Net tropospheric O3 accumulation occurs when sunlight acts on VOC and NOx emissions and the O3 production rate exceeds O3 loss (Trainer et al., 2000). Tropospheric O3 mixing ratios are affected by solar intensity, chemical formation and loss (e.g., deposition) rates of O3, the rate of dispersion of O3 and its precursors, meteorological factors, and vertical entrainment and transport of plumes. NO2 forms rapidly by reaction of NO with O3 and photolysis of NO2 produces O3, yielding steady-state mixing ratios of NO, NO2, and O3 in the absence of other species as expressed by the photostationary state, or Leighton relationship (Seinfeld, 1986).

In the troposphere, NO2 also forms by reaction of NO with peroxy (HO2) and alkyl peroxy (RO2) free radical species, which derive in turn from the reaction of VOCs with hydroxyl (HO), HO2, RO2, and alkyl radicals (Seinfeld, 1986). Radical production from VOCs creates a pathway for conversion of NO to NO2 that does not consume O3 (Atkinson, 2000), which then leads to higher O3 mixing ratios.

O3 accumulation is typically associated with high solar radiation intensity and temperatures favoring atmospheric reactions, lower wind speeds, and high anthropogenic emission rates (NARSTO, 2000). O3 accumulation requires NO mixing ratios exceeding approximately 10 to 30 pptv (Atkinson, 2000; Logan, 1985), along with the presence of HO2 and RO2 radicals that react with NO to form NO2. The former conditions are normally met in urban air; NOx mixing ratios are much lower under typical conditions in rural southeastern areas, but still well above 30 pptv (e.g., Hudman et al., 2007; Travis et al., 2016). Under these conditions, the O3 photochemical production rate is proportional to the ambient NO multiplied by the sum of HO2 and RO2 radical mixing ratios, where the latter are weighted by their rates of reaction with NO (Trainer et al., 2000). Field studies show that observed rates of rural O3 production are proportional to the rate of oxidation of NOx. Where VOCs are present for radical production and NOx is rate limiting (Trainer et al., 2000), regional O3 production can be expressed in terms of the derivative d[O3]/d[NOx], denoted as the O3 production efficiency (OPE) (Liu et al., 1987). OPE is understood as the number of molecules of O3 formed per molecule of NOx oxidized and OPE increases as NOx mixing ratios decrease (Liu et al., 1987; Trainer et al., 2000). OPE reflects the mean number of NO–NO2 cycles occurring, in which each photolysis of one NO2 molecule generates one O3 molecule until that NO2 molecule is oxidized to nitric acid (HNO3) or to other species such as peroxyacetyl nitrate (PAN). NOx reaction products, including HNO3 and PAN, comprise NOz. For chemical reactions, the quantity d[O3]/d[NOz] is equivalent to d[O3]/d[NOx], but with opposite sign, and has therefore been used to estimate OPE; limitations due to confounding influences of emissions, transport, and deposition are discussed in Sect. 4.3 and 4.4.

Empirically, the slope of a linear fit of afternoon O3 (or Ox = O3 + NO2) versus NOz has been used to estimate OPE (e.g., Trainer et al., 1993; Pollack et al., 2013). This estimate is subject to certain limitations because it does not explicitly account for (1) day-to-day variability in “old” (baseline or regional background) O3 mixing ratios, (2) mixing of air masses having different emission histories, (3) rapid loss of HNO3 (primarily through dry deposition, but also through gas-to-particle conversion) (Trainer et al., 2000), and (4) regeneration of NO2 from PAN and certain other species. Because PAN regenerates NO2, it can serve as a reservoir rather than a true NO2 sink (Singh and Hanst, 1981; Singh, 1987). In contrast, HNO3 largely terminates the cycling between NO and NO2. Therefore, the relative yields of PAN and HNO3 are of importance. Despite such limitations in using measurements to quantify OPE, data from field studies have been used since the 1990s to determine upper bounds for OPE and the results have continued to appear in the literature as an indicator of relevance to O3 chemistry (e.g., Berkowitz et al., 2004; Neuman et al., 2009; Kim et al., 2016). Investigators caution that field measurements reveal the net of production and loss, which potentially overestimates actual OPE by factors of 3 to 6 due to rapid chemical and deposition losses of HNO3 and other NOz species (e.g., Trainer et al., 2000). Additional discussion is found in Sect. 4.4.

In southern California, changes in the relative proportions of NOx-oxidation products have occurred and are thought to be instrumental in driving the rapid rates of O3 decline in that area (Pollack et al., 2013). These results indicate that measurements of HNO3 or PAN are needed to identify important changes in chemical pathways.

Between 1980 and 2013, the national average of the annual fourth-highest peak daily 8 h O3 mixing ratios, a metric relevant to the US O3 NAAQS, declined by 33 % (U.S. EPA, 2015d) as national VOC and NOx emissions decreased by 53 and 52 %, respectively (U.S. EPA, 2015e). Across the US and on multiple spatial scales from continental to urban, annual fourth-highest daily peak 8 h O3 mixing ratios between 1980 and 2013 show a statistically significant (p < 0.05) linear fit to either annual average or to 98th percentile daily maximum hourly NO2 mixing ratios; regression slopes are less than 1 : 1 and intercepts are in the range of 30 to 50 ppbv O3 (Hidy and Blanchard, 2015). Proportionalities between O3 and NO2 that are less than 1 : 1 are expected, and the observed intercept terms are approximately consistent with typical O3 mixing ratios of ∼ 20–50 ppbv observed at remote monitoring sites (Oltmans et al., 2008, 2013; U.S. EPA, 2012; Fiore et al., 2014; Lefohn et al., 2010, 2014; Cooper et al., 2012, 2014).

Although nonlinearity of O3 production and accumulation with respect to ambient VOC and NOx is well established (Lin et al., 1988), a tendency toward linearity is expected at sufficiently low NOx mixing ratios. As an example, the O3 photochemical production rate during June 1990 at Kinterbish, AL, was approximately linear over a range of ambient NOx from 0.1 to 2 ppbv (Trainer et al., 2000). Observed O3 extrema can also exhibit an apparent linear or near-linear response to ambient NOx mixing ratios if the extrema consistently fall within the lower-right quadrant (NOx-sensitive regime) of an O3–VOC–NOx diagram, a concise graphical representation first established empirically from southern California data and later generated using the Empirical Kinetic Modeling Approach (EKMA) (illustrated in Hidy and Blanchard, 2015). The O3–VOC–NOx diagram has been adopted by many investigators for displaying the output of box models (e.g., Fujita et al., 2003, 2015) and grid-based photochemical models (e.g., Reynolds et al., 2003, 2004).

Southern California historically has exhibited the highest peak O3 mixing ratios in the US since the 1960s. Because of high ambient O3 and precursor mixing ratios there and the complexity of the relationships of O3 with NOx and VOC, some investigators have described southern California O3 and precursor trends in terms of percentage changes. For example, Pollack et al. (2013) report that peak 8 h O3 mixing ratios in southern California declined exponentially over time at a rate of 2.8 % per year between 1973 and 2010, thus decreasing O3 levels by approximately a factor of 3. This rate of O3 decline exceeds rates occurring in other metropolitan areas (Hidy and Blanchard, 2015). O3 extrema in southern California decreased along with declining mixing ratios of ambient VOCs and NOx (7.3 % yr-1 and 2.6 % yr-1, respectively, 1960–2010) and declining ratios of VOC / NOx (4.8 % yr-1) (Pollack et al., 2013). The rates of atmospheric oxidation of NOx increased over time and changes in NOx oxidation reactions increasingly favored production of HNO3, a NOx reaction product associated with radical termination and quenching of the O3 formation cycle (Pollack et al., 2013). To our knowledge, changes in the relative proportions of atmospheric reaction products accounting for rapid rates of O3 reduction have not been reported for locations other than southern California.

Air quality monitoring data were obtained from the EPA Air Quality System (AQS) data archives for all sites in Georgia, Alabama, and Mississippi (U.S. EPA, 2016a). Daily measurement values (i.e., peak daily 8 h O3 mixing ratio) as well as annual summary statistics (e.g., maxima, annual averages) were acquired. We obtained deposition data from the two EPA Clean Air Status and Trends Network (CASTNET) monitoring sites located within the study region: Sand Mountain, AL (125 km east-northeast of the SEARCH site at Centreville), and Georgia Station, GA (102 km SE of the SEARCH site at Yorkville) (U.S. EPA, 2016b).

Annual, state-level emission trends data were obtained from the U.S. EPA (2016c, d), Xing et al. (2013), and Hidy et al. (2014). The comparability of inventories is discussed in the Supplement (Fig. S1). Because the EPA trend inventory utilized different methods for estimating mobile-source emissions prior to 2002 compared with 2002 and later years, we combined EPA trend estimates for 2002–2016 with the 1996–2001 emission estimates of Hidy et al. (2014), which are consistent with more recent EPA methods (see Supplement).

Hourly measurements of gases (NO, NO2, NOy, HNO3, and O3) were obtained from SEARCH public archives (ARA, 2017). All parameters measured at the sites are calibrated and audited to conventional reference standards, as described in ARA (2015). Network operations, sampling, and measurement methods are documented in Hansen et al. (2003, 2006); see also Table S1 in the Supplement. The network consisted of eight extensively instrumented monitoring sites located in the southeastern US along the Gulf of Mexico and inland (Fig. S2): Pensacola, Florida (PNS), and Gulfport, Mississippi (GFP), urban coastal sites (∼ 5 and 1.5 km from the shoreline, respectively); Pensacola – outlying (aircraft) landing field (OLF) and Oak Grove, Mississippi (OAK), non-urban coastal sites near the Gulf (∼ 20 and 80 km inland, respectively); Atlanta, Georgia – Jefferson Street (JST) and North Birmingham, Alabama (BHM), urban inland sites; and Yorkville, Georgia (YRK), and Centreville, Alabama (CTR), non-urban inland sites. PNS, OAK, and GFP were closed at the end of 2009, 2010, and 2012, respectively. SEARCH site locations are described in detail, including discussion of possible emission influences, in Hansen et al. (2003) and Hidy et al. (2014). SEARCH VOC data are available for JST as daily data from 1999 through 2008, and U.S. EPA VOC measurements are available for YRK as summer hourly data and as 24 h samples collected every sixth day throughout the year (Blanchard et al., 2010a). EPA VOC samples are also available for three other sites in the Atlanta area; only one of these additional sites reported data through 2014.

SEARCH meteorological parameters and gases are sampled at a height of 10 m, characteristic of lower-tropospheric mixing ratios near the surface (Hansen et al., 2003, 2006; Edgerton et al., 2007; Saylor et al., 2010). Gas and meteorological measurements commenced in 1992 at the rural sites of CTR, OAK, and YRK. The measurements at rural SEARCH sites included O3, NO, and NOy beginning in 1992, and NO2 and HNO3 measurements began in 1996. Consistent measurement methods have been utilized for all gases except NO2. NO2 measurements commenced network-wide in 2002, and three NO2 measurement methods have been employed during the network operations (Table S3). All three methods are NO2-specific, differing primarily in the light source used for photolysis of NO2. The NO2 data exhibit consistency with NO and NOy measurements but with some variations occurring during specific years (e.g., 2001 and 2002, Fig. S3). Because changes in NO2 measurement methods could affect the computed NOz (NOy–NO–NO2), we repeat some data analyses using HNO3 in place of NOz. As noted, HNO3 data also provide useful insight into NO2 termination reactions. HNO3 measurements are the difference between NOy and denuded NOy (Table S1; Hansen et al., 2006). The SEARCH measurements of NOy were designed to capture particulate nitrate and organic nitrates, as well as NO, NO2, HNO3, and other oxidized nitrogen species. The NOy sampler derives from the instrument identified in Williams et al. (1998) as Environmental Science and Engineering (ESE), which was one of five instruments for which measurements of NOy reproduced the sum of separately measured NOy species. Additional testing in 2013 showed that SEARCH NOy measurements agreed with the sum of measured mixing ratios of NO, NO2, HNO3, particulate nitrate, alkyl nitrates, and peroxy–alkyl nitrates (Hidy et al., 2014).

Trace gas calibrations were done daily for O3 and every third day for other gases. Reported detection limits (Table S1) are 0.05–0.1 ppbv for oxidized nitrogen species and 1 ppbv for O3 (Hansen et al., 2003, 2006). NO2 measurement uncertainties are estimated as ∼ 30 % prior to 2002 and ∼ 10 % after 2002 (Hansen et al., 2006). Measurement uncertainties are estimated to be 10 % or less for other oxidized nitrogen species and 5 % or less for ozone (2σ in all cases). Propagation of errors indicates corresponding 2σ measurement uncertainties averaging 0.5 ppbv for mid-afternoon NOz (< 0.1 ppbv for NOz < 1 ppbv) and 0.16 for the ratio NOz / NOy.

Multiple methods were employed to characterize the variability of ambient O3 and NOy mixing ratios. Analyses of seasonal variability used data from all months of each year. Diurnal hourly average mixing ratios were computed by year to characterize patterns of temporal change and to identify hours associated with O3 maxima. Observed slopes of regressions of O3 versus NOz were computed as previously done in measurement studies using afternoon O3 and NOz data (Trainer et al., 1993, 1995; Kleinman et al., 1994; Hirsch et al., 1996; Kasibhatla et al., 1998; Nunnermacker et al., 1998; St. John et al., 1998; Sillman et al., 1998; Zaveri et al., 2003; Griffin et al., 2004; Travis et al., 2016). Because past studies have examined O3 formation in photochemically aged air (i.e., at locations distant from fresh emissions, where atmospheric reactions have acted on emissions from earlier times) during summers (e.g., Trainer et al., 1993), our analyses focus on the months of June and July to select weeks nearest maximum solar radiation (∼ -20, +40 days). Additional analyses were carried out for other months to facilitate comparisons across seasons. As for earlier studies, the calculations are based on afternoon times, using hourly values starting at 14:00 local standard time to represent the daily peak O3 after morning production and before mixing ratios decline with decreasing photochemical reaction in later afternoon. In addition to characterizing O3 / NOz and its change with time, corresponding supporting analyses are presented for O3 / HNO3. As a supplemental analysis, rates of maximum diurnal increase of O3 and HNO3 during late morning and early afternoon were computed for comparison of ΔO3 with ΔHNO3.

Hidy et al. (2014) report a 63 % reduction of NOx emissions in the southeastern US between 1996 and 2014. The largest NOx emission changes in the southeast occurred between 2007 and 2009 due to reductions of emissions from electric generating units (EGUs) and from diesel engine vehicles, and they were accompanied by more gradual year-to-year reductions of gasoline-engine mobile-source NOx emissions (de Gouw et al., 2014; Hidy et al., 2014). NOx emission reductions led to approximately proportional responses of mean ambient NOy and NOz mixing ratios at SEARCH sites (Hidy et al., 2014).

The EPA CASTNET data show wet and dry nitrate deposition since the late 1990s declining at rates of ∼ 5 % per year (-0.045 ± 0.005 and -0.056 ± 0.005 yr-1), nearly identical to NOx emission changes of -0.046 ± 0.001 and -0.051 ± 0.003 yr-1 (Fig. 1). Total (wet plus dry) nitrate deposition fluxes decreased linearly in proportion to reductions of NOx emissions in Alabama and Georgia (Fig. 1). Linear regression slopes indicate that the annual nitrate deposition fluxes at the Georgia and Alabama CASTNET sites correspond to 30 % of Georgia emissions and 36 % of Alabama emissions on an annual and statewide basis (Fig. 1). Emissions are not spatially homogeneous and deposition losses likely vary with distance from emission sources. The two sites are situated differently in relation to metropolitan areas, possibly affecting deposition fluxes; Sand Mountain (SND) is northeast of Birmingham and Georgia Station (GAS) is south of Atlanta. The linearity and statistical significance of the regressions indicate that the fraction of NOx emissions lost to deposition has not changed over time (ratios of annual deposition to state emissions varied without trend from 0.23–0.34 at GAS and 0.30–0.45 at SND). Mean annual SEARCH NOy mixing ratios at rural CTR and YRK declined at ∼ 5–7 % yr-1 (Fig. S4). SEARCH and EPA CASTNET sites exhibit downward trends in mean annual HNO3 concentrations of ∼ 9–11 and ∼ 6–7 % yr-1, respectively (Fig. S4). Ambient NOy and HNO3 trends are not statistically different from state-level NOx emission trends.

Annual fourth-highest daily peak 8 h O3 mixing ratios at compliance monitoring sites in Georgia, Alabama, and Mississippi exhibit statistically significant (p < 0.0001) linear correlations with annual NOx emissions in those states between 1996 and 2015 (Fig. 2), qualitatively consistent with past work indicating that high O3 would respond to reductions of NOx emissions (Chameides and Cowling, 1995; Jacob et al., 1995; Kasibhatla et al., 1998). Intersite differences in the annual fourth-highest daily peak 8 h O3 mixing ratios have decreased (Fig. 2), consistent with an analysis of data from a larger number of US and European locations (Paoletti et al., 2014). The annual fourth-highest daily peak 8 h O3 mixing ratios are declining toward nonzero values, as indicated by the statistically significant (p < 0.0001) intercepts of ∼ 45–50 ppbv (Fig. 2). SEARCH data are used to characterize the southeastern O3 response to emission changes in greater detail. Between 1999 and 2014, the highest peak daily 8 h O3 mixing ratios occurring each month (monthly O3 maxima) declined at all SEARCH sites at statistically significant (p < 0.01) rates averaging ∼ 1–1.5 ppbv yr-1 (Fig. 3). These declines are comparable to the trend in the 95th percentile summer peak daily 8 h O3 mixing ratios in the southeastern US of ∼ -0.8 to -1.8 ppbv yr-1 reported by Lin et al. (2017), with downward trends occurring in other seasons as well. The observed SEARCH O3 trends are also consistent with other analyses of North American observations (e.g., Chan, 2009; Lefohn et al., 2010; Paoletti, 2014; Simon et al., 2015) and with the trends occurring at EPA monitors in the southeast (Fig. 2). Both EPA (Fig. 2) and SEARCH (Fig. 3) data suggest that O3 mixing ratios increased during the 1990s, then began declining. This result is consistent with modeling by Reynolds et al. (2004), which predicted an initially slow response of Atlanta-area O3 to emission reductions between 1996 and 2000, followed by increasing sensitivity to reductions of NOx emissions. The observed O3 decreases exceed those predicted by Reynolds et al. (2004) because actual NOx emission reductions (∼ 60 % between 1996 and 2014) exceeded the projected emission reductions (∼ 40 % by 2010 and ∼ 55 % by 2020) that were anticipated based on known and anticipated emission control rules at the time of the modeling study. The SEARCH trends are compared with emission changes in the southeast and with emission and O3 trends in southern California, in Table S2.

More complete understanding of regional O3 trends requires consideration of both regional emission changes and possible changes in background O3. Multiple definitions of the term “background O3” may be found in the literature, including global background, continental background, non-anthropogenic background, and regional background, among others. For the O3 trends shown in Figs. 2 and 3, the most relevant consideration is the amount of O3 transported into the study domain across upwind boundaries (denoted here as regional background or transported O3). The percentage reductions of O3 are larger if transported O3 can be estimated and subtracted from observed O3 mixing ratios, and this adjustment potentially provides a better assessment of the effects of regional emission reductions on the fraction of O3 that is manageable by means of local and regional emission control measures. For example, Parrish et al. (2017a) report that the O3 enhancement above background in southern California decreased by 4.5 % yr-1, which is larger than the unadjusted O3 decline of 2.8 % yr-1 given by Pollack et al. (2013). Similarly, rates of decline in southeastern US O3 are larger if regional background O3 is considered (Table S2).

Defining and estimating regional background (or transported) O3 are each challenging. We interpret the intercepts in Fig. 2 as indicators of mean O3 levels that would occur on days with weather conducive to high O3 in the absence of NOx emissions from AL and GA sources, i.e., as estimators of O3 transported into the region from outside the study domain (as discussed subsequently, multi-day carryover of local and regional emissions during stagnation events could also affect intercepts and slopes). Days with weather that is not conducive to high O3 likely have different levels of transported O3. The statistically significant slopes in Fig. 2 indicate O3 enhancements that are attributable to AL–GA emissions, except as noted next, and a comparison of the O3 decline to intercept-corrected O3 would then reveal the proportionality between AL–GA emissions and AL–GA O3 enhancements over O3 originating outside the study domain (i.e., in excess of regional background O3). Although the ∼ 30–35 % O3 declines are less than proportional to the ∼ 60 % decrease in NOx emissions, the decline in the median O3 is ∼ 60 % if the 50 ppbv intercept shown in Fig. 2 is subtracted from the O3 mixing ratios.

If the amount of O3 that has been transported from upwind regions has been changing over time, e.g., declining as NOx emissions and ambient O3 decline in adjacent regions, the slopes shown in Fig. 2 would reflect changes in both the O3 that originated upwind and in the O3 enhancements attributable to AL–GA emissions, confounding attribution. Related studies do not provide consistent evidence for a trend, either upward or downward, in regional background O3 in the southeastern US. For example, baseline O3 concentrations in air flowing into Texas from the Gulf of Mexico during May through October did not change significantly between 1998 and 2012 (Berlin et al., 2013). Mean regional background O3 mixing ratios were 48 to 59 ppbv in the Houston, TX, area on days with O3 levels exceeding the NAAQS, which includes O3 contributions from transport to the area from other regions of the US (Berlin et al., 2013). Observed trends in the 5th percentile O3 have previously been used as indicators of changes in either regional or continental background O3 (e.g., Wilson et al., 2012). The 5th percentile peak daily 8 h O3 mixing ratios decreased during summer at rural sites throughout the southeastern US between 1988 and 2014 (Lin et al., 2017). By this measure, regional background O3 levels did not increase in the southeastern US during our study period.

Large-scale transport affecting O3 in the boundary layer and at the surface is a function of altitude. For example, during June 2013, anthropogenic emissions and long-range transport (long-range tropospheric + stratospheric) O3 each accounted for about 40 % (15–20 ppbv each) of model-predicted O3 below 1 km altitude at Huntsville, AL, while long-range transport accounted for ∼ 80 % of model-predicted O3 above 4 km altitude (Johnson et al., 2016). This variation of source contributions with altitude provides an opportunity to differentiate between emission-related and transport-related trends derived from vertical soundings of upper-air O3 mixing ratios. Using ozonesondes that are generally launched on a weekly schedule, vertical O3 mixing ratio profiles have been determined by the University of Alabama in Huntsville, Alabama, since 1999 (Newchurch et al., 2003; Johnson et al., 2016; University of Alabama Huntsville, 2017; NOAA, 2017). We obtained these ozonesonde data (n=940 days) and identified the following statistically significant trends in the lower layers that are relatively more influenced by local and regional emissions according to Johnson et al. (2016): -0.25 ± 0.11 ppbv yr-1 (p < 0.05) in daily measurements at 0.5 km, -0.40 ± 0.10 ppbv yr-1 (p < 0.0001) at 1 km (daily), -0.42 ± 0.09 ppbv yr-1 (p < 0.0001) at 2 km (daily), and -0.57 ± 0.13 ppbv yr-1 in monthly averages of O3 measurements made throughout the interval 1–2 km (p < 0.001). At higher altitudes where Johnson et al. (2016) predicted that long-range transport is the dominant source of O3, no trends occurred: 0.06 ± 0.08 ppbv yr-1 (p > 0.1) at 4 km (daily) and 0.09 ± 0.19 ppbv yr-1 (p > 0.1) at 8 km (daily).

Global background is one component of regional background and trends in global background are expected to contribute to trends in regional background. Lin et al. (2017) show that rising NOx emissions in Asia have increased modeled North American background O3 levels (based on model simulations with zero North American emissions) by ∼ 0.2 ppbv yr-1 in the southeastern US in summer, which is a small effect even when accumulated over 20 years in comparison with the ∼ 25 ppbv reduction in the median annual fourth-highest peak daily 8 h O3 shown in Fig. 2. Multiple studies have demonstrated increasing trends in global background O3 mixing ratios (Ordóñez et al., 2007; Oltmans et al., 2008; Arif and Abdullah, 2011; Wilson et al., 2012). Parrish et al. (2017a) report that the highest O3 design values (the 3-year running mean of the annual fourth-highest peak daily 8 h O3 mixing ratio) in southern California are converging toward a limit of 62.0 ± 1.9 ppb, which they identify as the O3 design values that would result from US background O3 concentrations. Parrish et al. (2017b) report decreasing O3 transported across the Pacific into the western US after 2000. As noted, regional background O3 in the southeastern US does not appear to be trending either upward or downward, even though trends in background O3 have been established in other areas or globally.

In the southeastern US, the simple conceptual model of O3 transported into a study region across upwind boundaries is incomplete. High O3 typically occurs during multi-day stagnation episodes, which are associated with the presence of high barometric pressure over the domain and limited transport (Blanchard et al., 2013). Transport distances determined from 24 h back-trajectory computations are less than 300 km for the highest decile O3 (Blanchard et al., 2013). Mean 24 h transport distances are less than 350 km during June and less than 380 km during July (Blanchard et al., 2014). These distances are approximately equivalent to distances from Birmingham to Mobile, AL, or from Atlanta to Savannah, GA. Local and regional emissions can accumulate over multiple days and potentially could contribute to observed O3 concentrations (e.g., aloft) that are considered as regional background. In contrast to emissions originating upwind, carryover from emission sources within the study domain is a manageable component of efforts to reduce O3.

The seasonal oscillations of monthly O3 maxima in the southeast are coupled to local or regional meteorology, solar radiation, and emissions (e.g., Blanchard et al., 2013, 2014; Hidy et al., 2014). Variations of daily maximum temperature and midday relative humidity (RH) are associated with variations of daily peak 8 h O3 mixing ratios by ∼ ±30 % from mean peak 8 h O3 mixing ratios, after also accounting for variations of other meteorological factors (Blanchard et al., 2014). Air mass back trajectories originating from the south (∼ 150 to 200∘) exhibit peak 8 h O3 that is ∼ 5–10 % lower than average; daily peak O3 decreases as 24 h back-trajectory distances increase from zero to ∼ 600 km, consistent with association of higher O3 concentrations with air mass stagnation rather than transport (Blanchard et al., 2013, 2014). At SEARCH sites, the monthly O3 maxima (highest daily peak 8 h O3 each month) and mean daily peak 8 h O3 mixing ratios typically occurred in summer months, especially inland, and declined more than other monthly maxima (Figs. 3 and 4). Summer means were not always higher than spring averages, especially at rural and coastal sites and during more recent years (Fig. 4). Roughly constant winter monthly peak 8 h maxima of ∼ 40 ppbv occurred throughout the period of record (Fig. 3). The seasonal variability of the highest peak daily 8 h O3 therefore declined over time (see also Table S3). Similar results were found for monthly means of hourly measurements, discussed in Sect. 4.3 on diurnal variations. Other recent studies have reported decreasing seasonal variability of O3 across the US using data from large numbers of monitoring sites (Chan, 2009; Chan and Vet, 2010; Cooper et al., 2012; Paoletti et al., 2014; Simon et al., 2015). Declines in seasonal variability are thought to result from changing rates of O3 formation as precursor emissions have declined or from increasing influence of intercontinental background O3, not from changes in seasonal variations of temperature and other meteorological factors (Chan, 2009; Cooper et al., 2012; Simon et al., 2015).

The SEARCH data indicate that seasonal variations occur in ambient O3, NOy, NOz, HNO3, and the ratio of NOz / NOy (Fig. 5). Seasonal variations of temperature and other meteorological factors are known to cause seasonal variations of O3 and NOy species concentrations. The monthly average NOz and HNO3 mixing ratios indicate that active photochemical processing of NOx occurs during well over half the year in the warm climate of the southeastern US. The effects of VOC species on O3 formation depend on both their ambient concentrations and their reactivities. To describe VOC variations at sites with long-term VOC measurements, we use isoprene data as an indicator of biogenic VOCs and toluene as an indicator of anthropogenic VOCs (nominally emitted as a gasoline vapor). The importance of isoprene emissions for O3 production in the southeastern US is well established (e.g., Chameides et al., 1988; Chameides and Cowling, 1995; Frost et al., 1998; Starn et al., 1998; Wiedinmyer et al., 2006; Zhang et al., 2014; Lin et al., 2017). We also consider other reactive VOC species of interest, including α-pinene (biogenic) as well as ethylene and xylenes (anthropogenic). Summer (June–August) months exhibit elevated ambient mixing ratios of rural and urban isoprene, typically about 5–10 ppbC, that are 1 to 2 orders of magnitude greater than those occurring between October and April (Fig. 6). Transitions between low and high ambient isoprene mixing ratios occur in mid-May and mid-September in northern Georgia (Fig. 6). Annual mean isoprene mixing ratios were relatively constant, ∼ 2.5–3 ppbC, between 1998 and 2014. Biogenic VOCs, primarily isoprene, represent ∼ 20 % of the VOC reactivity at JST, ∼ 30 % at South DeKalb (SDK, located in metropolitan Atlanta ∼ 16 km southeast of JST), and ∼ 50 % at YRK, averaged over all samples collected between 1999 and 2007 (Blanchard et al., 2010a). Through precursor interactions, seasonal variations in isoprene mixing ratios are expected to affect seasonal variations in O3 mixing ratios and production rates.

Mean mixing ratios of ethylene and aromatic compounds vary substantially between urban and rural sites and exhibit less, and a different, seasonal variation than does isoprene, peaking in the fall rather than in the summer (compare Figs. 6, S5, S6). Daily-average mixing ratios of toluene, xylenes, and ethylene decline over the years, consistent with regulatory reductions of anthropogenic VOC emissions (Figs. S5, S6). Seasonal variations in ambient mixing ratios and trends in the anthropogenic emissions of aromatic compounds are expected to influence O3 mixing ratios and production in urban settings (rural anthropogenic VOC mixing ratios are lower but detectable).

The 24 h average VOC mixing ratios are of somewhat limited value for showing the influence of VOCs on O3 formation and accumulation. VOC influence is dependent on NOx mixing ratios, which vary depending on proximity to emission sources and time of day. Meteorological variability, including diurnal and day-to-day changes in temperature, vertical mixing, cloud cover, photolysis, and air mass transport, further obscures the quantitative effects of VOCs on seasonal and interannual variations of O3. Influences of anthropogenic VOCs at SEARCH sites have previously been reported (Blanchard et al., 2010b, 2014) and are not analyzed beyond this summary.

Summer (June–August) mean O3 mixing ratios exhibit characteristic nocturnal minima and midday (noon to 16:00, midpoint ∼ 14:00) maxima at all SEARCH sites (Fig. 7). This diurnal pattern remained essentially the same at both the urban and rural sites from 1999 through 2014, but the daytime maxima decreased. Between 1999 and 2014, the summer mean midday maxima declined by ∼ 30 ppbv at all sites, while nocturnal means exhibited variable responses (Fig. 7). Similar diurnal variations occur throughout the year, with smaller decreases in the mean midday O3 maxima occurring during seasons other than summer (Figs. S7–S9). By the end of the study period, diurnal O3 profiles were higher during spring (March through May) than summer at the rural sites (CTR and YRK, Figs. S7 and S8), consistent with the reduction in summer mean monthly daily peak 8 h O3 averages (Fig. 4). Decreasing summer diurnal mean NOy, HNO3, and NOz mixing ratios were also observed, with a general flattening of the profiles and with the times of maxima remaining consistent (Figs. S10–S12). O3 changes are discussed in relation to changes in NOy and NOz in Sect. 4.4, with emphasis on summer and additional consideration of spring months.

As discussed above, O3 mixing ratios vary seasonally and diurnally in response to variations in emissions, weather, background O3, and other factors. To reduce the influence of seasonal and diurnal variability, this section focuses on mixing ratios of NOz, HNO3, and O3 at 14:00 during June and July. Both temperature and solar radiation are typically high during June and July, and multi-day stagnation events occur frequently in association with high barometric pressure (Blanchard et al., 2013). Exceptions exist during the passage of frontal systems (Blanchard et al., 2013; Fig. S13). The 14:00 hour has the highest, or close to highest, average hourly O3 for all sites and years (Fig. 7). The atmosphere is well mixed by midday. Over the range of ambient mixing ratios observed across 15 years, the June–July 14:00 O3 values are distinctly nonlinear in relation to ambient NOz and HNO3 mixing ratios (Fig. 8). More variability is evident at urban sites than at rural sites, consistent with influence of urban NOx and perhaps VOC emissions on O3. The nonlinearity indicated in Fig. 8 is also evident when the data are restricted to days having the highest peak daily 8 h O3 mixing ratios (Fig. S14).