Two types of extreme weather events including heat waves and atmospheric stagnation, as well as their compound events, were investigated, considering their close relationship with ozone pollution (Hou and Wu, 2016). A heat wave is defined to occur when daily maximum 2 m air temperature exceeds a certain threshold continuously for 3 days or more. The threshold is set as the 97.5th percentile of the historical period (2001–2010 for WRF-Chem and 1991–2010 for CMIP5 in this study) and is location dependent to take into account the wide-ranging characteristics of different regions (Gao et al., 2012; Meehl and Tebaldi, 2004). An atmospheric stagnation day is defined to occur when daily mean 10 m wind speed, daily mean 500 hPa wind speed, and daily total precipitation are less than 20 % of the climatological mean condition (2001–2010 for WRF-Chem in this study) (Horton et al., 2014; Hou and Wu, 2016). A compound event occurs when both heat wave and atmospheric stagnation occur simultaneously on the same day. For each grid, the same threshold determined for the present period is used for the future period to evaluate the future changes.

To evaluate the ability of the regional model to reproduce the extreme weather events, Fig. 2 shows the distribution of the mean number of summer heat wave days, atmospheric stagnation days, and compound event days corresponding to coincidental heat wave and atmospheric stagnation during 2001–2010. Observations based on the NARR dataset and the model results are shown, along with scatter plots comparing the observations and simulations at each NARR grid point over land. Statistical metrics, including mean fractional bias (MFB), mean fractional error (MFE), and correlation coefficient (R), based on the Eqs. (A2), (A3), and (A6) in the Appendix, are shown in the scatter plots.

The spatial distributions of both heat waves and atmospheric stagnation are generally consistent between NARR and WRF-Chem (top and middle rows in Fig. 2). For example, for heat waves (Fig. 2a, b), the model captures the high frequency of occurrence in the western US and eastern central US albeit with widespread underestimations particularly in the northern US and the central Great Plains. For atmospheric stagnation (Fig. 2d, e), the observed dipole feature of high frequency of occurrence in the western and eastern US, separated by the central Great Plains, is well reproduced by the model but biases in the magnitude are noticeable. To quantitatively evaluate the simulations, the WRF-Chem model results were bilinearly interpolated to the NARR grid suggested by US EPA (2007), and scatter plots were drawn to show the results for all the NARR grid points (Fig. 2c, f). No benchmark is available regarding the statistical metrics for extreme weather events but we adopt the benchmarks widely used in air quality studies. For example, US EPA (2007) suggested 15%/35% (MFB and MFE) for O3 and 50%/75% (MFB and MFE) for PM2.5 species. From this perspective, the MFB and MFE for either heat waves or atmospheric stagnation are within or close to the benchmarks for O3 and well within the benchmarks for PM2.5 species. Moreover, the model results are correlated with NARR, with R equal to 0.61 and 0.40, respectively, for heat waves and atmospheric stagnation and statistically significant at the 95 % confidence level.

The western US receives most of its precipitation in the cold season when the North Pacific jet stream steers storm tracks across the region (Neelin et al., 2013). During summer, the North Pacific subtropical high-pressure center expands and exerts a stronger influence on the western US, increasing the frequency of atmospheric stagnation (Wang and Angell, 1999). Combining the low wind speed and low probability of precipitation during stagnation with low antecedent soil moisture conditions generally prevalent during summer, heat waves can develop to create a maximum center of combined extreme events beyond the coastal mountain ranges of the western US (Zhao and Khalil, 1993). The eastern central US is prone to heat wave and stagnation as a result of the upper level ridge that develops during summer in that region. These climatic conditions give rise to the dipole patterns of maximum heat wave and stagnation in the western and eastern central US. The dipole pattern becomes more obvious and magnified for the compound events because stagnation can promote the development of heat waves, as discussed earlier. For the compound events, the simulation performs well and even better than the metrics of atmospheric stagnation events. The high values in the western and southeastern US, as well as the low values in the central and upper Midwestern US, are reasonably captured by the model, with statistically significant correlation (R=0.58).

Thus, WRF-Chem in general reproduced the spatial patterns and frequency of the extreme weather events including heat waves, atmospheric stagnation, and their compound events well. Although atmospheric stagnation occurs on more than 20 days during the summer in large areas over the western and eastern US, heat waves do not occur for more than 10 days generally; thus the compound events of heat waves and stagnation are rather rare and occur on average for no more than 5 days during summer over the US. In the next section, ozone concentrations during these extreme weather events are analyzed.

MDA8 ozone is an important variable considering its close relationship with human health (US EPA, 2007) so we focus on the evaluation of MDA8 O3 during summertime. Figure S1 in the Supplement shows the spatial distributions of MDA8 ozone with or without extreme weather events in the WRF-Chem simulations and the NARR-AQS observations. MDA8 ozone with extreme weather events (Fig. S1; left panels) shows a similar increase compared to MDA8 ozone without extreme weather events in both model simulations and observations over the eastern US. On the west coast, the increase is slightly higher in model simulations than in observations. Overall, WRF-Chem reproduced the influence of extreme weather events on enhancing MDA8 ozone over the US well.

From the perspective of public health, the US EPA (2007) recommended attention to ozone values higher than 40 ppbv because the human impact of ozone is small for low ozone concentrations. Thus, we compare the mean ozone concentrations during summer of 2001–2010 between observed data (AQS) and model results for the following three conditions in Fig. 3: (1) days with heat waves but no atmospheric stagnation, (2) days with atmospheric stagnation but no heat waves, and (3) days with compound events (both heat wave and atmospheric stagnation). Thus the first two conditions identify single extreme events and the third condition identifies compound extreme events. We compare observed ozone concentration greater than or equal to 40 ppbv and the simulated ozone concentration corresponding to the same locations of the observations.

As depicted in Fig. 3, WRF-Chem reasonably reproduced the observed ozone concentrations during the extreme weather events, showing statistically significant correlations with the observed AQS data. Moreover, if the benchmark (15%/35% for MFB and MFE and 10%/20% for NMB and NME) suggested by the US EPA (2007) is used as a reference, all the statistical metrics based on evaluation against ozone higher than 40 ppbv in observations are within or much smaller than the benchmarks, illustrating promising ability of WRF-Chem to simulate the ozone concentrations during heat waves, stagnation, and compound events. Even if all ozone values including values below 40 ppbv are considered, the four metrics (MFB, MFE, NMB, and NME) are mostly within the benchmarks and the correlation coefficients between model and observation are only slightly reduced by 0.04, 0.11, and 0.1 for the three types of extreme weather events, respectively, and all values are still statistically significant. However, the general low biases of the simulations are obvious from the regression lines. Ozone concentrations during compound extreme events are clearly shifted to higher values relative to ozone concentrations during single extreme events.

To delve into spatial heterogeneity, ozone concentrations from model and observations for the three types of extreme weather events are shown using box-and-whisker plots in Fig. 4. Considering the detrimental effect on human health when MDA8 ozone concentration exceeds 70 ppbv by National Ambient Air Quality Standards (NAAQS), we evaluate the WRF-Chem simulated ozone concentrations above this particular threshold. We calculated the mean values of MDA8 ozone concentration exceeding 70 ppbv for each type of extreme weather event, and the mean values are marked at the top of each panel in Fig. 4.

The box-and-whisker plots show some unique features in the observations. For example, the mean ozone (red dot) concentrations tend to be slightly higher when heat waves and stagnation occur at the same time, while the mean values are relatively lower during atmospheric stagnation than during heat waves. These are consistent with Fig. 3 in which values are plotted regardless of the regions. This feature was reasonably captured by the model, in particular over regions in the eastern US, such as the Northeast and Southeast. Regarding high ozone concentrations (i.e., values higher than 70 ppbv), the model is skillful in the eastern US with major anthropogenic emissions. The mean bias could be as small as 0.4 ppbv (over the Southeast during heat waves), and mostly within 1 ppbv. However, for some regions, i.e., the West and Southwest, negative biases could reach a few parts per billion by volume; the negative biases in many regions are likely linked to an underestimation of heat wave intensity, which is reflected in the underestimation of heat wave days as shown in Sect. 3.1. Other possible reasons for the negative biases in surface O3 include uncertainties in precursor emissions and boundary conditions as well as overpredictions in precipitation, as reported in Yahya et al. (2017a).

To further evaluate the capability of WRF-Chem to model high ozone (beyond 70 ppbv), Fig. S2 displays the interannual variability in high ozone over the US in the WRF-Chem simulations and AQS observations. For observations, the variance of annual mean high ozone was calculated only for grids with more than 5 years of data. Similar to the ozone distribution in Fig. S1, larger values are mainly found on the west coast and in the eastern and central US. Variance over the eastern US in observations is high while WRF-Chem is in general slightly smaller. Considering the total high-ozone episodes in historical periods, the contributions of extreme weather events to the high-ozone episodes are shown in Fig. S3. Only grids having 10 days or more with high ozone are shown to avoid grid cells with very high fractions due to the small number of high-ozone episodes. WRF-Chem simulated a slightly larger fraction on the west coast compared to observations and captured the high fraction in the eastern US well. This feature is similar to the ozone distribution in Fig. S1. Hence overall, WRF-Chem demonstrates a reasonable capability of modeling high-ozone episodes and the contribution of extreme weather events to high-ozone episodes in the US.

To investigate the impacts of the extreme weather events on ozone concentrations, we composited the MDA8 ozone concentrations from WRF-Chem for the three types of extreme weather events and periods without any extreme event (non-extreme event) in summer of 2001–2010 using probability density functions (PDFs) shown in Fig. 5.

By comparing the solid lines (extreme event period) and dashed line (non-extreme event period) in Fig. 5, all extreme weather events have positive impacts on ozone, particularly at the high-end tail of the distributions. The difference between ozone concentrations with and without extreme events is statistically significant in all regions at the 95 % confidence level. For regions with mean ozone values exceeding 70 ppbv (numbers shown in Fig. 5), much larger differences are noticeable between the PDFs of extreme and non-extreme periods, with extreme events notably shifting both the low-end and high-end tails towards higher values. These regions include Northeast, Central, South, and West. Conversely, regions such as Northwest, West North Central, and Southwest shows negligible differences between the PDFs. The spatial heterogeneity is closely related to the spatial distribution of emissions in the US, i.e., regions with a larger increase in ozone concentration particularly near the high-end tail (i.e., Northeast, Southeast, Central, Upper Midwest, South, and West) due to extreme weather events are also areas with higher anthropogenic emissions in the US (see also Fig. 3 in Gao et al., 2013). Thus, stronger photochemical reactions in those regions may enhance the effect of extreme weather events on ozone formation.

Now comparing the effects of different types of extreme weather events on ozone concentrations (solid lines of different colors in Fig. 5), the effect of heat waves on ozone formation is generally larger than the effect of atmospheric stagnation, whereas the compound effect is larger than the effect of either type of single extreme weather event. This feature displays similar spatial heterogeneity as discussed above, i.e., the largest impact from the compound effect occurs in South and Central (about half of the compound events leading to MDA8 ozone higher than 70 ppbv), followed by Northeast, South, Upper Midwest, and West (11–28 % compound event days resulting in MDA8 O3 of 70 ppbv or higher), and negligible increase from the compound events for other regions (Northwest, West North Central, and Southwest).

In addition to the distinguishing impacts extreme events have on ozone relative to non-extreme days, how high the concentration of ozone can reach during extreme events may depend on the intensity of the extreme events and the emissions. Figure 6 shows the correlations between ozone concentration with the daily maximum 2 m temperature during heat waves and 10 m wind speed during atmospheric stagnation events. The correlations between temperature and ozone are positive and statistically significant in areas with high emissions such as Northeast, Central, Upper Midwest, South, and Southeast. For stagnation events, the correlations are statistically significant mainly in South, Southeast, and along the west coast. These correlations between ozone and the intensity of extreme events are consistent with the shift of the high-end tails of the PDFs to higher ozone values, as shown in Fig. 5. In areas with low emissions (e.g., Northwest and West North Central), ozone concentrations are not well correlated with the intensity of extreme events because the production of ozone is limited by the low emissions (Vingarzan, 2004). Hence only the low-end instead of the high-end tails of the PDFs are shifted to higher values in regions with low emissions, and the PDFs on extreme days are noticeably narrower compared to the PDFs on non-extreme days (Fig. 5). As climate change may increase the frequency as well as the intensity of extreme events, ozone concentrations may be affected, regardless of emissions control in the future.

Having investigated the impacts of extreme weather events on ozone concentration, we now focus on how ozone concentrations may change in the future with climate change, changes in biogenic emissions in response to changes in climate, and large anthropogenic emission reductions in the RCP8.5 scenario. Figure 7 shows the spatial variations in ozone concentrations composited during extreme weather events at present (top row) and in the future (bottom row). The spatial features displayed in the top row are in agreement with what have been observed from Fig. 5, showing larger impacts of extreme weather events on ozone formation east of the Rockies for both single extreme events and compound events (Fig. 7a, b, c). Similarly large impacts are also found in California, which are obscured in the regional average shown in Fig. 5. Averaged over the US, MDA8 ozone concentrations increase by 22 and 12 % during heat waves and stagnation events compared to non-heat wave and non-stagnation days. Compound events have a significantly higher impact on ozone compared to the single extreme events, with statistically significant differences of 13 and 16 %, respectively, for heat waves and stagnation (Fig. 7d, e). To understand why compound events have larger impacts than single extreme events, Fig. S4 shows that during compound event days, the daily maximum 2 m temperature is comparable to that during heat waves but 6.27 ∘C higher than that during stagnation events, leading to a 16 % increase in MDA8 O3 during compound events relative to stagnation events. Similarly, the 10 m wind speed during compound events is comparable to that during stagnation events but 1.4 ms-1 weaker than during heat wave days, leading to a 13 % increase in MDA8 O3 relative to heat wave days.

In the future, as anthropogenic emissions are projected to decrease substantially (i.e., Table 2 in Gao et al., 2013), the mean ozone concentration correspondingly decreases during both single extreme events and compound events compared to the present day (i.e., Fig. 7f, g, h vs. Fig. 7a, b, c). However, even with the dramatic anthropogenic emission reduction (i.e., 50 % or more reduction in non-methane volatile organic compounds and nitrogen oxides based on Table 2 in Gao et al., 2013), extreme weather events can still trigger the formation of high ozone concentrations (e.g., in the central eastern US in Fig. 7f, g, h) that reach or exceed the present-day national standard of 70 ppbv. From Fig. S4, the daily maximum 2 m temperature is 5.54 ∘C warmer during compound events than stagnation events, leading to a 13 % increase in MDA8 O3 during compound events relative to stagnation events. Similarly, the 10 m wind speed is 1.28 ms-1 weaker during compound events than heat wave events so MDA8 O3 increases by 10 % during compound events relative to heat wave events in the future. Hence, compound events increase ozone concentrations by 10 and 13 % more than the effect of heat wave only and stagnation only, respectively. These numbers shown in Fig. 7i, j are only 3 % lower than those of the present day (Fig. 7d, e).

Despite dramatic reduction in anthropogenic emissions in the RCP8.5 scenario (Riahi et al., 2011), extreme weather events are still important considerations for air quality and health in the future. This is because both frequency and intensity of extreme events increase in the future, which compensates partly for the effects of reduced emissions. From Fig. S5, heat waves occur on average 13.67 days more and are 0.98 ∘C warmer in the future relative to the present, with most of the increase occurring in the western US. There is no increase in the number of stagnation days in the future when averaged over the US (Fig. S5), and the change in wind speed during stagnation is also negligible (Fig. S6). However, the daily maximum 2 m temperature is 1.42 ∘C warmer during stagnation events in the future compared to the present (Fig. S5). Lastly, compound events occur on average 4.91 days more often, with temperature 1.25 ∘C warmer in the future compared to the present (Fig. S5). Hence the increase in the number of heat waves and the warmer temperature during heat waves as well as stagnation events increase their individual and compound effects on ozone concentrations in the future. These motivate analysis of changes in extreme events in the future using a multi-model ensemble for more robust results.