Numbers of data flags “-999” (i.e., invalid data), blank cells, and “0” data points in hourly O3, NO, NO2, and NOx concentrations were counted by year. Then data flags -999 were replaced with blank cells to maintain consecutive date and time for individual pollutants. If the total percentage of data flags and blank cells is greater than 40 % (3504 h yr-1) in a year, data in that year are considered to be invalid and excluded from further analysis. This is the case for hourly NO, NO2, and NOx concentrations in 2003. Results of data screening can be found in Zhang (2016) and in the Supplement (Table S1).

There are 176 VOCs reported in the NAPS dataset, of which 118 were used in this study. Missing samples were identified by comparing the sampling schedule with the dates of available samples in each year. Blank and 0 cells were counted for individual compounds in each year. A compound is excluded from analysis if the total number of blank and 0 cells is greater than 70 % during the study period of 1996–2015. Blank and 0 cells were also counted for each sample. Samples with less than 60 % of compounds that registered valid readings were removed. To reduce the undue influence of a few unusual events with extremely high concentrations, outliers were identified and removed.

Sixteen NMHCs were excluded from analysis because less than 30 % of samples had valid readings. Thus, 102 compounds were retained for further analysis. Out of 877 samples, 14 were excluded. The remaining 863 samples each had at least 60 % compounds with valid readings (range of 64 %–100 %, mean of 88 %, and median of 91 %), and they were used to calculate total NMHCs and OFPs. Daily NOx-to-NMHC ratios (referred to as NOx-to-VOC ratios hereafter) were calculated for the dates when VOC data are available. Hourly NO2/NOx ratios were calculated as well.

Following Akimoto et al. (2015), TO in Windsor was calculated with Eq. (1), [TO]=[O3]+[NO2]-0.1×[NOx]1=[O3]+[DO3], where [DO3] ([NO2]-0.1 × [NOx]) represents loss of O3 due to in situ NO titration; [O3], [NO2], and [NOx] are hourly concentrations; and the constant 0.1 is the fraction of NO2 in primary NOx emissions (Itano et al., 2007). In this study, the NO2 fraction was determined from the slopes of regression of [Ox] (= [O3] + [NO2]) vs. [NOx] in Windsor in each year during the morning NO and NO2 peak hours (from 05:00 to 08:00; all times are referred to in local time – LT) as described in Kurtenbach et al.  (2012). The 20-year average fraction was 0.1, consistent with that in the previous O3 study in Japan (Itano et al., 2007).

Diurnal variation of O3 concentrations in Windsor during 1996–2015 is shown in Fig. 2a and Table S2. There was a gradual increase in O3 concentrations from 06:00 to 14:00 and a gradual decrease from 15:00 to 06:00 next day. A similar trend was observed for TO. The diurnal variations for O3 and TO indicate that O3 photochemical production was enhanced by increased solar radiation and temperature (So and Wang, 2003). DO3 followed an opposite trend than O3, i.e. lower at noon to afternoon (11.2 ppb from 11:00–15:00) than that at other hours of the day (16.2 ppb), suggesting that relative loss due to the titration effect was reduced when O3 concentrations were high.

O3 concentrations were higher during the smog season than in the non-smog season, especially around noon, due to photochemical production (Fig. 2b and c). DO3 levels were lower throughout the day in the smog season, suggesting that relative loss due to the titration effect was reduced when O3 concentrations were high. Furthermore, TO (O3+DO3) diurnal variation was rather smooth in the non-smog season due to weak photochemical production of O3.

Monthly O3 concentrations increased from January to May, reaching peak values in June and July, then decreased from July until the minima in December (Fig. 3 and Table S3). This seasonal pattern is similar to that of solar radiation and ambient temperature, which control the photochemical production rate of O3. A similar seasonal variation was observed for TO, but DO3 followed an opposite trend than O3, i.e. higher in the non-smog season (16.6 ppb) and lower during the smog season (13.1 ppb). Similar to the diurnal variation, relative loss due to the titration effect appears to be reduced when weather conditions favored O3 formation. The seasonal O3 pattern observed in Windsor is consistent with the study by Gaudel et al. (2018) reporting that in North America, the maximum O3 daytime averages occurred in spring–summer and the minimum values were found in autumn–winter during 2010–2014.

ANOVA indicates that O3 concentrations on weekends (25.9 ppb) were statistically higher (p<0.05) than on weekdays (23.3 ppb). NO concentrations were lower on weekends (6.5 ppb) than on weekdays (9.6 ppb) due to less vehicular and industrial activities. Therefore, high O3 concentrations on weekends were likely attributed to decreased NO emissions and the weakened titration effect as reported by other researchers (Koo et al., 2012). This is supported by comparable TO concentrations between weekdays and weekends (39.2 vs. 39.5 ppb, p<0.05) which remove the titration effect. Differences in O3 levels between the weekday and weekend were also reported in other studies, e.g., in Nepal (Pudasainee et al., 2006) and Ontario, Canada (Huryn and Gough, 2014).

During 1996–2015, annual mean O3 concentrations increased significantly (0.452 ppb yr-1; Fig. 4a), while annual mean DO3 concentrations decreased at a greater rate (-0.524 ppb yr-1). Consequently, TO concentrations decreased slightly (-0.076 ppb yr-1, but not significant at p<0.05 level). In other words, O3 decreased slightly when the NO titration effect is removed, suggesting that the decreased NO titration effect is one of the reasons for the increased O3 concentrations in Windsor.

Significantly decreasing trends were observed in Windsor for annual mean NOx (-1.34 ppb yr-1), NMHC (-2.98 µg m-3 yr-1), and OFP (-9.77 µg m-3 yr-1) during the 20-year study period (Fig. 4b). The percent decreases were 58 %, 61 %, and 73 % for NOx, NMHC, and OFP, respectively, indicating effective emission control. It should be noted that during 1996–2008, some pollutants were changing at greater rates compared with the 20-year trend, including O3 (0.55 ppb yr-1), NMHC (-4.34 µg m-3 yr-1), and OFP (-13.5 µg m-3 yr-1). After 2008, concentrations of O3, NMHC, and OFP leveled off, while NOx and DO3 concentrations continued to decrease.

The decreased NO titration effect was further investigated by examining the ratio of NO/NOx (Fig. S1). Significantly decreased NO (-0.73 ppb yr-1) and NO2 (-0.66 ppb yr-1) were observed during the study period. Furthermore, the NO/NOx ratio decreased from 0.34 in 1996 to 0.16 in 2015, with an average rate of -0.012 yr-1, supporting the decrease in the NO titration effect in Windsor. Our results are consistent with studies in other countries. For example, NO2/NOx ratio increased from 0.08 in 2005 to 0.15 in 2010 in Japan (Itano et al., 2014), implying a decreased NO/NOx ratio. The NMHC/NOx ratios did not change much during the 20-year study period (min of 0.96, max of 1.3, and mean and median of 1.1). The low ratios of VOC to NOx (<5) suggest that the study area is VOC limited; thus reduced NOx emissions may lead to increased O3 concentrations (Sillman, 1999; USEPA, 2000).

Figure S2 depicts long-term O3 and TO trends at 5th, 25th, 50th, 75th, and 95th percentiles in Windsor during 1996–2015. The slopes of linear regression in three scenarios (i.e., all months, the smog season, and the non-smog season) are summarized in Fig. 5 and Table S4. Peak O3 concentrations (i.e., 95th percentile) decreased during the smog season and for all months, suggesting that reduced precursor emissions and photochemical production. O3 at all other percentile levels in all three cases had increased, with higher rates at 25th and 50th percentiles. The 25th percentile of O3 concentrations was commonly considered to be a background value (Lin et al., 2000; Aleksic et al., 2011; Parrington et al., 2013). Peak TO concentrations (95th percentile) deceased, especially during the smog season, due to effective emission control of O3 precursors. TO concentrations increased at all other percentile levels during the non-smog season, when O3 photochemical production was limited, suggesting rising background O3 concentrations.

In the smog season, O3 concentrations increased at the 5th–75th percentile levels, while TO concentrations decreased with a greater rate at higher percentile levels, suggesting that the decrease in NO titration is one of the causes of increasing O3 in Windsor. In terms of peak O3 concentrations (95th percentile), the decreasing rate of TO (-1.0 ppb yr-1) is more than twice that of O3 (-0.45 ppb yr-1). In other words, when the effect of NO titration is removed, peak O3 concentrations decreased more intensely due to reduced emissions of O3 precursors. During the non-smog season, the increasing rates of TO at 5–75th percentiles were much slower than those of O3. The results suggest that the decreased NO titration effect could be one of the causes for slower decrease in peak O3 in the smog season and increase in O3 at low-to-high percentiles during both the smog and non-smog seasons.

The decreasing trend of the 95th percentile O3 levels in Windsor is consistent with the decreasing concentrations at upper end of the distribution across the United States (Simon et al., 2015), which evaluated maximum daily 8 h average O3 at over 1000 sites during 1998–2013, when NOx and VOC emissions were decreasing. The declining peak O3 is also evident in the study of the fourth-highest daily maximum 8 h concentrations during 2000–2014 by Fleming et al. (2018), which indicated that up to 70 % of North American stations experienced significant negative trends (p<0.05). The results of the seasonal O3 trends in Windsor are consistent with previous studies. For instance, Simon et al. (2015) reported that the declining trends were more pronounced in summer than winter and that increasing O3 trends at all percentiles were found in both smog and non-smog seasons, except for decreasing peak values at urban sites of the East North Central region (close to Windsor; Simon et al., 2015). Moreover, Gaudel et al. (2018) reported the increasing O3 levels across North America in wintertime (December, January, and February).

This section further investigates which hour or hours of a day and which month or months of a year experienced greater or fewer changes in O3 concentrations during the 20-year study period and to what degree those changes could be explained by the change in the NO titration effect. The estimated month-of-year slopes by Mann–Kendall and Sen's test during 1996–2015 are shown in Fig. 6. The rates of change during the smog and non-smog seasons are summarized in Fig. S3.

The increased O3 levels in the non-smog season (mean of 0.58 ppb yr-1; Fig. S3) suggest a reduced titration effect and rising background O3 levels, since local photochemical production of O3 is limited. Analysis of ambient data conducted by USEPA demonstrated that mid-tropospheric O3 concentrations in the US and globally have increased over the past two decades by 0.4 ppb yr-1 (USEPA, 2015). Along the Pacific Coast, the rate of increasing background O3 was estimated to be 0.5–0.8 ppb yr-1 during 1985–2002. This trend of ground-level O3 is consistent with the rate of increase (0.51 ppb yr-1, 1994 to 2002) derived using aircraft measurements (Jaffe et al., 2003). Another reason of increased O3 is the decreased titration effect. A study in southeastern France demonstrated that the decrease in the NO titration effect could be one of the reasons for increased O3 concentrations in cold months (Sicard et al., 2011). The slower increasing rate of O3 in smog season (0.32 ppb yr-1, Fig. S3) is a result of increased background O3 levels, a decreased titration effect, and reduced local photochemical O3 production and regional transport (MOECC, 2017). A similar trend of a greater rate of increasing composite mean at 19 sites across Ontario in summer (49 %) than in winter (14 %) during 1991–2010 was largely attributable to the reductions in local NOx emissions and the rising global background ozone levels (MOE, 2012).

O3 concentrations increased while DO3 concentrations decreased in all months during 1996–2015 (Fig. 6). During the non-smog season, the increasing rate of O3 (0.58 ppb yr-1; Fig. S3) was higher than the decreasing rate of DO3 (-0.46 ppb yr-1). In other words, there was an additional increase in O3 beyond the decreased titration effect. After the NO titration effect is removed, TO concentrations increased in non-smog season (0.13 ppb yr-1; Fig. 6), suggesting rising background O3 levels. In the smog season, the increasing rate of O3 (0.32 ppb yr-1) was lower than the decreasing rate of DO3 (-0.50 ppb yr-1). TO concentrations had decreased in the smog season (-0.27 ppb yr-1; Fig. 6), being attributable to the decreased regional O3 production.

On an hourly basis, greater increasing rates in O3 concentrations were observed at evening and nighttime hours (18:00–03:00) in comparison with the early morning and daytime (04:00–17:00), as shown in Fig. 7. The two minima in the morning at 06:00 and 13:00 coincided with the lowest and highest O3 concentrations in a day, which were caused by different rates of change in smog and non-smog seasons (see below). Overall, O3 increased while DO3 decreased at all hours in a day during 1996–2015. The diurnal pattern of increasing rates for O3 almost mirrored that of decreasing rates for DO3. In other words, the increase in O3 concentrations could be explained largely by the decreased NO titration effect. At most hours, the increasing rates of O3 were higher than the decreasing rates of DO3, especially in the morning hours (06:00–12:00). Overall, TO concentrations increased slightly during daytime while decreasing a little in the evening.

O3 and DO3 concentrations showed different diurnal patterns during the smog season (Fig. 8). O3 concentrations increased while DO3 concentrations decreased at all hours as in the case of all months. During the daytime (09:00–19:00), there was a sharp decline in the rates of change for O3 until peak O3 hours (14:00–16:00) followed by a speedy recovery. The peak hour O3 concentrations have not changed much during the last 20 years, and daytime ozone levels have increased with a much slower rate (09:00–19:00, mean = 0.15 ppb yr-1) compared with the nighttime (20:00–08:00, mean = 0.46 ppb yr-1). The daytime DO3 decreasing trend is similar, however with less variability. The increasing rate of O3 is lower than the decreasing rate of DO3, and TO concentrations decreased at all hours, especially during the afternoon and early evening (14:00–19:00). This suggested decreased photochemical O3 formation during the smog season due to emission reduction.

During the non-smog season (Fig. 9), the rates of change in O3 and DO3 were similar as in the case of all months, i.e. the increase in O3 concentrations could be explained largely by the decreased titration effect. Also similar to that of all months, the rates of change were lower in the early morning (05:00–07:00). The greater rates of change were observed in the late afternoon and evening (16:00–20:00), instead of at night, with all months. The increasing rates of O3 were higher than the decreasing rates of DO3 at all hours. The hour-of-day TO trend is overall increasing with less diurnal variation, indicating rising background O3 levels.