel simulations of these future ratios, and at the same time relatesthe behavior of the ratio to what we know is a better simulatedquantity, mean temperature, while divorcing the projections from anyspecific scenario. For example, for a 3 °C annual average warmingover the United States, the ratio of record highs to record lows isprojected to be ∼15 ± 8.

DiscussionThis article builds on an earlier study (1) that examined US dailyrecord high maximum and daily record low minimum temperaturesin observations and a model from 1950 to 2006, as well as futurechanges of the ratio to 2100 in one future climate change scenario.Here, the period of the observations is expanded to include the warm1930s, and is updated with more recent observations to 2015. Simu-lations from a climate model at two different resolutions (CCSM4 atone degree and at a half degree) are analyzed for historical forcings inthe 20th century (taking the same period as the observations) andfuture climate simulations, using RCP8.5. These two models havesimilar characteristics, with regard to record highs and lows, as thelarger set of CMIP5 models. We set out to test the robustness of ourprevious findings when considering the warmer starting period of the1930s, and in the process, we investigate model biases. We argue thatsome systematic shortcomings in the simulation of maximum tem-perature may be at play (besides the difficulty of simulating an es-pecially warm period that was a result of not only internal variabilitybut also anthropogenic forcing through land use malpractice and itsfeedbacks). We propose an approach to evaluate the credibility of themodel projections in the context of observations, while also gener-alizing future increases in the ratio of record highs to record lows as afunction only of future mean temperature increases over the conti-nental United States that are independent of scenario.Earlier results (1) are confirmed, in that the ratio of daily record

highs to record lows over the United States has been increasing, suchthat the average value in the first decade of the 20th century wasabout 2–1, even when starting from a period as warm as the 1930s inthe United States. The newer CCSM4 simulations at both resolutions,as well as 23 other CMIP5 models, show a greater number of recordhighs compared with observations, although with a comparable de-crease in record lows. This is in part a result of the warm 1930s overthe United States, such that starting a compilation of daily temper-ature records in the warm decade of the 1930s makes it more difficultto set daily record highs later on. This is evidenced by the observedvalues of record highs lying below the expected 1/n line. Starting thecompilation at successively more recent start dates in decades coolerthan the 1930s produces better agreement with the expected 1/nvalues, but still points to a persistent warm bias in the model versions.Assuming the warm 1930s was partly a result of naturally occurring

internally generated climate variability related to tropical PacificSSTs, and partly a result of disastrous land use practices in large partsof the United States that exacerbated the warmth of the 1930s, we

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Fig. 5. Nonlinear fits as log plots of the ratio of daily record highs to recordlows as a function of US mean temperature increase for (A) observations1930–2015. (B) Large ensemble 1930–2100 with extensions of empirical fitfrom observations in A to 2100. (C) Same as B, except for half-degree 1930–2100. Gray-shaded ranges delimit the fits, using the smallest and largestvalues of the coefficient from the 1930/1950/1970 fits, plus or minus twotimes the (common) SD. The R2 values are given in figure panels. Black dotsare individual annual values from 1930–2015, red dots for 2016–2100.

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would not expect model simulations to capture those features of theobservations. An additional factor that has been identified in otherstudies as affecting the behavior of high temperature extremes isincreased evapotranspiration, which can contribute to lower daytimemaxima during summer, but does not have a particularly large in-fluence on nighttime minima. Using the well-observed quantity ofprecipitation as an indicator of evapotranspiration (daily Tmax isnegatively correlated with precipitation, whereas precipitation ispositively correlated with evapotranspiration), observations over theUnited States show a trend toward greater precipitation that is notmatched in the two model versions. Thus, the model simulationslikely have decreased evapotranspiration compared with the obser-vations, and this contributes to a greater number of simulated recordhigh maxima than observed. It is then desired to generalize futureprojections of temperature extremes, as represented by the ratio ofrecord highs to record lows, as a function of mean temperaturechange, so that the projections of the ratio in the future are in-dependent of scenario and independent of future precipitationtrends. For the latter, we have demonstrated how the effect ofobserved precipitation trends on Tmax trends is reproduced byCCSM4, and is therefore implicit in modeled future Tmax values.An empirical calculation involving a nonlinear fit for observationsas a function of mean temperature is extended to future warmermean temperatures and compared with a similar calculation fromthe future projections in the two model versions for 20th and 21stcentury climate (RCP8.5). This approach not only provides a wayto evaluate model projections in the context of the available ob-servations but also allows quantification of future changes of ex-tremes as a function of mean temperature increases that areindependent of scenario. This technique shows that future modelprojections of the increase in the ratio are likely biased somewhathigh mainly because of the model systematic error of simulatinggreater numbers of daily record highs compared with observations.Nevertheless, for example, for a 3 °C annual average warming overthe United States, the ratio of record highs to record lows isprojected to be ∼15 ± 8 compared to the present average ratioof just over 2.

Materials and MethodsWe use maximum, minimum, and precipitation daily records from a subset ofstations in the National Oceanic and Atmospheric Administration’s NationalCenters for Environmental Information (NOAA/NCEI) Global Historical Clima-tology Network (GHCN-Daily, Version 3.20) (23). The total number of stationswith coverage beginning at least by 1930 and updated to current dates is1,408. We do not perform any additional quality control (beyond what is

already performed over the stations in the GHCN), but we include all of the sta-tions available after checking that over the period 1950–2004; the results obtainedon the basis of the set of stations going back to 1930 are consistent with the resultsbased on the (larger) set of stations used in our 2009 study going back only to1950. On the basis of the new set, we expand the period under consideration from1950 to 2006 (1) back to 1930 and forward to 2015, such that the warm 1930s areincluded in the analysis, and the results are updated closer to present day. Theresults are presented as totals over the entire continental US region.

We are aware of two possible sources of observational bias. First, it is likely thatrecord lowminimafor some stationsare somewhat skewedtoacoolbias (e.g.,morerecord lows than should have occurred) because of changes of observing time (1,24), although this effect is considered to be minor and should not qualitativelychange the results. In addition, some stations used two types of thermometers torecord maximum and minimum temperatures (1). There was a switch to the Max/Min Temperature System in the 1980s at about half the US stations, such thatthermistor measurements are made for maximum and minimum, although thiseffect is considered to be small (25).

The model data are from two versions of the National Center for AtmosphericResearch (NCAR) Community Climate System Model 4 (CCSM4). One has thestandard 1° latitude–longitude resolution in the atmosphere (CAM4) that was runfor simulations of 20th-century and 21st-century climate within the CMIP5 protocol(26), where for the 20th century, both natural (volcanoes and solar) and anthro-pogenic [greenhouse gasses (GHGs), ozone, and direct effect of sulfate aerosols]forcings are included. For this particular experiment, however, a large ensemble of30 realizations from slightly perturbed initial conditions was run, starting from1920 (27). The other model version uses the same configuration of ocean, sea ice,and land surface components, but the atmospheric model is configured to run at ahigher resolution of one-half degree in latitude/longitude. The half-degree versionis run for four realizations of 20th-century climate. The two model versions, dif-fering only in resolution of the atmosphere, are then run for a future climatesimulation to 2100, using RCP8.5 with the same number of ensemble members asin the 20th-century simulations (i.e., 30 and 4, respectively). A full discussion anddescription of evapotranspiration-related processes in themodels is given in ref. 28.

ACKNOWLEDGMENTS. We acknowledge insightful and ongoing discussions onthis topic over the years with Guy Walton. Portions of this study were supportedby the Regional and Global Climate Modeling Program of the US Department ofEnergy’s Office of Biological & Environmental Research Cooperative AgreementDE-FC02-97ER62402 and the National Science Foundation. The National Centerfor Atmospheric Research is sponsored by the National Science Foundation.Computing resources (ark:/85065/d7wd3xhc) were provided by the Climate Sim-ulation Laboratory at NCAR’s Computational and Information Systems Labora-tory, sponsored by the National Science Foundation and other agencies. Thisresearch also used the resources of the Oak Ridge Leadership Computing Facility,located in the Oak Ridge National Laboratory, which is supported by the Officeof Science of the Department of Energy under Contract DE-AC05-00OR22725,and an award of computer time was provided by the Innovative and NovelComputational Impact on Theory and Experiment program.

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13982 | www.pnas.org/cgi/doi/10.1073/pnas.1606117113 Meehl et al.

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