Detecting causal relationships between fine particles and ozone based on observations in four typical cities of China

As the concentration of fine particles (PM2.5) is declining, ozone (O3) concentration has been increasing in China in recent years. To collaboratively control PM2.5 and O3, it is critical to understand the relationship between the two and identify major controlling factors. We use a convergent cross-mapping method to detect the causal relationship between daily PM2.5 and maximum daily 8 h average (MDA8) O3 concentrations in Beijing, Taizhou, Shenzhen and Chengdu, China, in the four seasons in 2015–2021. In addition, we also examined causal effects of atmospheric oxidation capacity, precursors and meteorological elements on PM2.5 and MDA8 O3 in the four cities. PM2.5 and MDA8 O3 are strongly positively correlated and show bidirectional causal relationships during the Beijing and Taizhou summer and in the four seasons in Shenzhen, due mainly to the strong photochemical reactions in the daytime. During the Beijing winter, PM2.5 and MDA8 O3 show bidirectional causal relationships, but the two are significantly negatively correlated, driven by NO2 and relative humidity. Weak bidirectional, unidirectional and no causal effects between PM2.5 and MDA8 O3 are detected in other seasons in the four cities. In these seasons and cities, the top three causal factors of PM2.5 differ from those of MDA8 O3. Season-, city- and pollutant-specific control measures of PM2.5 and MDA8 O3 are required.


Introduction
With high concentrations and numerous human health effects, surface fine particle (PM 2.5 ) and ozone (O 3 ) are two typical air pollutants in China (Yang et al 2023).In 2022, PM 2.5 and O 3 concentrations in one third of the 376 cities (with in situ measurements) in China still exceeded the national ambient standards (annual mean PM 2.5 : 35 µg m −3 ; 90 percentile maximum daily 8 h average (MDA8) O 3 : 160 µg m −3 ).Collaborative control of PM 2.5 and O 3 is required, particularly in the following key regions: North China Plain (NCP), Yangtze River Delta (YRD), Pearl River Delta (PRD), Chuan Yu region (CY) (Liu et al 2021, Dong et al 2023, Qi et al 2023).Thus, it is critical to study the relationship between PM 2.5 and O 3 and identify their controlling factors.However, several mechanisms affect the two pollutants in different directions and with different magnitudes, making their relationship complex.
First, PM 2.5 directly affects O 3 formation through heterogeneous reactions.A heterogeneous process that has been widely discussed is hydroperoxyl (HO 2 ) radical uptake by aerosols, which terminates the radical chain and suppresses O 3 production.Contradictory conclusions on the importance of this process in controlling O 3 concentration have been derived in recent publications.Some studies suggest that this was the controlling process for O 3 increase in 2013-2017 in NCP (Li et al 2019, Ivatt et al 2022), while others suggest marginal influence (Song et al 2021).In contrast to the suppression effect of HO 2 uptake, heterogeneous uptake of NO 2 enhances O 3 formation by converting NO 2 to nitrous acid (HONO) (Tan et al 2022), which is a large source of HOx (OH + HO 2 ) radicals in the daytime (Zhang et al 2022).Tan et al (2022) showed that heterogeneous uptake of HO 2 and NO 2 changes the MDA8 O 3 concentration by −4% and 42%, respectively, in October in Shenzhen.
Second, aerosol-radiation feedback affects O 3 formation by changing actinic fluxes and atmospheric dynamics.PM 2.5 attenuates solar radiation and thus suppresses the photochemical reactions that form O 3 .According to Wang et al (2019a), light extinction of aerosols reduces the photolysis frequency of NO 2 and O 1 D by 24% (30%) and 27% (33%) during the summer (winter) compared to aerosol-free atmosphere and thus reduces net O 3 production by up to 25% in Beijing.In Shenzhen, light extinction by PM 2.5 reduces O 3 by 45% in October (Tan et al 2022).Changes in atmospheric dynamics due to aerosol-radiation feedback increase O 3 during the summer but decrease O 3 during the winter (Xing et al 2017).Zhu et al (2020) showed opposite effects, where O 3 is enhanced during COVID-19 lockdown due to the aerosol-radiation feedback induced by physical advection and vertical mixing processes.
Third, nitrogen oxides (NO x ) and volatile organic compounds (VOCs) are common precursors of PM 2.5 and O 3 .With the strong reduction of sulfur dioxide in China, the contribution of nitrate is increasing and becoming the major inorganic aerosols in most of China (Xu et al 2019, Qi et al 2022).Secondary organic aerosols formed largely from oxidation of VOCs are also critical components of PM 2.5 in China (Chang et al 2022).Both the responses of PM 2.5 and O 3 to precursor emissions are non-linear and vary with space and time (Seinfeld and Pandis 2016), making the relationship more complex.
Finally, O 3 is an important component of atmospheric oxidation capacity (AOC: OH, O 3 , NO 3 ), which enhances the secondary formation of PM 2.5 (Huang et al 2021a).In the daytime, OH is the major component of AOC (>90%), while in the nighttime O 3 (20%-35%) and NO 3 radical (15%-60%) dominates (Dai et al 2023, Wang et al 2023).OH mainly comes from photolysis of O 3 in the daytime, and NO 3 is formed by O 3 and NO 2 at night.Wang et al (2022) showed that AOC is a better indicator of photochemical reactions that form secondary aerosols and O 3 than O 3 isopleth diagram and sensitivity methods in NCP, YRD and PRD in China.During the nighttime, O 3 oxidizes NO 2 and produces NO 3 , which further reacts with NO 2 and produces N 2 O 5 .Hydrolysis of N 2 O 5 produces nitrate.Recent studies have shown the increased importance of nighttime oxidation in major Chinese cities (Wang et al 2023, Yan et al 2023).PM 2.5 reduction due mainly to strong primary emission reduction during COVID-19 was compensated by the enhanced secondary formation, proving that AOC is critical to the formation of secondary aerosols in most regions of China (Huang et al 2021a, 2021b, Qin et al 2022, Tang et al 2022).Reducing AOC is regarded as a promising method to mitigate pollution in China.
Model simulations are usually used to study the relationship between PM 2.5 and O 3 and quantify the contributions from different processes.In 2013-2017 the decline in NO 2 and lack of VOC control were responsible for the O 3 increase, while in 2018-2020 the potential decline of O 3 due to synergistic control of VOCs and NO x was offset by the increase in O 3 resulting from the reduction of PM 2.5 (Liu et al 2023).Ma et al (2021) showed that precursor emission reductions (45%) and radiative forcing changes due to PM 2.5 reduction (23%) were the major factors for the fast increase of O 3 in 2013-2019 based on chemical transport model experiments.Tan et al (2022) showed that the enhancement of O 3 by NO 2 uptake is counteracted by the suppression of O 3 by aerosolradiation feedback in Shenzhen.
Very little evidence is provided based on observations, except for correlation analysis (Chu et al 2020, Shao et al 2021).However, correlation analysis does not provide causality information.Sugihara et al (2012) introduced a convergent cross-mapping (CCM) method to detect causality in complex nonlinear ecosystems.The method successfully detected the causality relationship between sardine, anchovy and sea surface temperature (Sugihara et al 2012).This method has been used in many different scenarios to detect causal relationships, including in the atmospheric sciences.Xing et al (2021) detected the causal relationship between economic activity reduction inferred from NO 2 and the COVID-19 case deceleration.Li et al (2021b) identified O 3 formation regime based on satellite observations of formaldehyde (HCHO) and NO 2 using the CCM.The CCM was also used to quantify the causal influence of meteorological elements on PM 2.5 and O 3 concentrations (Chen et al 2017(Chen et al , 2019(Chen et al , 2020b)).
In this study, we use the CCM method to detect the causal relationships between observed daily PM 2.5 and MDA8 O 3 in Beijing, Chengdu, Taizhou and Shenzhen in the four seasons.We also investigate the causal effects of their common precursors; surface NO 2 (in situ measurements), column HCHO (satellite observations, as a proxy for VOCs), meteorological elements (in situ measurements) and O x (O 3 + NO 2 , as a proxy for AOCs) on surface PM 2.5 and MDA8 O 3 in the four cities in 2015-2021 to identify major controlling factors of the two pollutants in different cities and seasons.

Data sources 2.1.1. In situ PM 2.5 , O 3 and NO 2 measurements
We collected hourly PM 2.5 , O 3 and NO 2 data (µg m −3 ) at in situ measurement sites from the China National Environmental Monitoring Center

Satellite observations of HCHO
We use HCHO column density data from the ozone monitoring instrument (OMI) on board the Aura satellite.We use daily level-3 grided OMI HCHO product (OMHCHOd) with horizontal resolution of 0.1 • latitude × 0.1 • longitude.The value given in any grid cell is an area-weighted average of the values of the corresponding field (molec cm −2 ).The error in HCHO column density was effectively controlled within 30% (González Abad et al 2015).The products of HCHO are available from the Goddard Earth Sciences Data and Information Services Center (https://disc.gsfc.nasa.gov/,last access: 24 June 2023).

In-situ meteorological measurements
We use in situ meteorological measurements in the four cities from the National Climatic Data Center of the National Oceanic and Atmospheric Administration (http://ftp.ncdc.noaa.gov/pub/data/noaa/isd-lite).Temperature (T), dew point, wind direction (WD) and wind speed (WS) are hourly, and sea level pressure (SLP) and precipitation (Prep) data are 3 and 6 hourly, respectively.Based on these observations, we estimated maximum, minimum and mean daily T (maxT, minT and meanT), daily mean relative humidity (RH, estimated according to T and dew point), most frequent WD and daily mean WS, SLP and daily accumulated Prep to investigate the causal effects of meteorology on PM 2.5 and O 3 .

CCM method
The relationship between PM 2.5 and O 3 , and factors that might affect the relationship, such as common precursors, O x and meteorology, are shown in figure 1.We use the CCM (Sugihara et al 2012) to detect causal relationships between daily PM 2.5 and MDA8 O 3 in Beijing, Chengdu, Taizhou and Shenzhen in the four seasons in 2015-2021.To test the robustness of the causal relationship over time, we also detected the causal relationships in 2015-2017 and 2018-2021.We also compared the causal effects of MDA8 O 3 and nighttime O 3 on daily PM 2.5 .In addition, we detected the causal relationship between precursors NO 2 (surface in situ observations) and VOCs (using HCHO column density from OMI as a proxy), AOC (using O x = O 3 + NO 2 as a proxy), and meteorological elements (in situ measurements of meteorological elements) in the daily mean PM 2.5 and MDA8 and nighttime O 3 .The inter-annual variations of seasonal mean PM 2.5 , MDA8 O 3 , NO 2 and column density of HCHO can be seen in section S1, table S1 and figure S2.Details of the main idea of the CCM can be found in previous publications (Sugihara et al 2012, Li et al 2021b).
The CCM calculates cross-map skill (ρ value), which explains the quantitative causal relationships.A convergent ρ curve (x xmap y) indicates that one variable (y) imposes causal influence on the other variable (x), whilst a non-convergent curve denotes no causality between two variables.Larger ρ value indicates larger causal effect.We also use a timedelayed CCM to distinguish between bidirectional causality and synchrony led by strong unidirectional causality (Ye et al 2015).A negative lag for crossmapping indicates a true causal direction, while a positive lag means no causal effect in this direction (Ye et al 2015).In addition, the lag time also informs the time delays in causal effects.Since the existence of missing values imposes a impact on the CCM results, only the consecutive time series was retained for this research.The CCM was implemented using the 'rEDM' package in R.

Bidirectional causal relationships between PM 2.5 and O 3 3.1.1. Strong bidirectional causal effects with positive Pearson correlations
Strong bidirectional causal relationships between PM 2.5 and MDA8 O 3 and positive Pearson correlations (r = 0.48-0.79,table S2) were detected during the Beijing and Taizhou summer and in the four seasons in Shenzhen in 2015-2021 (figures 2 and S3).This pattern is consistent in 2015-2017 and 2018-2021, except during the Shenzhen winter, when and where MDA8 O 3 shows no causal effect on PM 2.5 in the latter period (figures S4 and S5).The bidirectional causal effects are mainly driven by strong photochemical reactions in the daytime based on the following reasons.First, the magnitude of causal effects of MDA8 O 3 on PM 2.5 is equal to that in the reverse (figure 2).Second, O x is the major driving force of PM 2.5 , exceeding the causal effects of precursors and meteorological elements (figures 3 and S8).Third, the causal effect of MDA8 O 3 on PM 2.5 is larger than that of nighttime O 3 (figure S9).Fourth, the causal effects of PM 2.5 on MDA8 O 3 are of similar magnitude or larger than those of precursors and meteorological elements (figures 4 and S10).
Previous studies have also found strong influence of AOC on the co-variance of PM 2.5 and O 3 during the Beijing and Taizhou summer.Wei et al (2021) showed that PM 2.5 pollution was boosted by high OH and O 3 during the Beijing summer, and PM 2.5 was more sensitive to OH and O 3 during the summer than during the winter.Chemical transport model simulation showed that AOC was the driving force of the co-variance of PM 2.5 and O 3 in July in YRD (where Taizhou locates) because the coefficients of determination between PM 2.5 and O 3 were larger at higher AOC levels (r 2 = 0.6 and 0.7 with AOC above 50th and 75th percentiles) than at lower AOC levels (r 2 = 0.01 and 0.4 with AOD below 25th and 50th percentiles), and PM 2.5 was independent of O 3 at low AOC level (Qin et al 2022).
Shenzhen is located in the south of China (22.3 • N) and receives a large solar radiation flux throughout the whole year (Beijing: 93 W m −2 versus Shenzhen: 135 W m −2 ) and stays warm even during the winter (Beijing: −0.6 • C versus Shenzhen: 18 • C).Secondary aerosols, driven mainly by the AOC, account for ∼80% of PM 2.5 in Shenzhen (Huang et al 2018, Tang et al 2022).During the resurgence of COVID-19 in March 2022 in Shenzhen, reducing daytime O x was more effective in reducing secondary organic aerosols than reducing precursor emissions (Tang et al 2023).In the fall, PM 2.5 promoted MDA8 O 3 formation by scattering light, and thus influencing the photolysis frequency of NO 2 and O 1 D (Lin et al 2023).During the winter, Tang et al (2022) showed that the decline in both PM 2.5 and O 3 during COVID-19 lockdown was directly driven by the decline in O x , rather than the large precursor emission reductions in Shenzhen.

Bidirectional causal effects with negative Pearson correlation
During the Beijing winter, we find significant negative correlation (r = −0.38,table S2) and bidirectional causal relationship between PM 2.5 and MDA8 O 3 (figures 2 and S3).This bidirectional effect is lower in 2018-2021 than in 2015-2017 (figures S4 and S5).In contrast, MDA8 O 3 is 16% larger in 2018-2021 than in 2015-2017.NO 2 and RH are the top two causal factors of PM 2.5 and MDA8 O 3 (figures 3 and 4) and their causal effects are also lower in 2018-2021 than in 2015-2017 (figures S4-S7).The above comparisons indicate that the bidirectional causal effect of PM 2.5 and MDA8 O 3 during the Beijing winter is mainly driven by NO x , followed by RH.
NO 2 is strongly positively related to PM 2.5 (r = 0.82) but negatively related to MDA8 O 3 (r = −0.73)and the causal effects of NO 2 on PM 2.5 and MDA8 O 3 exceed the causal effects of other factors (figures 3 and 4), indicating that NO x is the driving force of the bidirectional causal relationship betwen PM 2.5 and MDA8 O 3 .Xu et al (2019) showed that the mass fraction of nitrate increases from 13% to 25% before 2013 to 20% to 40% after 2017 in Beijing, and nitrate concentration is largely controlled by NO 2 during the winter (Qi et al 2022).In addition, O 3 formation is in the VOC-limited regime during the NCP winter (Li et al 2021a).The strong reduction in NO x emissions drives the decrease in PM 2.5 and increase in O 3 in NCP during COVID-19 lockdown (Zhu et al 2020).
RH, the second largest causal factor of PM 2.5 and MDA8 O 3 during the Beijing winter (figures 3 and 4), is strongly positively related to PM 2.5 (r = 0.72), but  negatively related to MDA8 O 3 (r = −0.80).Higher humidity enhances the hygroscopic growth, secondary formation of PM 2.5 and promotes gas-to-particle partitioning, thus increasing the mass concentration of PM 2.5 (Chen et al 2020a).The adverse effect of RH on O 3 formation is mainly due to the enhanced heterogeneous uptake of peroxyl radicals and O 3 at higher RH (Nguyen et al 2022).

Weak bidirectional causal effects
Weak bidirectional causal effects between PM 2.5 and MDA8 O 3 are detected during the Beijing spring, Chengdu summer, and Chengdu and Taizhou fall (figures 2 and S3).In these seasons and cities, the top three causal factors of PM 2.5 differ from those of MDA8 O 3 (figures 3 and 4).
During the Beijing spring, the weak bidirectional causal effect is consistent in 2015-2017 and 2018-2021 (figures S4 and S5).The causal effects of RH on PM 2.5 and MDA8 O 3 are larger than the causal effects between the two (figures 3 and 4), and RH shows moderate correlation with PM 2.5 (r = 0.41) and MDA8 O 3 (r = 0.30).In addition, the causal effect of PM 2.5 on MDA8 O 3 is smaller at a lower PM 2.5 level in 2018-2021 than in 2015-2017 (figure S4).As such, the weak bidirectional causal effects are partly due to the transitional causal effect of RH and partly due to the direct causal effects between PM 2.5 and O 3 .
During the Chengdu summer, NO 2 drives PM 2.5 variations and is the third largest causal factor for MDA8 O 3 (figures 3 and 4).Moreover, NO 2 is positively related to both PM 2.5 (r = 0.73) and MDA8 O 3 (r = 0.35).In the Chengdu fall, maxT is the third largest causal factor of PM 2.5 and is the major driving force of MDA8 O 3 (figures 3 and 4).The causal effect of PM 2.5 on MDA8 O 3 is larger with a lower PM 2.5 level in 2018-2021 than in 2015-2017 during the Chengdu summer and fall (figures S4 and S5).These comparisons suggest that the bidirectional causal effects between PM 2.5 and MDA8 O 3 are mainly attributed to the transitional causal effect of NO 2 during the Chengdu summer and maxT in the fall.
In the Taizhou fall, no common driving forces are found for PM 2.5 and MDA8 O 3 (figures 3 and 4).The causal effect of PM 2.5 on MDA8 O 3 is smaller in 2018-2021 with a lower PM 2.5 level than in 2015-2017, but the causal effect in the reverse is larger in 2018-2021 (figures S4 and S5).This indicates that the weak bidirectional causal effect is mainly attributed to the direct causal effects between PM 2.5 and MDA8 O 3 .

Unidirectional causality 3.2.1. Unidirectional causal effect of PM 2.5 on MDA8 O 3
The causal effect of PM 2.5 on MDA8 O 3 is detected in the Beijing fall, but the causal effect in reverse is not detected (figures 2 and S3).In addition, PM 2.5 and MDA8 O 3 are uncorrelated (table S2).A similar comparison is also found in 2015-2017 and in 2018-2021 (figures S4 and S5).In addition, the causal effect of PM 2.5 on MDA8 O 3 is smaller at a lower PM 2.5 level in 2018-2021 than in 2015-2017 (figure S5), indicating that the causal effect of PM 2.5 on MDA8 O 3 is mainly due to the direct effect.This is in agreement with previous estimates.An observation-based model of Jia et al (2023) showed that heterogeneous uptake of HO 2 by PM 2.5 leads to a 15% and 41% decrease in the O 3 production rate during O 3 and PM 2.5 episodes, respectively, in rural Beijing during the fall of 2019.
The largest causal factor for PM 2.5 variations in the fall is NO 2 , followed by RH (figure 3).The two factors are strongly positively related to PM 2.5 (r = 0.81 and 0.56).In contrast, MDA8 O 3 variation is mainly controlled by maxT, and this causal effect is larger in the fall than in the other seasons (figure 4).NO 2 and RH show similar magnitudes of causal effects on O 3 variations (figure 4), but the former is weakly negatively correlated with O 3 (r = −0.25),while the latter is positively correlated with O 3 (r = 0.13).The opposite influencing direction of NO 2 and RH on O 3 results in limited transitional causal effects from the two common factors.
Neither MDA8 O 3 nor nighttime O 3 show any causal effect on PM 2.5 in the Beijing fall.This is consistent with previous estimates.Wang et al (2019b) showed that O 3 is the major oxidation pathway of nitrate in PM 2.5 in the Beijing fall, and the contribution of O 3 oxidation pathway increases with increasing NO 2 concentration but does not change with O 3 concentration.

Unidirectional causal effect of MDA8 O 3 on PM 2.5
During the Chengdu and Taizhou spring, a unidirectional causal effect of MDA8 O 3 on PM 2.5 is detected, but the reverse effect is not, and this comparison pattern is consistent in 2015-2017 and 2018-2021 (figures 2 and S3).In addition, this causal effect is larger than that of nighttime O 3 , and the effect increases overtime (larger in 2018-2021 than in 2015-2017), indicating that the importance of daytime photochemical reactions is increasing (figures S4 and S5).In addition, no common causal factors are found for PM 2.5 and O 3 in Chengdu (figures 3 and 4).Thus, there are no transitional causal effects from other factors.During the Taizhou spring, maxT is the third largest causal factor of PM 2.5 and the largest causal factor of MDA8 O 3 (figures 3 and 4).However, the lag times of the two causal effects differ, and thus the transitional effects of maxT on PM 2.5 and MDA8 O 3 is small (figures S8 and S10).

No causal relationships between PM 2.5 and O 3
No causal relationships between PM 2.5 and MDA8 O 3 are detected during the Chengdu and Taizhou winter (figures 2 and S3).The comparison is consistent in 2015-2017 and 2018-2021 during the Chengdu winter, but in Taizhou PM 2.5 shows a causal effect on MDA8 O 3 in 2018-2021, due mainly to the transitional causal effect from NO 2 (figures S4-S7).Moreover, nighttime O 3 shows a causal effect on PM 2.5 during the Taizhou winter (figure S9), emphasizing the importance of nighttime oxidation to PM 2.5 accumulation.
During the Chengdu winter, PM 2.5 is mainly controlled by NO 2 and O x (figure 3), while MDA8 O 3 is controlled by maxT and RH (figure 4), meaning that no common causal factors are found for PM 2.5 and MDA8 O 3, and thus there are limited transitional causal effects.In addition, the causal effects of NO 2 on PM 2.5 and MDA8 O 3 show opposite trends over time; a decrease for the former but an increase for the latter (figures S4 and S5), emphasizing the important role of NO x reduction in collaborative control of PM 2.5 and MDA8 O 3 during the Chengdu winter.During the Taizhou winter, no major causal factor of MDA8 O 3 is found in this study, which calls for further indepth analysis.

Conclusion and policy implications
To collaboratively control PM 2.5 and O 3 in China, it is critical to understand the relationship between the two and identify their major controlling factors.We used the CCM method to detect the causal relationships between daily PM 2.5 and MDA8 O 3 concentrations in Beijing, Chengdu, Taizhou and Shenzhen in China in 2015-2021 in the four seasons.We also detected causal effects of O x , surface NO 2 and column density of HCHO and meteorological elements on PM 2.5 and O 3 in the four cities.
Strong bidirectional causal effects between PM 2.5 and MDA8 O 3 and positive correlations are detected during the Beijing and Taizhou summer and in the four seasons of Shenzhen.Daytime photochemical reactions are the driving force for co-variance of PM 2.5 and MDA8 O 3 .Thus, controlling O x is effective in controlling PM 2.5 and MDA8 O 3 simultaneously during the Beijing and Taizhou summer and in the four seasons in Shenzhen.
During the Beijing winter, PM 2.5 and MDA8 O 3 showed bidirectional causal relationship and negative Pearson correlation.NO 2 was positively related to PM 2.5 but negatively related to O 3 , and the causal effects of NO 2 on PM 2.5 and O 3 exceeds the effects from other factors, indicating that NO 2 is the driving force for PM 2.5 and O 3 in Beijing.Thus, reducing NOx emissions would reduce PM 2.5 but increase O 3 , requiring proper reduction of VOC emissions to control O 3 simultaneously.
Weak bidirectional causal effects between PM 2.5 and MDA8 O 3 were detected during the Beijing spring, Chengdu summer and Taizhou fall.During the Beijing spring, the weak bidirectional causal relationship was attributed to both the direct effects between the two and the transitional causal effects from RH.During the Chengdu summer and fall, the bidirectional causal effect was mainly attributed to the transitional causal effect of NO 2 and maxT, respectively.In the Taizhou fall, a direct causal effect between the two was the major driving force.The causal effect of PM 2.5 on MDA8 O 3 was detected in the Beijing fall, but the causal effect in reverse was not detected.The causal effect of PM 2.5 on MDA8 O 3 was mainly attributed to HO 2 uptake.O 3 was the major oxidation pathway of nitrate, but the process was controlled by NO 2 instead of O 3 .The unidirectional causal effect of MDA8 O 3 on PM 2.5 was detected during the Chengdu and Taizhou spring.In these seasons and cities, separate control measures for PM 2.5 and MDA8 O 3 are needed.

Figure 1 .
Figure 1.Factors influencing the relationship between PM2.5 and O3 in this study.

Figure 2 .
Figure 2. CCM of daily PM2.5 and MDA8 O3 in Beijing, Chengdu, Taizhou and Shenzhen in the four seasons.Skill of cross-map estimates is indicated by the correlation coefficient (ρ).Increasing ρ with time-series length (library size) with convergence means that the causal relationship is detected.

Figure 3 .
Figure 3. CCM of Ox, O3, surface NO2, column density of HCHO and meteorological elements (maxT, minT, RH and WS) on daily mean PM2.5 with increasing time-series length (library size) in the four seasons in Beijing, Chengdu, Taizhou and Shenzhen.

Figure 4 .
Figure 4. CCM of PM2.5, surface NO2, column density of HCHO and meteorological elements (maxT, RH and WS) on MDA8 O3 with increasing time-series length (library size) in the four seasons in Beijing, Chengdu, Taizhou and Shenzhen.