The CMAQ model version 5.2 was applied to simulate the photochemical pollution over the YRD and its surrounding areas (Fig. 1) in July 2017. The simulation was performed at a 4 km resolution, using the chemical mechanism of saprc07tic. A regional O3 pollution event that occurred from 22 to 31 July with the mean level of the observed daily maximum 8 h average (MDA8) O3 exceeding 85 ppb over the YRD was selected to study the relationship between the O3–NOx–VOC sensitivity and the values of the photochemical indicators. The CMAQ model was driven by a mesoscale meteorological model, the Weather Research and Forecasting (WRF) version 4.2.2. The 2017 emission inventory of anthropogenic air pollutants in the YRD compiled by the Shanghai Academy of Environmental Sciences (An et al., 2021) was adopted, with the details of the other emissions (i.e., biogenic emissions and open burning) found in Hu et al. (2016).

The model performance on O3 was examined by comparing the simulation with observational data at the monitoring sites supervised by the China National Environmental Monitoring Center (CNEMC) in 13 cities in Jiangsu Province. Three metrics (the normalized mean bias (NMB), the normalized mean error (NME), and the correlation coefficient (r)) as in Sheng et al. (2022) were calculated to evaluate the agreement between the simulation and observations. The criteria of the model performance were recommended by Emery et al. (2017). Table S1 in the Supplement shows that the NMB (NME) values in 12 (10) out of 13 cities met the criteria, indicating that the overall performance was good. In general, the model overestimated O3, with the NMB in the range of -2 % to 17 %. The correlations of the simulation with the observations (all r values above 0.5) indicated that hourly variations in the simulation agree well with the observations. Additionally, three sites in Nanjing (a megacity in Jiangsu), including Caochangmen (CCM), Zhonghuamen (ZHM), and Laoshan (LS), representing downtown, upwind, and downwind areas of the city (see Fig. 1), respectively, were selected to examine the consistency between the photochemical indicators and the O3 isopleths in the implication of O3-precursor sensitivities. Figure S1 in the Supplement shows that the model well reproduced the O3 pollution events at the three sites during the simulation period.

Other species involved in the photochemical indicators, such as HCHO, HNO3, NO2, and NOy (NOy (g)=NO+NO2+NO3+2×N2O5+HONO+HNO3+HNO4+peroxyacetyl nitrate and its homologs (PANs)+alkyl nitrates (ANs) and nitrogen oxychlorides (ClNOx) in the model), were examined and compared with observations during the EXPLORE-YRD campaign (Li et al., 2021; Sun et al., 2022). Figure S2 shows that HCHO was underestimated by 51 %, while NO2 and NOy were slightly overestimated, with NMBs of 16 % and 7 %, respectively. The anthropogenic emission inventory and model were set up as in the simulation for the EXPLORE-YRD campaign, and the simulated ratios of HCHO/NO2 and HCHO/NOy in this study could have been underestimated. In addition, the simulation could represent an environment with less abundant VOCs than in the real atmosphere over the YRD.

The use of photochemical indicators requires threshold values that differentiate O3 formation regimes. In this study, the thresholds of the indicators were derived based on the association of the O3 reduction relative to the baseline emission scenario resulting from NOx or VOC emission reductions (i.e., ΔO3NOx or ΔO3VOC), with concurrent indicator values at all grid cells in Jiangsu Province. Therefore, two additional runs with either a 35 % decrease in NOx or a 35 % decrease in VOC emissions were performed following Sillman et al. (1998) and other studies (Xie et al., 2014; Peng et al., 2011). The resulting O3 changes (ΔO3NOx and ΔO3VOC) were obtained to identify the O3 formation regimes at each grid cell, with the criteria given in Table 1. It should be noted that the average changes in O3 during 13:00–16:00 LT (local time) during the simulation period were used when O3 peaked and was of most concern.

This study focused on four photochemical indicators that are frequently used, including PH2O2/PHNO3, HCHO/NO2, HCHO/NOy, and NOy, with the underlying mechanisms extensively described in the literature (Xie et al., 2014; Kwok et al., 2015; Sillman, 1995; Duncan et al., 2010). The indicator values for each grid cell were calculated based on the simulated concentrations of related species, except for PH2O2/PHNO3, which were obtained using the integrated reaction rate (IRR) of the CMAQ process analysis tool (Gipson and Young, 1999). The percentile distribution of the indicator values for the VOC-limited grid cells and the NOx-limited grid cells were examined individually. The photochemical indicators typically showed higher values at NOx-limited grid cells than in VOC-limited locations. Finally, the thresholds of a certain indicator were determined using the 95th-percentile value of the indicator for the VOC-limited grid cells and the 5th-percentile value for the NOx-limited grid cells as the lower and upper limits of the transition intervals, respectively. Indicator values lower than the transition intervals suggested O3 formation was VOC-limited, while higher values than the transition intervals were associated with NOx-limited regimes. In some cases, the 95th-percentile VOC-limited value was higher than the 5th-percentile NOx-limited value, indicating the indicator was invalid and could not be used to determine the O3 sensitivity properly.

In Sect. 2.3, the O3 formation regimes were presumably identified according to changes in O3 with the emission reductions, while the rules could be different in detail. For example, Liang et al. (2006) examined changes in the 8 h O3 with a 25 % reduction in VOC or NOx emissions instead of the 1 h O3 with 35 % reductions as in Sillman (1995). Accordingly, the criteria changed from 5 to 2.5 ppb. Zhang et al. (2020) explored the correlation of indicator values with the relative O3 changes resulting from a 50 % reduction in the NOx or VOC emissions. Du et al. (2022) applied the decoupled direct method (DDM) to investigate the sensitivity of O3 to precursors, instead of perturbing emissions. The impacts on the derived thresholds of the indicators were explored by conducting a few individual tests:

The criteria for the O3 reduction (see Table 1) were set at 2, 3, and 6 ppb.

The changes in the O3 concentrations when reducing VOC or NOx emissions were used to determine the O3 formation regimes. Figure 2a shows that high O3 concentrations (averaged from 13:00 to 16:00 LT during 22–31 July) primarily occurred along the Yangtze River and southern Jiangsu, and O3 in northern Jiangsu was relatively low. The NOx emission reduction predominantly led to O3 decreases in Jiangsu, while only a few locations, such as near the estuary of the Yangtze River, showed an increased O3 relative to the base case (Fig. 2b). The VOC emission reductions resulted in less significant O3 decreases compared to the NOx reduction scenario (Fig. 2c). The O3 sensitivity regime for each grid cell in Jiangsu was identified with the method described in Sect. 2.3 (Fig. 2d). The O3 formation in central and southern Jiangsu, where O3 is abundant, is typically NOx-limited as a result of a relatively low NOx concentration in the afternoon (Duncan et al., 2010; Jin et al., 2017; Jin and Holloway, 2015). Some areas along (and on) the Yangtze River were characterized to be VOC-limited regimes, with substantial emissions of NOx from ship emissions and industry (Sheng et al., 2022). However, not all grid cells in Jiangsu were assigned to the VOC- or NOx-limited regimes. The white areas in Jiangsu in Fig. 2d indicate that O3 was insensitive to both NOx and VOCs (i.e., ΔO3VOC<5 and ΔO3NOx<5 ppb); alternatively, O3 was sensitive to NOx (VOC) emissions but showed small changes in O3 with the perturbation of NOx (VOC) relative to the VOC (NOx) reduction scenario (i.e., |ΔO3VOC-ΔO3NOx|<5 ppb).

The O3 reductions (ΔO3NOx or ΔO3VOC) against photochemical indicator values at all grid cells over the domain were examined (Fig. 3). The mean values of the ΔO3NOx slightly increased with higher PH2O2/PHNO3, while the ΔO3VOC values showed a decreasing trend, indicating that a reduction in NOx (VOC) emissions became more (less) effective for O3 abatement in the locations with higher indicator values. Other indicators displayed a similar pattern except for NOy, which displayed an opposite result. Due to the contrasting dependence of the ΔO3NOx and the ΔO3VOC on the indicator values, the thresholds of the photochemical indicators that separate the O3 formation regimes were determined (Table 3 and vertical lines in Fig. 3). The localized thresholds for PH2O2/PHNO3 [0.55, 0.75] were remarkably higher than that implemented in the model, i.e., 0.35, which would lead to misattribution of the VOC-limited or the transitional regime to the NOx-limited regime in some locations if the single value was directly used. The thresholds differed from those proposed by researchers in other countries, and some regions in China had significantly distinct thresholds as well (Du et al., 2022; Zhang et al., 2020; Tonnesen and Dennis, 2000a; Liu et al., 2010a).

This work revisited other photochemical indicators including the surface HCHO/NO2, HCHO/NOy, and NOy. The transition interval of HCHO/NO2 was determined as [0.81, 1.35], showing a higher and wider range than in other work (Jin et al., 2017; Liu et al., 2021; Du et al., 2022) but relative consistency with Tonnesen and Dennis (2000b). It is worth noting that the values mentioned above are all based on measurements or simulations at the ground level, while column HCHO/NO2 retrieved from satellite measurements are more widely used, with thresholds of [1, 2] (Jin and Holloway, 2015; Jin et al., 2017; Duncan et al., 2010; Wang et al., 2021). The transition range for the column HCHO/NO2 is typically broader than that for the surface ratio, e.g., the former of [1.17, 2.42] versus the latter of [0.36, 0.45] in East China (Du et al., 2022). The thresholds of HCHO/NOy and NOy in this study were [0.38, 0.60] and [8.18, 17.63], respectively, comparable to the values proposed previously. The comparison shown in Table 3 suggests that the thresholds were mostly location-specific, possibly as they are dependent on atmospheric conditions and emission features. However, the methodology that is used to derive thresholds can also lead to distinct threshold values, and this is discussed in Sect. 3.4.

The spatial distributions of the O3 formation regimes identified by the photochemical indicators with localized thresholds are exhibited in Fig. 4. Most of the areas in Jiangsu (>80% of the grid cells covering Jiangsu, Table S2) were attributed to NOx-limited regimes in terms of the summertime O3 formation in the afternoon using all indicators. A few urban centers and some locations near the Yangtze River were identified as VOC-limited or transitional regimes where the four indicators largely showed differences. The O3 formations in these areas were primarily VOC-limited according to PH2O2/PHNO3 and showed a transition from VOC-limited to NOx-limited at the surrounding grid cells. However, other indicators tended to assign the areas along and to the south of the river to transitional regimes. The fraction of the VOC-limited regimes in the area in Jiangsu with PH2O2/PHNO3 (∼13%) was considerably higher than that using HCHO/NO2 and HCHO/NOy (4 %–5 %). NOy, which is the least impacted by VOC emissions, attributed the fewest areas to the VOC-limited regimes (∼2%) concerning O3 formation. Accordingly, transitional regimes were the lowest using PH2O2/PHNO3, ∼5% compared to 13 %–15 % using HCHO/NO2, HCHO/NOy, and NOy.

Table 4 shows the accuracy of the photochemical indicators in splitting the O3 formation regimes with thresholds derived in this study. As expected, the ErrB and OA for the application in Jiangsu in 2017 (see the case Sim_2017+Jiangsu in Table 4) were approximately 5 % and 95 %, respectively, as a result of the nature of the method (see Sect. 2.3). The values of ErrA were lower than ErrB, suggesting that chemical regimes determined by the indicator values were largely consistent with that based on O3 changes when perturbing emissions. However, it is more likely that sensitivities indicated by O3 changes do not necessarily correspond to indicator values in the correct intervals. Additionally, the ErrA_VOC and ErrA_NOx for PH2O2/PHNO3 were higher than that of the other indicators, likely due to less area associated with mixed O3 sensitivity using PH2O2/PHNO3 (see Table S2), which could increase the chance of misclassification.

The above evaluation also showed that emissions could have a minor effect on the performance of the indicators on a regional scale. The thresholds derived from the simulation in Jiangsu well identified O3 sensitivities in other regions of the YRD (see the case Sim_2017+Other), where emissions were different (e.g., abundant biogenic VOCs in the southern YRD vs. dominance of anthropogenic emissions in Jiangsu) and with OAs greater than 98 % for all the indicators. This suggests that it is plausible to specify region-wide thresholds for photochemical indicators. In addition, the indicators can generally separate O3 formation regimes in Jiangsu for the same period in 2018 (see the case Sim_2018+Jiangsu) when the meteorology could differ from that in 2017. However, HCHO/NOy and HCHO/NO2 appeared to be more easily affected by meteorology, as indicated by the ErrB_NOx that showed that many NOx-limited grids had indicator values lower than the upper thresholds. The OAs were relatively high in the case when both the emissions and meteorology changed (see the case Sim_2018+Other), although the ErrB_VOC was remarkably higher. This was due to fewer VOC-limited grids in the YRD, half of which had indicator values within the transition intervals and thus were misclassified as the transitional regime. The evaluation showed that indicators could perform better in detecting O3 formation regimes that were predominant. However, the drawback of the evaluation is that it does not account for grids that are neither VOC-limited nor NOx-limited in terms of the O3 formation based on the ΔO3NOx or the ΔO3VOC (i.e., the white area in Jiangsu in Fig. 2d), and the uncertainties of the photochemical indicators in these areas are unknown.

O3 formation regimes identified by the indicator values with varied combinations of VOC and NOx emissions were plotted together with the O3 isopleths to examine the indicators for implications in effective emission control strategies. Figures 5 and S3–S4 show the comparison at the CCM, ZHM, and LS sites, respectively. As no significant variations were found at the three sites, only the plot for CCM is shown in the main text. The PH2O2/PHNO3 value with the base emission points to a VOC-limited regime at the CCM site, whereas the isopleths suggest that a reduction in the NOx emissions should lead to reduced O3. This also happens in some cases with lower VOC and NOx emissions, indicating that PH2O2/PHNO3 is likely to underestimate the positive sensitivity of O3 to NOx. The indicators were assumed to have constant thresholds that do not change with emissions; this could partially explain the inconsistency of the indicators with the O3 isopleths. The PH2O2/PHNO3 values at the LS and ZHM sites showed similar results, except that the O3 formation at the LS site shifted from VOC-limited to a transitional regime earlier with decreasing NOx emissions than at the other two sites as indicated by the ratio.

It appears that HCHO/NOy was the most consistent with the O3 isopleths among the four indicators, followed by HCHO/NO2. Both HCHO/NOy and HCHO/NO2 suggest that all three sites resided in transitional regimes under the base emission scenario, except for CCM using HCHO/NO2, which showed that O3 would respond to NOx changes negatively. However, HCHO/NOy and HCHO/NO2 had more emission scenarios assigned to transitional regimes compared with PH2O2/PHNO3, which was in agreement with the spatial distributions shown in Fig. 4. This implies that the two indicators emphasize controlling both VOC and NOx rather than a single pollutant. However, the HCHO levels could be affected by primary emissions (Liu et al., 2021) or be highly variable due to the dependence of isoprene on temperature (isoprene dominating HCHO production with intensive biogenic emissions) (Duncan et al., 2010). Therefore, the link between the HCHO/NOy (or HCHO/NO2) values and the O3–VOC–NOx sensitivity and resulting emission control strategies of anthropogenic precursors (that are controllable) is more uncertain under certain conditions.

The O3 formation at the CCM site was dominated by NOx-limited regimes based on NOy, which was predominantly affected by NOx emissions, and did not show a sole sensitivity to VOCs (Fig. 5d). This was different from other indicators as well as the O3 isopleths in terms of policy implications. The comparison between the O3–VOC–NOx sensitivity revealed by NOy and the O3 isopleths showed that the indicator tended to overestimate the response of O3 to NOx (i.e., the VOC-limited regimes were misclassified as transitional regimes in the upper left corner of Fig. 5d) or underestimate the O3–VOC sensitivity (i.e., the transitional regimes were misclassified as NOx-limited regimes in the middle left portion of Fig. 5d).

Apart from local emissions and meteorology that could partially explain the gap between the indicator thresholds proposed earlier and in this work, we found that the methodology to derive the thresholds could be slightly different and the impacts are unknown. Therefore, a series of tests were conducted to examine how those details in the methodology alter the thresholds of PH2O2/PHNO3 (Fig. 6) and other indicators (Figs. S6–S8).

First, the VOC-limited (NOx-limited) grid cells were defined as the locations where the reduction in O3 as a response to the VOC (NOx) reduction exceeded the O3 reduction associated with the reduced NOx (VOC) by more than 2, 3, and 6 ppb instead of the original 5 ppb (see Table 1). The threshold intervals are wider with higher criteria, e.g., the range of [0.3, 0.8] with sensitivity differences of >6 ppb versus [0.55, 0.75] with >5 ppb, leading to fewer VOC- or NOx-limited grid cells based on the indicator and more transitional grid cells with less chance of misclassification (Fig. 6a). However, the sensitivity differences of 2–3 ppb are too small to differentiate sensitivity types of the grid cells using the indicators, as the 95th percentile of the indicator values at the VOC-limited grids is higher than the 5th percentile of the values at the NOx-limited grids when determining the thresholds (see Sect. 2.3). Hence, the indicators are invalid. Similarly, if the relative changes in O3 were applied to quantify the O3–VOC–NOx sensitivity, such as using the differences of 2 %, 5 %, or 8 % as the criteria, the derived thresholds would be considerably different as well (Fig. 6b). The relative changes make more sense since O3 changes of ∼5 ppb due to a certain amount of VOC or NOx reduction are less likely to take place in locations with low O3 than in relatively polluted regions. As a result, the grid cells with low O3 are seemingly insensitive to precursors and were excluded from the VOC- or NOx-limited grids that were used to derive the thresholds. This can particularly affect the lower limits of the thresholds with much fewer VOC-limited grids, as in this study, and vice versa.

In Fig. 6c, the VOC and NOx emissions were individually reduced by 20 % or 40 % instead of 35 % but with a constant criterion of >5 ppb for the sensitivity differences. The lower reduction in emissions resulted in wider threshold intervals [0.18, 1.12] with a 20 % reduction versus [0.55, 0.75] with a 35 % reduction and [0.55, 0.60] with a 40 % reduction. This was similar to the case with higher criteria (Fig. 6a). In addition, if the VOC- or NOx-limited grids were defined based on the S1 VOCs and S1 NOx in the HDDM (see Table 1 and DDM1 in Fig. 6d), the indicator values for the VOC-limited grids and the NOx-limited grids would overlap to a large extent, with the 95th percentile of the indicator values at the VOC-limited grids of 1.0, and the 5th percentile of the values at the NOx-limited grids of 0.37. Therefore, the indicator could not be used. S1 VOCs and S1 NOx approximate the O3 changes with a 100 % reduction in the VOC and NOx emissions, respectively, without considering the nonlinearity (i.e., higher-order sensitivities) in O3 chemistry. This finding is consistent with Fig. 6c, which shows a quite narrow range of threshold intervals with more reduction in the precursor emissions. Additionally, the upper and lower thresholds derived with the DDM2 approach were 0.50 and 0.11, lower than 0.75 and 0.55, respectively. This was due to the lower O3 changes estimated with the second-order Taylor expansions than with the perturbed simulations (Fig. S5), similar to the case with a 20 % reduction in the VOC or NOx emissions and possibly reflecting the importance of higher-order terms in the HDDM as well. The results of HCHO/NO2, HCHO/NOy, and NOy (Figs. S6–S8) were similar. They all indicated that the thresholds of the photochemical indicators are dependent on the methods or parameters in the methodology. This could be one of the major uncertainties in the application of indicators to determine O3 chemical regimes.