The hourly O3 and PM2.5 data during April–October 2013–2017 were derived from the National Urban Air Quality Real-time Publishing Platform (http://106.37.208.233:20035/, last access: 15 October 2019). According to technical regulation for ambient air-quality assessment (HJ 663-2013, http://www.mee.gov.cn/, last access: 15 October 2019), the MDA8 O3 concentration was calculated for each monitoring site based on the hourly data from the time period 08:00–24:00 for the days with at least 14 h of measurement data. If less than 14 h of valid data are available, the results are still valid if the MDA8 O3 concentration exceeds the national concentration limit standard. Each city has at least two monitoring sites, and the MDA8 O3 levels for a city are the corresponding averages over all sites in that city. The MDA8 O3 values were collected in only 14 cities for the time period from 2013 to 2017 and in an additional 44 cities for the time period from 2015 to 2017, and detailed information is shown in Fig. 1 and Table S1 in the Supplement. The original units for the ozone observations were micrograms per cubic meter, and the conversion coefficient from the mixing ratios (unit: ppbv) to micrograms per cubic meter was a constant (e.g., 0.5 at a temperature of 25 ∘C and pressure of 1013.25 hPa). In this study, we used the original units. Unless otherwise noted, the analysis of O3 refers to MDA8 O3 during April–October in this paper.

Gridded-mean sea level pressure data, 10 m U and V wind components (U10 and V10, respectively), boundary layer height (BLH), and 2 m temperature (T2) with a 1∘ horizontal resolution and vertical velocity (ω) from 1000 to 100 hPa (27 levels) and wind divergence (div) from 1000 to 850 hPa (seven levels) in 6 h intervals (Beijing time 02:00, 08:00, 14:00 and 20:00) for 2013–2017 were obtained from the European Centre for Medium-Range Weather Forecasts European Reanalysis Interim (ERA-Interim).

Four measurements per day for temperature (T), relative humidity (RH), total cloud cover (TCC), rain, wind speed (ws), wind direction (wd) and pressure (pre) in 58 cities during April–October 2013–2017 were obtained from the China Meteorological Information Comprehensive Analysis Process System (MICAPS). Then, daily mean meteorological factors were averaged from four measurements (scalar averaging for most factors and vector averaging for wind speed and wind direction, which involved using the u (U) and v (V) components for averaging). The meteorological station with a minimum distance from the city center was chosen.

The Lamb–Jenkinson weather type approach (Lamb, 1972; Yarnal, 1993; Conway and Jones, 1998; Trigo and Dacamara, 2000; Mckendry et al., 2006; Demuzere et al., 2009; Russo et al., 2014; Santurtún et al., 2015; Pope et al., 2016; Liao et al., 2017) has been widely employed to classify synoptic circulation. On the basis of the Lamb–Jenkinson method, the weather type circulation pattern for a given day is described using the locations of the high- and low-pressure centers that identify the direction of the geostrophic flow; the method uses coarsely gridded pressure data on a 16-point moveable grid (Demuzere et al., 2009). In our study, northern China was set as the center. The specific schematic diagram is shown in Fig. 1a. The daily mean sea level pressure data were averaged over four time points to determine the daily weather type. The detailed classification procedure can be found in Trigo and Dacamara (2000) and in the Supplement (Sect. S1).

To quantify the interannual variability captured by the variations in the surface circulation pattern, Comrie and Yarnal (1992) suggested an algorithm to separate synoptic and non-synoptic variability in environmental data; by multiplying the overall mean value of a particular pattern by the occurrence frequency of that type of year, the climate signal can be obtained as follows: 1O3m‾‾(fre)=∑k=126O3k‾Fkm, where O3m‾‾(fre) is the reconstructed mean MDA8 O3 concentration influenced by the frequency of changes in the weather type from April to October for the year m, O3k‾ is the 5-year mean MDA8 O3 concentration for weather type k, and Fkm is the occurrence frequency of weather type k during April–October for year m.

Hegarty et al. (2007) suggested that variations in the circulation patterns are attributed to not only frequency changes but also intensity variations; moreover, they noted that the environmental and climate-related contributions to the interannual variations in ozone could be better separated by considering these two changes. As a result, Eq. (1) was modified into the following form: 2O3m‾‾fre+int=∑k=126O3k‾+ΔO3kmFkm, where O3m‾‾(fre+int) is the reconstructed mean MDA8 O3 concentration influenced by the frequency and intensity of the changes in circulation patterns from April to October for year m; ΔO3km is the modified difference on the fitting line, which is obtained through a linear fitting of the annual MDA8 O3 concentration anomalies (ΔO3) to the circulation intensity index (CII) for circulation pattern k in year m. ΔO3km represents the part of the annual observed ozone oscillation caused by the intensity in each circulation pattern. Hegarty et al. (2007) used the domain-averaged sea level pressure (mslp) to represent the CII.

To better characterize intensity variations, we used an additional five CIIs: the difference between the highest pressure and lowest pressure (gradient), the center pressure of the highest-pressure system (max slp), the center pressure of the lowest-pressure system (min slp), the distance from the highest-pressure centers to the study city (dis max), and the distance from the lowest-pressure centers to the study city (dis min). Among the above six CIIs, the one with the strongest correlation coefficient (r) with ΔO3 was selected as an effective circulation intensity index (ECII). Thus, ECII was used in Eq. (2) to calculate ΔO3km. All CIIs for the 14 cities were calculated based on 10∘ × 10∘ grids covering northern China (32–42∘ N, 110–120∘ E). An example of ΔO3km (weather type C in ZJK, which is a city located in Hebei Province) is shown in Fig. 7a. Here, min slp has the highest r (-0.97) among the six CIIs in type C in ZJK, so min slp is selected as the ECII.

The utilization of a segmented synoptic-regression approach can aid in minimizing the errors when using linear regression to model a nonlinear relationship and effectively forecast ozone variations (Robeson and Steyn, 1990; Liu et al., 2007, 2012; Demuzere and van Lipzig, 2010). Based on locally monitored meteorological data, their 24 h time lag values and weather type classifications, stepwise linear regression was used in every weather category to construct the ozone potential forecast model. The details of the main methods are shown in Sect. S2. Notably, in this research, after excluding the missing data and disordering the time sequences, 80 % of these days were used to build the potential forecast equations, and the remaining 20 % were used to validate the accuracy of the equations.

Statistical model performances were evaluated according to the following factors: R2 (variance in the individual model's coefficients of determination), RMSE (root-mean-square error) and CV (coefficient of variation defined as RMSE / mean MDA8 O3). All statistics are based on MATLAB R2015b.

The MDA8 O3 concentration is one of six factors used to calculate the daily air-quality index in China. Five ranks were separated, representing different air-quality levels: excellent, good, lightly polluted, moderately polluted and heavily polluted days, with cutoff concentrations of 100, 160, 215 and 265 µg m-3, respectively. The daily limit for the Grade II National Ambient Air Quality Standard is 160 µg m-3. The spatial distribution of the averaged MDA8 O3 concentration (Fig. 1b) and exceedance ratio, which represents the proportion of days exceeding the standard (160 µg m-3) (Fig. 1c), as well as detailed information on the 58 cities (Table S1), showed a severe ozone pollution problem during the last 5 years in northern China. The domain-averaged MDA8 O3 concentration for 58 cities was 122±11 µg m-3, with an increasing rate of 7.88 µg m-3 yr-1 and an exceedance ratio of 22.2±8.2 %. Notably, the most polluted cities were concentrated in Beijing, the southeast of Hebei, and the west and north of Shandong, where the average MDA8 O3 concentration was 130±9 µg m-3 and the exceedance ratio was 27.9±7.2 %.

The daily evolution of MDA8 O3 concentrations in 14 cities from 2013 to 2017 (Fig. 2a) indicated periodic, consistent and regional characteristics of ozone pollution. The most highly polluted periods were from mid-May to mid-July. In particular, the frequency and level of ozone pollution increased significantly in 2017, and the number of regionally persistent ozone pollution events increased. The rate of the increase in the MDA8 O3 concentration from 2013 to 2017 was 0.87 µg m-3 per month (Fig. 2b), and this growth was accompanied by a decrease in the PM2.5 concentration (Fig. S1). A reduction in particle extinction due to a decreased PM2.5 concentration can lead to an increase in radiation reaching the ground; in addition, Li et al. (2019) suggested that decreased PM2.5 concentrations slowed the sinking of hydroperoxyl (HO2) radicals and thus stimulated ozone production. Thus, the rise in ozone was partly due to the decline in PM2.5. Overall, the annual domain-averaged MDA8 O3 concentrations for 58 cities were 102, 109, 116, 119 and 136 µg m-3 in 2013, 2014, 2015, 2016 and 2017, respectively (Fig. 3a). The exceedance ratios for all cities were found to be 12.9 %–19.4 % from 2013 to 2016 but reached 31.1 % in 2017.

The monthly mean MDA8 O3 concentrations (Fig. 3b) from April to October were 112, 138, 149, 132, 124, 117 and 75 µg m-3, respectively, and the corresponding exceedance ratios were 9.4 %, 30.1 %, 41.1 %, 26.1 %, 20.3 %, 20.1 % and 3.3 %. The highest domain-averaged MDA8 O3 concentration and exceedance ratio occurred in June, followed by those in May, July, August, September, April and October. Meteorological conditions led to high ozone concentrations in June, and monsoon circulation in July and August resulted in cloudy, rainy conditions and less radiation in the study area (Y. Wang et al., 2009; Tang et al., 2012). The higher ozone concentrations in April than those in October could be associated with strong winds, resulting in a downward transport of ozone due to the lower stratosphere folding mechanism (Stohl and Trickl, 1999; Cooper et al., 2002; Delcloo, 2008; Verstraeten et al., 2015). Notably, this conclusion is different from that of Tang et al. (2012), who reported that the ozone concentration in July was higher than that in May in northern China during 2009–2010. However, as our study indicated that the domain-averaged MDA8 O3 in May was even higher than that in July, the concentrated pollution episode occurred earlier, especially in 2017. The second half of May was the most polluted period, when the exceedance ratio was 46.1 %, which is higher than the ratios observed in the first half of June (39.5 %), the second half of June (45.4 %) and the first half of July (35.6 %). The reason for this difference is probably the abnormally high temperatures in May, especially the second half of May, from 2013 to 2017 and particularly in 2017 (Fig. S2). Many studies have found a strong positive correlation between ozone levels and temperature (Bloomer et al., 2009, 2010; Demuzere et al., 2009; Pusede et al., 2015).

Based on the five weather categories defined in Sect. 3.2.1, a segmented synoptic-regression analysis approach (introduced in Sect. 2.5) was established to quantify the impact of weather patterns on the day-to-day ozone concentration and to construct the ozone potential forecast model.

The contributions of local meteorological factors to the day-to-day variations in ozone can be evaluated by the explained variance (RE2) calculated from the synoptic-regression-based models (Hien et al., 2002; W. T. Wang et al., 2009). Overall, the predicted versus observed MDA8 O3 concentrations for the validation data are shown in Fig. 9; the predicted concentrations were obtained by inputting the validation data (the part that was not used to build the model, which was 20 % of the total data) into the corresponding model equations for the five weather categories for each city. Local meteorological parameters explained 57 %–63 % and 41 %–52 % of the day-to-day variability in the MDA8 O3 concentration for the northern cities (except for QHD, 34 %) and southern cities (except for ZZ, 20 %), respectively.

In addition, the results of segmented synoptic-regression analysis in 14 cities, i.e., the daily MDA8 O3 potential forecast equations for each category in each city, are shown in Table S3. Table 2 represents the number of cities (14 total) from which the meteorological factors were used in a stepwise regression model under each weather category. The results show that Tmax exhibited a strong positive correlation with ozone; thus, this factor is the primary influencing factor in all categories and all cities, as high temperatures are related to high ozone concentrations in northern China. V exhibited a positive correlation with O3 in the northern part of this region (at the north–south boundary at approximately 38.5∘ N), which means that southerly flow caused an increase in the ozone concentration. Therefore, as discussed in Sect. 3.2.2, high temperatures and southerly winds were the main factors that contributed to increased ozone concentrations in northern China from a regional perspective. Both RH_lag and RH showed a negative correlation with O3, and the former had more occurrences and greater weights in the equations than the latter. This phenomenon may exist because RH of approximately 40 %–50 % (Zhao et al., 2019) generates more hydroxyl radicals (OH), facilitating ozone formation, and ozone is stored in the residual layer and transported to the surface the next day via convection and diffusion. In addition, TCC is a key factor.

Three statistical measures (R2, RMSE and CV) for the building and validation datasets for the five weather categories and the composite model, which integrates the five weather categories, in the 14 cities (Table S4) indicate that the potential forecast equations for MDA8 O3 were acceptable in most cities. Scatterplots of predicted versus observed MDA8 O3 concentrations in the composite validation datasets in each city are shown in Fig. 9. For the validation data, the prediction of ozone concentration was obtained by inputting the meteorological factors into the simulated formula for the corresponding weather category in each city; therefore, the composite validation datasets indicated the integrated predicted ozone concentrations for the five categories. The results of validation show that R2 was higher than 0.50, except for QHD, Shijiazhuang (SJZ) and ZZ (0.24–0.47), while CV was lower than 40 %, except for Taiyuan (TY) and ZZ.

The results reveal that most of the validation data are within the acceptable error range, as they are concentrated within the 2:1 and 1:2 ratio lines, and the scatters are distributed evenly around the 1:1 line. For example, the comparison of the observed and predicted ozone in Beijing during our study period is shown in Fig. S10. This finding also indicates that the segmented synoptic-regression approach is practical for constructing ozone potential forecasting models in most cities in northern China.

In brief, the aforementioned results can provide references for daily MDA8 O3 prediction for each city and facilitate the understanding and evaluation of the impact of local meteorology on daily ozone variations on an urban scale.