The European heat wave of 2003, the Russian heat wave of 2010, and the extreme pollution and mortality increase that accompanied both events underline the danger of heat waves and the accompanying air pollution. Summertime increases in temperature are expected in the next century in all climate scenarios (), with future heat waves expected to be more intense, more frequent and longer lasting (e.g., ). Here we examine the relationship between temperature extremes and ozone extremes in measurements and in current and future model simulations. An analysis of the joint extremes in ozone and temperature together may be particularly important as their joint impact on mortality is likely to be nonlinear (; ; ).

Over most of the US temperature is the first meteorological covariate with ozone (). The relation between ozone and temperature is complex: it is determined not only by temperature-dependent ozone chemistry () but also by other processes that correlate with temperature: for example, through meteorological factors such as stagnation events or cloud cover (e.g., see ) or through temperature-dependent emissions (e.g., ). The ozone–temperature relationship is often measured with a linear slope (e.g., ). Increases in ozone with temperature have been reported in the range from 0 to 6 ppbv ∘C-1 depending on details of the analysis (). The mechanisms accounting for variations in the ozone–temperature slope are still uncertain but can be at least partially explained by the emission regime: the slope generally increases as ozone precursor emissions increase (e.g., ).

When it comes to extreme values, the relationship between temperature and ozone becomes more complicated (e.g., ; ), such that an overall linear slope fit does not necessarily capture the relationship. The extremal dependence between ozone and temperature has been explored using various methods. calculated the conditional probability of a high ozone day (ozone above the 90th percentile) given a high temperature day (temperature above the 90th percentile). They found probabilities that range from approximately 50 % in the northeastern US to somewhat less than 20 % in the western US. and calculate the joint probability that ozone and temperature are extreme (above the 95th percentile) compared to the probability that either one of them is high. find that high temperature events and high ozone events co-occur up to 50 % of the time over the northeastern US between 1 April and 30 September. obtain a qualitatively similar geographic pattern in the joint extremes of temperature and ozone. Here we propose a new method to measure the joint extremes of temperature and ozone based on the spectral dependence of the extremes. Changes in the future relation between ozone extremes and temperature extremes depend on (i) changes in the nature of future temperature extremes and (ii) the impact of these extremes on ozone. Globally the future increase in extreme temperatures (temperatures at the 20-year return period) in CMIP3 are similar to the increase in mean temperature (), although there are some important regional exceptions. This would suggest that for the most part the future temperature probability distribution simply shifts to higher temperatures but does not change in shape consistent with measured trends (). Conversely, many studies suggest that the ozone distribution will increase predominantly on the high end due to changes in climate (e.g., see ), although not all (e.g., ). find increases in the high end of the probability distribution of both temperature and ozone in the midwestern US in 2050, attributing this to an increase in stagnation episodes with soil–moisture feedbacks impacting the temperature distribution. At high enough temperatures (>312 K), find that the ozone increase with temperature is suppressed. hypothesize that this is due to the diminished role of peroxyacetyl nitrate (PAN) chemistry and isoprene emissions at high temperatures. show that ozone suppression at high temperature occurs at 23 % of the CASTNET sites but hypothesize that the suppression is meteorologically induced. Based on the statistical relationship between ozone and temperature in the present climate, predict that future temperatures will lead to an average increase of 2.6 ozone violations per year in 2060 across the US. examine the impact of an increase in future heat waves on ozone in two sets of future simulations: one with changing anthropogenic precursor emissions following Representative Concentration Pathway 6 (RCP6) and one in which the anthropogenic emissions remain fixed.

This article is organized as follows: in Sect. , we describe the data sets and model simulations used; in Sect. , we introduce the statistical procedures used to quantify the relationship between ozone and temperature. In Sect. , we present the results and then discuss these results in Sect. . Section gives the conclusions.

In this study we examine the simulated and measured relationship between ozone and temperature extremes over the US. In particular we analyze a number of specified dynamics REFC1SD simulations from the Chemistry-Climate Model Initiative (CCMI) (see ) for the period from 1992 to 2010. This allows a robust evaluation of simulated ozone and temperature extremes using analyzed meteorological fields and changing emissions against measurements. We also examine the impact of climate change on ozone and temperature extremes, comparing simulations of the current and future climate with fixed emissions. These latter simulations are free-running simulations in that the meteorology, sea surface temperatures (SSTs) and sea ice are calculated internally within the simulations. The free-running simulation of the current climate is compared with the REFC1SD simulations and the available measurements.

Most of the analysis in this paper emphasizes simulations with the Community Atmospheric Model with chemistry (CAM4-chem) within the Community Earth System Model (CESM1) . evaluate both the specified dynamics and free-running model configurations of CAM4-chem against measurements over the US, including comparisons of ozone return periods. The horizontal grid resolution in the CESM1 simulations analyzed here is 1.9∘×2.5∘; the free-running simulations have 26 vertical levels while the CESM1 REFC1SD simulation has 56 vertical levels. The CESM1 REFC1SD simulation (see ) uses analyzed meteorological data from Modern-Era Retrospective Analysis for Research and Applications (MERRA) from 1992 to 2010 and time-changing anthropogenic and biomass burning emissions as specified in Table . In the Supplement we include results from the REFC1SD simulations in an additional four models: the CHASER, CMAM, MOCAGE and MRI models. The number of REFC1SD models analyzed is limited to those with sufficient output to derive the maximum daily temperature and the maximum daily 8 h average ozone concentrations (MDA8). In the CMAM and MRI simulations both MDA8 ozone and daily maximum temperature are available daily; in the CHASER and MOCAGE simulations only daily MDA8 ozone data are available. Details on the additional model simulations are given in .

The analysis of how extremes change with climate is limited to the CESM1 simulations. In the present-day free-running CESM1 simulation (the GCM2000 simulation) the CO2 concentration is specified at 369 ppm, representative of the year 2000; in the future simulation (the GCM2100 simulation) the CO2 concentration is specified at 669 ppm, representative of the 2100 concentration of CO2 in the Representative Concentration Pathway 6 (RCP6) (see Table ). The concentrations of all other greenhouse gases including methane are fixed at their year 2000 concentrations in both these simulations. Biogenic emissions are also fixed and are representative of the year 2000. Both the GCM2000 and GCM2100 simulations are 25-year simulations branched off of the CCMI CESM REFC2 simulations in the year 2000 and the year 2100, respectively (). The first 5 years of each simulation are used as spin-up, with the latter 20 years analyzed. The global mean temperature change over the continental US between GCM2000 and GCM2100 is 2.1 ∘C, while the temperature difference in the parent CCMI REFC2 simulations following RCP6 is 2.8 ∘C. The smaller temperature increase between the GCM2000 and GCM2100 simulations is likely due to the fact that the emissions of greenhouse gases and short-lived forcing agents are held constant at the year 2000 levels in both simulations. In particular the aerosol emissions remain the same.

Hourly measured ozone and temperature data are taken from 23 CASTNET (Clean Air Status and Trends Network) stations with a nearly continuous data record during the period from 1992 to 2013 for the months of June, July and August (92 days each summer). In addition, to enhance the data record, we included two additional stations (Beaufort, NC, and Lassen Volcanic, CA) at which the first 2 or 3 years of data were missing, respectively. See Fig.  for station locations. CASTNET sites are situated to sample regional ozone concentrations so as to minimize the more local impact of urban areas. We supplement the CASTNET data with temperature and ozone measurements from the Environmental Protection Agency (EPA) Air Quality System (AQS) Data Mart for the years 1992–2010. This gives an additional 124 stations with nearly complete ozone and temperature data (see Supplement). Ozone data from the first model level provide a good estimate of 10 m ozone concentrations as measured by CASTNET (). The maximum daily 2 m temperature is used in both the CASTNET measurements and the simulations.

To render the data approximately stationary on both an interannual and seasonal basis, we adopt the procedures in . Formally, let xy,d represent the data on day d in year y, where x refers to either daily maximum temperature or MDA8 ozone. Since there are 91 days included in each summer period and 20 years (19 years for REFC1SD), d=1 refers to 1 June and d=91 refers to 30 August.

To minimize year-to-year variability so as to minimize any ozone trends while still keeping extreme data relevant, for each year y, we take the average of the data over that year but omit a number (a) of the highest values. That is, for a fixed year y, the resulting average is my,a:=1D-a∑i=1D-axy,(i), where D=91 is the total number of days for each year, and xy,(i) is the order statistic of the fixed year y: xy,(1)≤xy,(2)≤…≤xy,(D). Then, we calculate a daily ozone deviation: x^y,dG=xy,d-my,a.

In our analysis, we use a=10 as the default value, which preserves about 11 % of the extreme data. Sensitivity tests at a number of stations suggest the result is not sensitive to a. To eliminate seasonal effects, we average x^y,dG for each day d over all years Y=20 (or Y=19 for REFC1SD). That is, for each day d, we calculate Md=1Y∑y=1Yx^y,dG.

Md is then smoothed using a local polynomial regression since our sample size is rather small. In order not to overburden the notation, we will still use the notation Md for the smoothed values of the estimates. Then we normalize the data by x^y,dDS=x^y,dG-MdSDd, where SDd=1Y∑y=1Y(x^y,dG-Md)2 is the standard deviation of day d. Later in the text, we refer to Eq. () as a normalized scale.

In addition to the transformations from , we add another procedure to revert the normalized scale data back to its original scale while keeping the stationarity. That is, we rescale x^y,dDS back to its original scale (x^y,dres) by using the formula x^y,dres=x^y,dDS×1D∑d′=1DSDd′+1D∑d′=1DMd′+1Y∑y′=1Ymy′,a, where Y=20 (or Y=19 for REFC1SD).

In this study in addition to using conventional methods, such as correlations, to quantify the relationship between temperature and ozone, we also propose a novel metric to capture the relationship between ozone and temperature extremes. Correlation coefficients are inadequate for capturing the relationship between the extremes of two variables since they are estimated from all observations and extremes represent a small percentage of these observations. An alternative metric is proposed using only the largest values of two variables. After some transformations which act to normalize the two variables (see Appendix ), their extreme dependency is characterized by a probability density function (pdf) that measures the angular density when the variables are plotted against each other. The area under the pdf is 1 by definition and the range of the pdf is 0,π2. If the mass of the pdf is concentrated near 0 or near π2, extremes of the two variables are unlikely to be significant at the same time, which points to an independence of the extremes. Conversely, if the mass of the pdf is concentrated away from the end points 0,π2, then simultaneous extremes of the two variables are likely. We refer to the procedure which normalizes the tails of the data so that the method described above works as the ranks method (see Appendix ).

Since the area under the curve from 0 to π/2 is 1, we can consider only the area of the “middle” part, which we define to be between π8 and 3π8, to represent the extreme dependence between two variables. Denote this amount by φ: φ:=areaπ8,3π8.

See the detailed explanation in Appendix . Note that the range of φ is [0,1], where φ=1 refers to extreme dependence and φ=0 implies extreme independence.

Figure  shows different scenarios of correlation and extreme dependence. Figure a gives a scenario of data with high correlation, yet the extremes of the data are only moderately dependent (Fig. c). In contrast, Fig. b gives an example of data with low correlation but highly dependent extremes (Fig. d).

In this section we compare measured and simulated temperature and ozone records separately (Sect. ) and then their joint dependence is analyzed in Sect. . The extremes of ozone and temperature and their extremal dependence is emphasized. Simulated ozone and temperature records from the REFC1SD, GCM2000 and GCM2100 CESM1 simulations are given in the main body of the paper. Simulated results from the REFC1SD simulations for the CHASER, CMAM, MOCAGE and MRI models are given in the Supplement. In the main body of the paper all the measurements shown are from CASTNET. Additional measurements at the AQS sites are given in the Supplement. For any given simulation, all percentiles are given with respect to that particular simulation. In particular, percentiles for the future simulations are given in terms of the future distributions. Note, in addition, that all quantities shown have been rescaled following Eq. (5).

All the CCMI REFC1SD simulations (the CESM1 REFCS1D, CHASER, CMAM, MOCAGE and MRI) and the GCM2000 simulation show a fundamental mismatch between the locations where the width of the rhs of the temperature distribution is large and those locations where rhs of the ozone distribution is large. As measured by the difference between the 20-year return temperature and the mean temperature (Figs. , S4) or the difference between the 90th percentile temperature and the mean temperature (Figs. , S1), the width of the rhs of the temperature distribution is highest in the northern portion of the domain with a southward extension through the midwestern states and into the northwestern states. This pattern is consistent with increased temperature variability at higher latitudes (e.g., , and references therein) and a higher temperature variance in the interior of the country due to its greater continentality. However, ozone is most sensitive to temperature changes, as measured by the slope of ozone versus temperature, where ozone precursor emissions are large (). This is consistent with the fact that the width of the rhs of the ozone distribution is widest (Figs. , , and S2–S5) in the eastern third of the country, where emissions of ozone precursors are generally the largest. Ozone is also most sensitive to high temperatures in the eastern part of the US (Figs.  and S7). Geographical differences between the shape of the ozone and temperature distributions over the US impact the relationship between ozone and temperature extremes.

The response of ozone to changes in temperature is in part determined by the temperature–ozone correlation. Details of the temperature–ozone correlation are different in all simulations (see Figs.  and S6). Important differences include the location of the region of low correlations in the south central part of the US, the relative strength of the correlation in the northeastern and southeastern US and the pattern of correlations in the western US. Thus we might expect the ozone response to temperature extremes to differ in the different simulations. The CASTNET and AQS measurements (Figs.  and S6) generally support high temperature–ozone correlations in the northeastern US, low correlations along the Gulf of Mexico coast and generally high correlations in the Rockies and west coast states (also see ).

Some of the differences between the CESM1 REFC1SD and GCM2000 simulations are likely due to meteorological differences: while the CESM1 REFC1SD simulation is driven with analyzed meteorology, the GCM2000 simulation is driven with model-calculated meteorology. In general, the CESM1 REFC1SD simulation captures the measured relation between ozone and temperature better than the GCM2000 simulation over the northeastern US, although it does not fully capture their strong measured correlation (e.g., see Fig. ). In the southeast the measured response appears to be generally well simulated in both simulations. Overall the GCM2000 fails to capture the extreme dependence as measured by φ between temperature and ozone at the 95 % level; in the CESM1 REFC1SD simulation we cannot reject the null hypothesis that the simulated and measured values are the same.

A poor simulation of the Bermuda high in the CGM2000 simulation may be important in explaining some of the differences between the CESM1 REFC1SD and GCM2000 simulations. The position of the Bermuda high strongly impacts ozone distribution over the US (), with the second empirical orthogonal function of ozone variability strongly correlated with the location of the Bermuda high (). A westward extension of the Bermuda high is correlated with high temperatures and low ozone over much of the southeastern US () consistent with the low correlation between ozone and temperature in all the REFC1SD simulations extending northward from the Gulf of Mexico (Figs. , S6). We note this region of low correlations in the CMAM and MRI REFC1SD simulations is to the west of that simulated in CESM1 REFC1SD. In the GCM2000 simulation the Bermuda high is simulated too far to the west (not shown). Consistent with this, a maximum covariance analysis shows that the mode of variability associated with the Bermuda high is also displaced too far to the west (not shown). Thus, it is likely the pattern of variability associated with the Bermuda high is incorrectly simulated in the GCM2000 simulation. In particular, the GCM simulations do not show a region of low correlation extending northward from the Gulf of Mexico, but instead a region of low correlation is situated well to the north over Kansas. show the Bermuda high is not well simulated in the majority of GCMs. This has important implications for the simulation of the ozone response to temperature over large sections of the country.

In this study, we introduce a new spectral method using multivariate extreme value theory to measure extremal dependence between temperature and ozone in both the observations and model simulations. We find, through the use of this new metric, joint extremes of temperature and ozone occur together up to approximately 35 % of the time in a few regions, although on average their joint occurrence is significantly less. Previous studies have used different methodologies to capture the extremal dependence in measurements between ozone and temperature (; ; ). The analysis here uses a somewhat different methodology so it cannot be compared quantitatively with the previous results, but qualitatively the overall patterns are similar to those found previously. The advantage of the spectral method for finding joint extremes of temperature and ozone is that it gives detailed information about the joint extremes and is not restricted to a particular quantile of the distribution. It can be used to forecast joint extremes even out of the range of available samples.

The various model simulations differ in their simulation of φ (measuring the joint spectral extremes of ozone and temperature), again suggesting ozone may respond differently to high temperatures in the different simulations. In the central part of the country where the rhs of the temperature distribution is particularly wide, φ is relatively small (Figs. , S7) in all but the REFC1SD CESM1 simulation (Figs. , S7). φ is high in the CMAM and the MRI simulations in the northeastern US but not in the CESM1 REFC1SD or GCM2000 simulations; conversely, in the CESM1 REFC1SD, the GCM2000 and the MRI simulations φ is high in the southeastern US but not in the CMAM simulation. φ is high in the majority of the simulations in the northwestern states.

In general (with some exceptions along the US west coast) the geographical pattern of averaged MDA8 ozone conditioned on daily maximum temperature greater than the 90th percentile (mean(O3|T>90%)-mean(O3)) is qualitatively similar to that of φ in the model simulations and the measurements. However, it is important to note that while the measurement sites used here are sufficiently dense in the eastern US to resolve some of the regional features, they are nowhere dense enough to resolve regional features in the western two-thirds of the country. The CASTNET measurements show the northeast region and some sites in the southeast have the largest response of ozone to temperature extremes (Fig. ). These same regions have the highest spectral dependence between ozone and temperature extremes (Fig. ) and the highest measured correlations between temperature and ozone conditioned on temperature greater than the 90th percentile level (Fig. ). Note that the CASTNET measurement sites in the far southeastern part of the country have comparatively small measured variations in relatively extreme temperature (mean(T|T>90%)-mean(T)). Thus, at some sites over the southeastern US the sensitivity of ozone to changes in temperature is relatively large. In contrast, over the northeastern US both the relative variations in the width of the rhs of the MDA8 ozone distribution (mean(O3|O3>90%)-mean(O3)) and the rhs of the daily maximum temperature (mean(T|T>90%)-mean(T)) are relatively high and thus the ozone sensitivity to temperature change is relatively small.

Comparing the GCM2100 and the GCM2000 simulations, the mean future temperature increases everywhere in relation to the current climate, although in some places the width of the rhs of the future temperature distribution decreases. The future difference between summertime maximum daily temperatures at the 90th percentile minus mean maximum daily temperature increases by up to 20 to 30 % compared to the present day (Ψ(T,T)) over parts of the southern Mississippi basin extending to the northern Midwest and the northwest coast (Fig. ). The pattern of this increase bears a striking resemblance to those locations where measured summertime inter-annual extreme temperatures increase relative to inter-annual increases in the mean (), a process linked to drying of the soils (). In other parts of the country the relative future increase is small or negative. Note that the increase in (Ψ(T,T)) over the lower Mississippi valley occurs in a location strongly impacted by the Bermuda high and thus warrants further investigation. Note also, this increase occurs in those locations where the CESM1 REFC1SD simulation gives a low correlation between ozone and temperature.

To what extent are the relative changes in the future width of the MDA8 ozone distribution determined by the relative future changes in that of the maximum daily temperature distribution? In most locations the future width of the ozone distribution decreases. An exception is in the Midwest where the increase in the future width of the maximum daily temperature distribution is most pronounced. The spatial correlation between Ψ(T,T) and Ψ(O3,O3) is significant but weak, with a correlation coefficient of 0.3. This suggests a weak relationship between changes in the rhs of the future MDA8 ozone distribution and the future maximum daily temperature distribution. Overall, future ozone is less responsive to temperature than present-day ozone (mean(O3|T>90%)-mean(O3)) but the effect is small averaged over the continental US (-0.26 ppb), suggesting only relatively modest temperature suppression. The ratio of future sensitivities to temperature compared to the present varies regionally, ranging from -50 % to +50 % (Fig. ). Interestingly, ozone does become more responsive to temperature changes in the lower Mississippi valley (Fig. ), in precisely the region in which the width of the temperature distribution increases (Fig. ). However, even in this region the rhs of the future ozone distribution does not become significantly wider than its present-day values (Fig. ).

There have been different predictions as to whether climate change increases future ozone extremes with respect to the increase in the mean (e.g., see ). On average the width of the rhs of the future MDA8 ozone distribution increases slightly by 0.26 ppb in the future simulation (mean(O3|O3>90%)-mean(O3)) (Fig. 3, but also see Fig.  for the relative change in the 20-year return level), but in many locations the relative width decreases (Ψ(O3,O3), Fig. ). Where it increases, the increase is always less than 20 %. Our results generally suggest that the increase in future ozone is primarily due to a shift in the ozone distribution and not due to an increase in ozone at the high end.

We investigate high temperature and ozone extremes and their joint occurrence over the United States during the summer months (JJA) in measurements and simulations of the present and future climate. Three simulations using the CESM1 with chemistry were analyzed: the CESM1 CCMI reference experiment using specified dynamics (REFC1SD) between 1992 and 2010, a 25-year present-day simulation branched off of the CCMI REFC2 simulation in the year 2000 (GCM2000) and a 25-year future simulation branched off of the CCMI REFC2 simulation in 2100 (GCM2100). Distinct from the CCMI REFC2 simulations, the emissions and long-lived greenhouse gas distributions (except CO2) are held constant in the GCM2000 and GCM2100 simulations at values representative of the year 2000. In addition, we analyzed the REFC1SD simulation in four additional models with data available at a sufficiently high temporal frequency: the CHASER, CMAM, MOCAGE and MRI models. All the CCMI REFC1SD simulations (CESM1 REFCS1D, CHASER, CMAM, MOCAGE and MRI) and the GCM2000 simulation have a large bias in maximum daily ozone. Scaled ozone biases are 12 and 21 ppb, respectively, in the CESM1 REFC1SD and GCM2000 simulations. Consistent with many global model simulations, the ozone bias is particularly pronounced over the eastern US. The simulation of daily maximum temperatures shows considerable variability among the various model simulations.

The average global mean daily maximum temperature change between the present-day simulation (GCM2000) and the future simulation (GCM2100) is 2.1 ∘C, less than the 2.8 ∘C difference in the parent CCMI REFC2 simulations. The difference between these sets of simulations is most likely attributable to the fact the GCM2100 simulation includes the effect of increased CO2 forcing in the future but does not account for the impact of projected future aerosol decreases. Thus, in the GCM2100 simulation the relatively large aerosol radiative forcing acts as a buffer against the increased CO2. Over the continental US ozone increases by approximately 2.1 ppb between the GCM2000 simulation and the GCM2100 simulation.

The main conclusions from this study are as follows.

Five out of six of the simulations analyzed underestimate the width of the measured tail at the high end of the ozone distribution in the present climate, despite the fact that all simulations overestimate the mean ozone. The 20-year return period of ozone minus its mean is underestimated by more than 9 ppb in the GCM2000 simulation evaluated over all CASTNET sites, while in the REFC1SD CESM1 simulation it is underestimated by somewhat more than 3 ppb. The 20-year return period of temperature minus its mean is generally about 2 ∘C less than measured in both the GCM2000 and the CESM1 REFC1SD simulations. Despite large biases in mean daily maximum temperature the bias in the width of the rhs of the temperature tails in the CMAM and MRI simulations (mean(T|T>90%)-mean(T)) is less than 1 ∘C.