Detecting the causality influence of individual meteorological factors on local PM2.5 concentration in the Jing-Jin-Ji region

Due to complicated interactions in the atmospheric environment, quantifying the influence of individual meteorological factors on local PM2.5 concentration remains challenging. The Beijing-Tianjin-Hebei (short for Jing-Jin-Ji) region is infamous for its serious air pollution. To improve regional air quality, characteristics and meteorological driving forces for PM2.5 concentration should be better understood. This research examined seasonal variations of PM2.5 concentration within the Jing-Jin-Ji region and extracted meteorological factors strongly correlated with local PM2.5 concentration. Following this, a convergent cross mapping (CCM) method was employed to quantify the causality influence of individual meteorological factors on PM2.5 concentration. The results proved that the CCM method was more likely to detect mirage correlations and reveal quantitative influences of individual meteorological factors on PM2.5 concentration. For the Jing-Jin-Ji region, the higher PM2.5 concentration, the stronger influences meteorological factors exert on PM2.5 concentration. Furthermore, this research suggests that individual meteorological factors can influence local PM2.5 concentration indirectly by interacting with other meteorological factors. Due to the significant influence of local meteorology on PM2.5 concentration, more emphasis should be given on employing meteorological means for improving local air quality.


Characteristics and variations of PM 2.5 concentration within the Jing-Jin-Ji region.
For the study period between Jan 8 th , 2014 and Dec 31 st , 2014, daily PM 2.5 concentration for main cities in the Jing-Jin-Ji region was analyzed respectively. Previous studies 14,21,34 proved that air quality in China was of notable seasonal variations. In this study, PM 2.5 concentration is also analyzed for each season respectively. In the Jing-Jin-Ji region, central heating is provided for cities during Nov 15 th to March 15 th . Thus this period is commonly categorized as winter for this region. According to the characteristics of high temperature, the period from June 1 st to August 31 st is defined as the summer. Accordingly, spring is defined as the period from March 16 th to May 31 st whilst autumn is defined as the period between September 1 st and Nov 14 th . The criteria for categorizing four seasons are consistent with a common phenomenon in Beijing, which is described by old sayings as "The spring and autumn in Beijing hardly last long". General characteristics of PM 2.5 concentration for different cities are demonstrated as Table 1 and Fig. 2.
As shown in Table 1 and Fig. 2, it is noted that general PM 2.5 concentration in the Jing-Jin-Ji region is much higher than Global Guidelines set by the World Health Organization (WHO) (24-hour mean: 25 μ g/m 3 ). As concluded by previous studies 21,22 , PM 2.5 concentration for Beijing is the highest in winter. This phenomenon also applies to other cities in the Jing-Jin-Ji region. The notably deteriorated air quality in winter may mainly attribute to the fact that central heating by burning coal materials, is supplied widely for the Jing-Jin-Ji region and thus leads to extra emission of airborne pollutants. According to PM 2.5 concentration, the Jing-Jin-Ji region can be divided into three sub-regions; slightly polluted region: Zhangjiakou, Chengde, Qinghuangdao; moderately polluted region: Beijing, Langfang, Tangshan, Tianjin, Cangzhou; heavily polluted region: Baoding, Hengshui, Xingtai, Shijiazhuang.

Meteorological factors correlated with PM 2.5 concentration. Based on a case study in Beijing,
Shanghai and Guangzhou, Zhang et al. 14 suggested that relative humidity, temperature, wind speed and wind directions were main meteorological factors correlated with the concentration of airborne pollutants. In addition, some other scholars [29][30][31][32][33][34][35] pointed out that radiation, evaporation, precipitation and air pressure also influenced PM 2.5 concentration. Therefore, to comprehensively understand meteorological driving forces for PM 2.5 concentration in the Jing-Jin-Ji region, a set of factors was selected as follows: evaporation, temperature, wind, precipitation, radiation, humidity, and air pressure. To better analyze the role of these meteorological factors in affecting local PM 2.5 concentration, these factors are further categorized into sub-factors: evaporation (small evaporation and large evaporation, short for smallEVP and largeEVP), temperature (daily max temperature, mean temperature and min temperature, short for maxTEM, meanTEM and minTEM), precipitation (total precipitation from 8am-20pm and total precipitation from 20pm-8am, short for PRE8-20, PRE20-8), air pressure (daily max pressure, mean pressure and min pressure, short for maxPRS, meanPRS and minPRS), humidity (daily mean and min relative humidity, short for meanRHU and minRHU), solar radiation (daily sunshine duration, short for SSD) and wind (daily mean wind speed, max wind speed, extreme wind speed and max wind direction, short for meanWIN, maxWIN, extWIN and dir_maxWIN). As there are one or more observation stations for each city, the daily value for meteorological factors for each city was acquired by averaging the value from all available observation stations.
Through correlation analysis, meteorological factors strongly correlated with PM 2.5 concentration were extracted for each city (Table 2). According to Table 2, meteorological factors strongly correlated with PM 2.5 concentration were of notable characteristics in different seasons. PM 2.5 concentration was the highest in winter and there were more influential meteorological factors on PM 2.5 concentration in winter. Additionally, there was no meteorological factor strongly correlated with PM 2.5 concentration for all cities or all seasons. In this case, it is more meaningful to analyze correlations between meteorological factors and PM 2.5 concentration on a seasonal basis rather than an annual basis.
Due to complicated interactions between different meteorological factors in the atmospheric environment, correlation analysis may extract mirage correlations. Additionally, the value of correlation coefficients cannot directly reflect the quantitative influence of individual meteorological factors on PM 2.5 concentration. However, correlated meteorological factors provide important reference for the following causality analysis. Although the correlation between two variables does not guarantee their causality, two coupled variables (except for some weak coupling) are usually correlated. Therefore, meteorological factors correlated with PM 2.5 concentration are further selected for the causality analysis.
The causality influence of individual meteorological factors on local PM 2.5 concentration. By analyzing two time-series variables using the CCM method, researchers can understand their coupling according to an output convergent map. If the interaction between two variables is featured using generally convergent curves with increasing time series length, then the causality is detected. On the other hand, if the interaction between the two variables is featured as curves without any general trend, then no causality exists between the two variables. The value of predictive skills (denoted by ρ value), ranging from 0 to 1, presents the strength of influences from one variable on another variable. The CCM method is highly automatic and detailed parameter setting for this model is explained in the method section.
The quantitative coupling between PM 2.5 concentration and individual meteorological factors is explained using convergent cross maps. Thus, there should be a convergent cross map for each variable in Table 2. It is not feasible to present more than 100 convergent maps here to explain the causality between PM 2.5 concentration and  each meteorological factor respectively. Hence several convergent cross maps ( Fig. 3) are displayed to demonstrate how CCM method works. For the rest causalities, Table 2 is presented to explain the quantitative influence of each meteorological factor on PM 2.5 concentration (ρ value). It is worth mentioning that ρ value can be extracted through the CCM tool directly, instead of the visual interpretation of the convergent cross map. If ρ is convergent to a certain value (in other words, Δ ρ is approaching to 0) with increasing time series, then the causality is detected and the ultimate ρ value for the coupling is set as the convergent constant. The ρ extraction approach based on computation allows the application of the CCM method to a national or global scale, where a diversity of interactions between variables should be examined. As Fig. 3 demonstrates, the coupling between meteorological factors and PM 2.5 concentration can be bidirectional. On one hand, some meteorological factors have important influences on PM 2.5 concentration. On the other hand, PM 2.5 concentration has significant feedback effects on these meteorological factors. Therefore, the meteorological factor can continuously influence local PM 2.5 concentration through even more complicated processes. For instance, local meanRHU has a strong influence (ρ = 0.738) on Beijing PM 2.5 concentration in winter whilst local PM 2.5 concentration has a strong feedback effect (ρ = 0.786) on meanRHU. Unlike GC analysis, the CCM method does not indicate the positive or negative causality between two variables directly. However, taking the correlation analysis into account, it is known that meanRHU has a positive influence on PM 2.5 concentration whilst PM 2.5 concentration has a positive feedback on meanRHU. In this case, high meanRHU in Beijing is more likely to cause high PM 2.5 concentration, which results in even higher meanRHU. In turn, higher meanRHU can further increase local PM 2.5 concentration. By analogy, the process how other meteorological factors influence local PM 2.5 concentration can be understood as well. Table 2 suggests that the causality influence of individual meteorological factors on PM 2.5 concentration is better revealed using the CCM method than the correlation analysis. By comparing the correlation coefficient and ρ value in Table 2, one can see that some correlations between meteorological factors and PM 2.5 concentration may result from mirage correlations (e.g. the correlation between meanRHU and PM 2.5 concentration in Hengshui in summer). Secondly, CCM analysis reveals weak or moderate coupling (e.g. the interactions between  Table 2, only strongly correlated factors are listed. If there are several strongly correlated variables (e.g. meanWIN and maxWIN), which belong to the same meteorological category, then only the one with the largest correlation coefficient is listed. NA indicates that no significant correlation exists between the meteorological factor and PM 2.5 concentration.
SSD and PM 2.5 concentration in Cangzhou in summer) whilst correlation analysis cannot. Additionally, due to interactions between different meteorological factors, the value of correlation coefficients cannot interpret the quantitative influence of individual meteorological factors on PM 2.5 concentration. Instead, the ρ value from CCM method is designed to understand the coupling between two variables by excluding influences from other factors. Through comparison, the value of the correlation coefficient for some meteorological factors is notably different from the ρ value for these meteorological factors. A large correlation coefficient for one meteorological factor may correspond to a much smaller ρ value from the CCM analysis (e.g. the correlation and causality between smallEVP and PM 2.5 concentration in Beijing in winter). Although some limitations exist, correlation analysis provides valuable reference for understanding the relationship between PM 2.5 concentration and meteorological factors. Firstly, the CCM method cannot directly indicate positive or negative causality between two variables. In this case, the correlation coefficient (with "+ " or "− ") provides researchers with a possible way to understand the causality direction. Secondly, even if the correlation coefficient is not an indicator of quantitative causality, it can be employed as a qualitative indicator for understanding the interactions between PM 2.5 concentration and meteorological factors. Based on Table 2, it is noted that except for very few mirage correlations, meteorological factors strongly correlated with PM 2.5 concentration, also have a causality influence on PM 2.5 concentration. If the research objective is to simply extract meteorological factors that influence PM 2.5 concentration and the analysis of quantitative influences is not required, then the correlation analysis can be an alternative approach (with a small possibility of mirage correlations) for analyzing the qualitative relationship between PM 2.5 concentration and individual meteorological factors. To properly demonstrate the influence of different meteorological factors on local PM 2.5 concentration, a wind rose was produced for each city through R programming. Firstly, a histogram featuring ρ value of each meteorological factor was produced. Next, according to the maximum of ρ value of each meteorological factor, the range of y axis was decided. Finally, a wind rose was made by transforming the histogram into polar-formed graph. Thus, seasonal wind rose maps that feature the causality influence (ρ value) of individual meteorological factors on PM 2.5 concentration in the Jing-Jin-Ji region are shown as Fig. 4.
Compared with Table 2, Fig. 4 presents seasonal influences of individual meteorological factors on local PM 2.5 concentration using easily understandable maps. According to these wind rose maps, some notable characteristics can be found: a PM 2.5 concentration in winter is notably higher than that in other seasons. Accordingly, the number of meteorological factors that influence PM 2.5 concentration in winter is more than that in other seasons. Furthermore, the quantitative influence (ρ value) of meteorological factors on PM 2.5 concentration in winter is much stronger than that in other seasons. On the other hand, PM 2.5 concentration in summer is the lowest and there are fewer meteorological factors that influence PM 2.5 concentration than in other seasons. The meteorological influences on PM 2.5 concentration in summer are also smaller than other seasons. This phenomenon is consistent with strong coupling between PM 2.5 concentration and meteorological factors, as explained above. The higher PM 2.5 concentration, the stronger influences it exerts on meteorological factors. In turn, corresponding meteorological factors can have a stronger feedback effect on PM 2.5 concentration. b There is no meteorological factor that consistently influences PM 2.5 concentration across seasons. In summer, the PM 2.5 concentration is the lowest and there are very limited meteorological factors that influence PM 2.5 concentration notably. The meteorological factor, temperature (especially minTEM), which has little influence on PM 2.5 concentration in other seasons, plays a dominant role in influencing PM 2.5 concentration in summer. In winter, PM 2.5 concentration is the highest and there are many meteorological factors that significantly influence PM 2.5 concentration. It is difficult to extract one dominant influential meteorological factor for PM 2.5 concentration, as Humidity, SSD and Wind work together to exert significant influences on PM 2.5 concentration in winter. c The correlation between some meteorological factors (temperature, wind and humidity) and air quality in big cities in China has been well discussed by previous studies 14 . However, the role of radiation is not considered fully. As shown in Fig. 4, SSD exerts notable influences on PM 2.5 concentration in all seasons, especially in winter. As a result, more emphasis should be given on understanding the role of radiation in influencing local PM 2.5 concentration.

Discussion
Although the CCM method proved the causality between PM 2.5 concentration and individual meteorological factors, it did not explain why these variables were interacted. To better understand meteorological influences on PM 2.5 concentration and its feedback effects, we attempt to explain the mechanisms of some typical bidirectional coupling.
Wind, humidity and SSD are the most influential meteorological factors for PM 2.5 concentration in winter. Herein, we take the three factors as example to briefly explain underlying interactions between meteorological factors and PM 2.5 concentration.
Negative bidirectional coupling between wind and PM 2.5 concentration. On one hand, winds, especially strong winds blow airborne pollutants away and reduce PM 2.5 concentration effectively. On the other hand, high PM 2.5 concentration, especially a quickly rising PM2.5 concentration brings the atmospheric environment to a comparatively stable status, which prevents the form of winds and reduces the wind speed in smog-covered areas.
Positive bidirectional coupling between humidity and PM 2.5 concentration. higher humidity causes more vapors attached to the Particulate Matter (PM) and significantly increases the size and mass concentration of PM, namely the hygroscopic increase and accumulation of PM 2.5 36 . On the other hand, the larger mass and higher concentration makes it difficult for PM 2.5 to disperse and leads to a stable polluted atmospheric environment, which is not favorable for the vapor evaporation and further increases the environmental humidity.
Negative bidirectional coupling between SSD and PM 2.5 concentration. Previous studies 7,9 have proved that organic carbon (OC) is an important component for PM 2.5, and atmospheric photolysis could occur on OC to reduce PM 2.5 concentration. Therefore, longer SSD has a negative influence on PM 2.5 concentration. On the other hand, SSD is a general indicator of cloudiness (https://en.wikipedia.org/wiki/Sunshine_duration). The more cloud, the less SSD is recorded by the ground observation station. By analogy, serious smog (thick black fog) caused by high PM 2.5 concentration notably blocked radiation emitted to the ground and thus the PM 2.5 concentration has a negative feedback effect on the SSD.
High PM 2.5 concentration in the Jing-Jin-Ji region makes the improvement of air quality a top priority for central and local governments. Taking Beijing for instance, we explain why and how to employ meteorological means for improving air quality. A series of traffic and industrial restriction regulations has been proposed in recent years and the air quality in Beijing has been improved significantly. However, PM 2.5 concentration in Beijing remains much higher than standard recommended by the WHO. In this case, as well as economic and administrative means, growing emphasis should be given on improving air quality through meteorological means.
Scientific RepoRts | 7:40735 | DOI: 10.1038/srep40735 Meanwhile, some scholars suggested that meteorological factors were external driving forces whilst the exhaust of traffic and industry pollutants was the fundamental reason for high PM 2.5 concentration. Therefore, adjusting meteorological factors was not the essential and most effective approach for mitigating local PM 2.5 concentration.
Although these arguments all make sense, based on findings of our previous work 22 and this research, enhancing air quality through meteorological means can be highly effective. Chen, Z. et al. 22 found that air quality in Beijing experienced frequent sudden changes throughout a year. During Jan 8 th , 2014 to Jan 7 th , 2015, there were more than 180 days that experienced notable air quality change (air quality index difference, Δ AQI ≥ 50). Considering that the amount of traffic and industry induced exhaust is unlikely to change significantly on a daily basis, meteorological influences on daily PM 2.5 concentration are crucial. This research further supports this hypothesis. The smog weather, resulting from high PM 2.5 concentration, occurs most frequently in winter. Meanwhile, according to Table 2 and Fig. 4, the coupling between meteorological factors and PM 2.5 concentration is the strongest in winter.
In addition to influence PM 2.5 concentration directly, individual meteorological factors can indirectly influence PM 2.5 concentration by interacting with other meteorological factors. Taking the wind factor for instance. in winter, three meteorological factors, humidity, wind and radiation (SSD) all strongly influence PM 2.5 concentration in Beijing. As well as the direct influence (ρ > 0.5), the wind factor influences local PM 2.5 concentration through some indirect mechanisms. Through correlation and causality analysis, quantitative interactions between wind and other factors in winter were summarized as follows: a The correlation coeffienct between maxWIN and SSD was 0.508** and the quantitative influence of maxWIN on SSD (ρ value) was 0.362. So wind factor has a strong positive influence on SSD. (The mechanism for the positive influence of wind on SSD may not be evident, so a brief explanation is given here. As introduced above, SSD is the general indicator of cloudiness. The fewer clouds, the higher SSD is. Since the wind, especially strong wind, effectively disperses clouds, it notably increases SSD for the region as well). b The correlation coeffienct between maxWIN and meanRHU was − 0.639** and the quantitative influence of maxWIN on meanRHU (ρ value) was 0.576. So the wind factor has a strong negative influence on RHU. c The correlation coeffienct between maxWIN and smallEVP was 0.633** and the quantitative influence of maxWIN on smallEVP (ρ value) was 0.602. So the wind factor has a strong positive influence on EVP.
The changing wind factor leads to the change of HUM, SSD and EVP conditions, which further influence local PM 2.5 concentrations accordingly. As shown in Table 2, the correlation coefficient between SSD and PM 2.5 concentration in winter was − 0.715**, and the quantitative influence of SSD on PM 2.5 concentration was 0.577 (ρ value), indicating the strong negative influence of SSD on PM 2.5 concentration. By analogy, the correlation coefficient between meanRHU and PM 2.5 concentration in winter was 0.759** and the quantitative influence of meanRHU on PM 2.5 concentration was 0.738 (ρ value), indicating the strong positive influence of RHU on PM 2.5 concentration. The correlation coefficient between smallEVP and PM 2.5 concentration in winter was − 0.494** and the quantitative influence of EVP on PM 2.5 concentration was 0.287 (ρ value), indicating the comparatively strong negative influence of EVP on PM 2.5 concentration.
According to the strong influences of wind factor on local PM 2.5 concentration and strong interactions between wind factor and other meteorological factors, which also exert notable influences on PM 2.5 concentration, the change of wind condition can be a promising meteorological mean for improving local air quality. By analogy, the change of SSD, RHU, EVP, Precipitation and other meteorological factors can also lead to significant change of local PM 2.5 concentration.
In spite of the dominant role of energy conservation and emission reduction in improving local air quality, the significant influence of meteorological factors on PM 2.5 concentration should be given enough emphasis. More research should be conducted to understand the complicated mechanism how different meteorological factors influence local PM 2.5 concentration comprehensively. Meanwhile, researchers and decision makers should work together to design and employ feasible meteorological means, which may adjust local humidity, wind, precipitation or so forth, for improving local and regional air quality.

Materials and Methods
Data sources. The data of PM 2.5 concentration are acquired from the website PM25.in. This website collects official PM 2.5 data published by China National Environmental Monitoring Center (CNEMC) and provides hourly air quality information for all monitoring cities. Before Jan 1 st , 2015, PM25.in publishes data of 190 monitoring cities. Since Jan 1 st , 2015, the number of monitoring cities has increased to 367. By calling specific API provided by PM25.in, we have collected hourly PM 2.5 data for these target cities since Jan 8 th , 2014. The daily PM 2.5 concentration for each city was calculated by averaging hourly PM 2.5 concentration measured at all available local observation stations. The meteorological data for each city are obtained from the China Meteorological Data Sharing Service System (http://data.cma.cn/)s. The meteorological data provided by this website are compiled through thousands of observation stations across China. The meteorological observations include precipitation, temperature, wind speed, humidity and so forth. For this research, we obtained meteorological data for each city from Jan 1 st , 2014 to Dec 31 st , 2014. Based on the available PM 2.5 and meteorological data, the study period for this research was set from Jan 8 th , 2014 to Dec 31 st , 2014.

Methods
This research mainly aims to quantify the causality influence of individual meteorological factors on local PM 2.5 concentration in the Jing-Jin-Ji region. Firstly, Pearson correlations between a set of meteorological parameters and local PM 2.5 concentration are examined. As introduced, interactions between different meteorological factors are complicated and it can be highly difficult to quantify the influence of individual meteorological factors on PM 2.5 concentration through correlation analysis. Therefore, correlation analysis works to preliminarily filter some meteorological factors that are not correlated with PM 2.5 concentration and provide information for the following comparison. Meteorological factors correlated with PM 2.5 concentration do not necessarily influence local air quality. Instead, some correlations may result from the underlying relationship between these factors and one agent factor 37 . To quantify the causality influence of individual meteorological on PM 2.5 concentration and examine the performance of correlation analysis in complicated atmospheric environment, a robust approach for quantitative causality analysis is required.
Sugihara et al. 37 suggested that mirage correlations might not be detected using correlation analysis. To detect the causality in complex ecosystems, Sugihara et al. 37 proposed a convergent cross mapping (CCM) method. Different from Granger causality (GC) analysis 38 that can be problematic in systems with weak to moderate coupling, the CCM algorithm is suitable for identifying causation in ecological time series. To examine the reliability of the CCM method under different situations, Sugihara et al. 37  Since there are underlying interactions between individual meteorological factors, individual meteorological factors influence local PM 2.5 concentration through complicated mechanisms. Furthermore, compared with Granger causality and forward-only dynamic time-warping (DTW), CCM method considers feedback relationship and thus reveals bidirectional causality 39 . Since heavily concentrated PM 2.5 may also have a feedback effect on local meteorology, the CCM method is highly suitable for detecting potential bidirectional interactions between PM 2.5 concentration and meteorological factors.
In this research, only several parameters need to be set for running this algorithm: E (number of dimensions for the attractor reconstruction), τ (time lag) and b (number of nearest neighbors to use for prediction). The value of E can be 2 or 3. A larger value of E produces more accurate convergent maps. The variable b is determined by E (b = E + 1). A small value of τ leads to a fine-resolution convergent map, yet requires much more processing time. Through a diversity of experiments, it was noted that the adjustment of these parameters simply affected some details of convergent maps whilst the general shape and information of curves remained unchanged. This indicates that the CCM method is not sensitive to manual setting of parameters and can extract reliable causality between different variables. In this research, to acquire optimal presentation effects of convergent cross maps, the value of τ was set as 2 days and the value of E was set 3.