The sampling site (40.04∘ N, 116.42∘ E) is located at the campus of Chinese Research Academy of Environmental Sciences and was described in our previous work (Zhang et al., 2021). Briefly, the station is located 2 km from the north 4th Ring Road and surrounded by a mixed residential and commercial area. The concentrations of VOCs, NOx, CO, O3, and PM2.5 were measured at 8 m above ground level at this location. Meteorological parameters, including temperature (T), relative humidity (RH), wind speed and direction (WS&WD), and solar radiation (SR), were monitored at 15 m above ground level. VOCs were measured by an online commercial instrument (GC-866, Chromatotec, France), which consisted of two independent analyzers for detecting C2–C6 and C6–C12 hydrocarbon components. More details about the observations can be found in the Supplement (Sect. S1). The calculation of initial VOCs and sensitivity tests can be found in Sect. S2

The random forest (RF) is a type of ensemble decision tree that can be used for classification and regression (Breiman, 2001). In this work, we performed O3 and RI calculations using the RF method in MATLAB's Statistics and Machine Learning Toolbox. During the training process, the model creates a large number of different decision trees with different sample sets at each node and then averages the results of all decision trees as its final results (Breiman, 2001). To avoid over-fitting, we trained the random forest model using cross-validation for the normalized data, which can improve the robustness of the model. Briefly, we randomly divided the normalized data into 12 subsets, then alternately took one subset as testing data along with the rest as training data. By doing this, every data point has an equal chance of being trained and tested. The length of the input data from 2014 to 2016 was 1190, 1062, and 872 rows, respectively, in which different types of VOCs, NOx, CO, PM2.5, and meteorological parameters (including temperature, relative humidity, solar radiation, wind speed and direction) were used as input variables and O3 as output variables. The mean values (± standard deviation) of input/output parameters are shown in Table S1 in the Supplement. Approximately 1/3 of the samples are excluded from the sample, when the decision tree is built and used to calculate the out-of-bag data error. Hence, RF can evaluate the RI of variables via the changes in out-of-bag (OOB) data error (Svetnik et al., 2003), 1RIi=∑errOOB2i-errOOB1i/N, where N represents the number of decision trees, and errOOB1 and errOOB2 represent the out-of-bag data error of feature i before and after randomly permuting the observation, respectively. The RIi is used to evaluate the importance and sensitivity of feature i to O3 formation in this study. More details about workflow of RF model and the hyperparameter tuning can be found in Sect. S3. The optimized parameters are shown in Table S2. To verify the stability of the model, we performed a significance test on the model results. The results showed that there was no significant difference among the different tests (P>0.05, R2>0.98).

When plotting the O3 formation sensitivity curves, we made a virtual matrix of inputs by varying the concentrations of NOx and VOCs from 0.9 to 1.1 times (with a step of 0.01) of their mean values while keeping all other inputs unchanged (i.e., the mean values). Then, the new matrix was used as testing data, while all the measured data were taken as training data. Thus, the testing data should represent the mean sensitivity regime of O3 in Beijing, while the training data actually covered all the sensitivity regimes of O3 formation to guarantee a sufficient coverage in the NOx-limited regime for the RF model simulations. The EKMA curves were plotted using the daily maximum 8 h (MDA8) O3. More details can be found in the Supplement.

Figure 1 shows the time series of air pollutants and meteorological parameters during the observations from 2014 to 2016. In 2014, 2015, and 2016, the wind direction was dominated by northwest winds (Fig. S1 in the Supplement), with mean wind speeds of 3.1±2.7, 2.3±2.2, and 1.3±1.2 m s-1, respectively, and the mean daytime temperatures were 22.3±5.8, 23.9±5.0, and 24.0±4.4 ∘C, respectively. The average value of SR decreased from 162.9 to 150.8 W m-2 during the observation period. As shown in Fig. 1f–g, in 2014, 2015, and 2016, the mean VOC concentrations were 20.3±10.9, 15.8±8.3, and 12.1±7.7 ppbv, respectively, while the mean initial VOC concentrations were 28.1±25.7, 27.2±32.6, and 16.4±16.1 ppbv, respectively. Both the measured VOCs and initial VOCs showed a decline along with a decrease in PM2.5 concentration from 67.2±53.5 to 61.1±48.6 µgm-3 due to the Air Pollution Prevention and Control Action Plan in China (Zhao et al., 2021). However, O3 concentrations showed a slight downward trend from 44.3±32.4 to 42.7±27.9 ppbv from 2014 to 2015 and then reach to 44.0±29.6 ppbv in 2016. A slight upward trend was observed for NOx concentrations (Fig. S2). As shown in Fig. 1f–g, the concentrations of four types (alkanes, alkenes, alkynes, and aromatics) of VOCs showed significant differences from 2014 to 2016 due to the variations in emission sources (Zhang et al., 2021). In addition to VOC species, the variations in other parameters, such as meteorological conditions and PM2.5, should have a complex influence on O3–VOC–NOx sensitivity (Li et al., 2019; S. Ma et al., 2021).

To build a robust model, we evaluated the prediction performance of the RF model for the ambient O3 simulation. Figure 2 shows the O3 prediction performance in 2015 when chemical species (including VOCs, NOx, PM2.5, CO) and meteorological factors (i.e., WS, WD, SR, T and RH) were used as inputs in the RF model. The prediction performance of RF model for 2014 and 2016 is shown in Figs. S3 and S4, respectively. The details of the modeling and input parameters are shown in Table S2. Figure 2a–c show the time series of the measured and modeled O3 concentrations, which were simulated using the TVOCs, measured VOC species, and initial VOC species as part input variables along with the same set of other parameters. The correlation coefficients (R2) of the training data were 0.77, 0.82, and 0.81 for the TVOCs, measured VOC species, and initial VOC species, respectively. The corresponding root mean square errors (RMSEs) for the predicted O3 concentrations were 17.4, 12.6, and 13.9. Figure 2d–f show the prediction performance of the testing dataset under these three circumstances. When the TVOCs were split into measured or initial VOC species, the R2 increased obviously as the number of data features increased. Therefore, the VOC composition has a significant influence on O3 prediction using the RF model. In previous studies using TVOCs, the influence of VOC composition was neglected (Liu et al., 2021; R. Ma et al., 2021). Our results indicate that the RF model can accurately predict O3 concentrations when the concentrations of measured/initial VOC species are considered.

It should be pointed out that if the training dataset does not have sufficient coverage in the NOx-limited regime, then the trained algorithm essentially attempts to extrapolate in that regime, which is prone to overtraining. To avoid such overtraining, a 12-fold cross-validation by randomly dividing the observation data in each day into 12 subsets and alternately taking 1 subset as testing data and the rest as training data ensures that each data point has an equal chance of being trained and tested. The curves of the predicted O3 concentrations in Fig. 2 were spliced using the testing datasets in all runs. Thus, our results actually covered all the sensitivity regimes of O3 formation. This means that the model is robust.

Figure 3a shows the RIs of different ambient factors, including chemical and meteorological variables on O3 formation. The difference in the RIs is also compared using the TVOCs and the VOC species as inputs. Chemical factors (including VOC species, NOx, PM2.5 and CO) accounted for 79.1 % of the contribution to O3 production in the summer of 2016. Meanwhile, VOC species accounted for approximately 63.4 % of O3 production while the RIs using TVOC concentrations accounted for only 2.1 %. S. Ma et al. (2021) analyzed the contribution of meteorological conditions and chemical factors to O3 formation on the North China Plain (NCP) using the CMAQ model in combination with process analysis and found that chemical factors dominate O3 formation in summer. Using probability theory, Ueno and Tsunematsu (2019) also found that VOCs/NOx dominates O3 production compared to meteorological variables. Thus, our results are similar to those of previous studies based on chemical models (Ueno and Tsunematsu, 2019), which demonstrates that the RF model can reflect the contribution of VOC species to O3 production even if the observed VOC species are used.

Here, we compared the RIs of VOCs calculated using the initial VOC species and the observed VOC species with the OFPs. The OFPs were calculated by the maximum incremental reactivity (MIR) method (Carter, 2010). As shown in Fig. S5, the RIs showed good correlations with the OFP. Interestingly, the initial concentrations of VOC species improved the correlation coefficients between the RIs and OFPs. Furthermore, we calculated the RIs and OFPs of different species using the observed data during the campaign study in Daxing District in the summer of 2019 (Zhan et al., 2021), and a stronger correlation was observed between the RIs of the initial VOC species and the OFPs (Fig. S6). These results indicate that the RIs of the initial VOCs species in the ML model should partially reflect the chemical reactivity of VOCs to produce O3 in the atmosphere.

Although the RIs calculated using the initial VOC species slightly changed compared to those calculated using the observed VOCs (Table S3), VOCs still dominated O3 formation (Fig. 3a). For example, the initial VOCs dominated O3 production in 2014, 2015, and 2016, with RI values of 64.0 %, 59.0 %, and 63.3 %, respectively. Li et al. (2020a) used a multiple linear regression (MLR) model to study the contribution of anthropogenic and meteorological factors to O3 formation in China from 2013–2019 and found that meteorological factors accounted for 36.8 % and anthropogenic factors accounted for 63.2 %, which is similar to our results. Figure 3b–d show the top 10 factors having a strongly influence on O3 production. Interestingly, NOx and RH showed negative responses to O3 formation, while other variables, including T, SR, CO, and all of the VOCs, showed positive responses. Thus, a decrease in NOx or RH will lead to an increase in O3 concentration, while a decrease in T, SR, CO, and VOCs will lead to a decrease in O3 concentration. Although O3 formation is highly related to the photolysis of NO2, a previous study demonstrated that it is VOC-limited in summer in Beijing (Zhan et al., 2021). This finding is consistent with the observed negative response of O3 to NOx in this work. High RH usually coincides with low surface O3 concentrations in field observations, which can be ascribed to the inhibition of O3 formation by the transfer of NO2/ONO2-containing products into the particle phase and the promotion of dry deposition of O3 on the surface (Kavassalis and Murphy, 2017; Yu 2019). In addition, it has been shown that RH is negatively related to the rate constant of HONO formation (Hu et al., 2011). Thus, RH might also affect the O3 formation by influencing atmospheric OH radicals from photolysis of HONO. It should be noted that the negative response of ozone to RH might also have resulted from the dependence of RH on other parameters/conditions, such as SR. However, RH and SR showed a bad correlation (r<0.1). We further tested the dependence of the RI on RH and SR with or without the counterpart as input. The stable RI values (Table S4) mean that RH and SR are independent from each other. These previous works can well explain the observed negative response of O3 to RH in Fig. 3b–d. Previous studies have observed a positive correlation between the O3 concentration and T or SR (Steiner et al., 2010; Paraschiv et al., 2020; Li et al., 2021). Temperature can directly affect the chemical reaction rate of O3 formation (Fu et al., 2015), and SR can promote the photolysis of NO2 (Hu et al., 2017; Y. Wang et al., 2020a), thus accelerating O3 formation. As mentioned above, O3 formation is VOC-limited in Beijing; thus, a positive response of O3 concentration to VOCs is observed in Fig. 3b. Interestingly, the RIs of isoprene showed an increasing trend from 2014 to 2016 because of the obvious reduction in anthropogenic VOCs (Fig. S7) (Zhang et al., 2021). In the context of global warming, studies should focus on the factors that affect O3 formation, including biogenic emissions, T, and SR. Thus, additional efforts will be required to reduce anthropogenic pollutants in the future.

To further analyze the sensitivity of O3 to VOCs and NOx from 2014 to 2016, we plotted sensitivity curves for O3 generation using the RF model, and the results are shown in Fig. 4a–c. Moreover, EKMA curves in 2015 were also obtained using the OBM (Fig. 4d). As shown in Fig. 4a–c, O3 formation was sensitive to VOCs in the summer of Beijing during our observations, which is consistent with previous studies that used box models (Li et al., 2020b) and chemical transport models (Shao et al., 2021). This result is also consistent with the RIs of VOCs or NOx to O3 formation (Fig. 3b–d). Interestingly, the O3 formation sensitivity to VOCs decreases or gradually shifts from the observed point to the transition regime from 2014 to 2016 (Fig. 4a–c), which is similar to that reported by Zhang et al. (2021). These phenomena can be ascribed to the increased relative importance of meteorological factors, such as T, SR, and RH, for O3 formation and the variation in anthropogenic VOC emissions (Steiner et al., 2010; S. Ma et al., 2021).

We compared the relative error of simulated MDA8 O3 calculated using the RF and OBM model in 2015, as shown in Fig. S8. The mean relative error of simulated MDA8 O3 between RF model and box model was 15.6 %. Hence, a combination of the RF model and initial VOCs species can accurately depict the sensitivity regime of O3 formation, while the calculated RIs correlate well with the OFPs.