We obtained 3-hourly meteorological data across China for January–December 2020 from the China Meteorological Administration. The meteorological variables used in this study included temperature, precipitation, wind direction, wind speed and atmospheric pressure, which were closely related to PM2.5, PM10 (Chen et al., 2020a) and O3 concentrations (Chen et al., 2020b). For cities with more than one observation station, the average of records from multiple stations was employed. For a multi-scale comparison, the 24 h meteorological data were produced by conducting an average operation on the 3 h meteorological data. Previous studies have proved that the pollutant–meteorology association presented notable seasonal variations, and if convergent cross mapping (CCM) were conducted based on a whole year's data, the p value would not be significant in many cases and thus the comparison cannot be made. Therefore, in this research, we considered the experiments based on the respective seasonal data. For analysing seasonal variations of pollutant–meteorology association, December, January and February were set as winter; March, April and May as spring; June, July and August as summer and September, October and November as autumn.

Hourly concentration data of PM2.5, PM10 and O3 during the same period were obtained from China National Environmental Monitoring Centre, CNEMC. The meteorological data were matched according to cities and air pollutant stations, and the pollution monitoring station nearest the city was selected as its surrounding meteorological conditions. A total of 101 cities were successfully matched. For cities with more than one observation station, the average of records from multiple stations was employed. To match the temporal scale of meteorological data, the per-3 and per-24 h pollutant data were produced by conducting an average operation on the hourly concentration data.

Since 2013, when PM2.5 pollution was observed across China, research on airborne pollution has been widely conducted. Amongst a diversity of topics, research on the meteorological influences on major airborne pollutants (e.g. PM2.5 and O3) has received growing emphasis. However, the major challenge for extracting and comparing the influence of individual meteorological factors lies in the complex interactions between multiple meteorological factors, which cause large uncertainties when applying traditional correlation analysis (Chen et al., 2020a). To address this issue, we employed an advanced causation model, convergent cross mapping (CCM), to quantify the influence of each meteorological factor on PM2.5, PM10 and O3. By removing the influence of disturbing factors, CCM (Sugihara et al., 2012) is capable of extracting reliable coupling between two variables in complex ecosystems. CCM calculates the causal influence of variable A on the target variable B as the p value, ranging from 0 to 1. Like the correlation coefficient, the p value can be used for comparing the influence of multiple variables on the target variable.

Thanks to its advantage in effectively extracting the asymmetric, bidirectional association between two variables and identifying mirage correlation in complex ecosystems with a diversity of variables, we have widely employed CCM to evaluate the influence of multiple meteorological factors on PM2.5 (Chen et al., 2017, 2018), O3 (Cheng et al., 2019; Chen et al., 2020b) and net primary production (NPP) (Gao et al., 2022) and achieved reliable outputs. Based on a multi-model comparison experiment, our recent research (Chen et al., 2022) proved that CCM was the most suitable model for causation inference in complex atmospheric environments. CCM is specifically designed to deal with the nonlinear relationship between two variables and is fully suitable for the nonlinear relationship between atmospheric factors. Compared to other mainstream statistical models, CCM was advantageous in identifying unique pollutant–meteorology association in local areas while maintaining general characteristics of pollutant–meteorology association across China. Furthermore, CCM-generated meteorology–pollutant associations were highly consistent with prior knowledge. For this research we also employed CCM to quantify and compare the influence of temperature, precipitation, wind speed, wind direction and atmospheric pressure on PM2.5, PM10 and O3 concentrations. CCM automatically considers all possible interaction forms and lag effects between the time series of two variables, which effectively reduces the influence of interference and avoids the influence of other factors. CCM is largely automatic in removing the uncertainty of manual settings, and only the setting of three parameters is required: τ (time lag), E (number of dimensions) and b (number of nearest neighbours). For this research, τ, E and b were set as 2, 3 and 4 d, as per previous studies (Chen et al., 2018, 2020b).

Based on rarely employed 3 h meteorological data sources, we compared the effects of temporal scales on the extracted pollutant–meteorology causation. Due to the data limitation at the 3 h scale, which did not include humidity and sunshine duration, we could only consider a limited number of meteorological factors (temperature, precipitation, wind speed, wind direction and atmospheric pressure). This is fewer than in our previous studies based on meteorological data at the 24 h scale and why some meteorological factors (e.g. humidity and sunshine duration) were missed in this research. However, since we compared the same set of these major meteorological factors at both 3 and 24 h scales, the calculated consistence and difference could effectively reveal the potential effects of different temporal scales on the quantitative (the detailed p value) and qualitative (the dominant meteorological factor) findings of pollutant–meteorology association. The limited number of meteorological factors had limited influence on the temporal effects on pollutant–meteorology association. This is because CCM simply considers the causality between the target variable and one influencing variable and removes the influence from other variables (Sugihara et al., 2012; Chen et al., 2020). Another limitation of these data was that this data set only included 1 year's data and thus the inter-annual variation of temporal effects on pollutant–meteorology association could not be revealed. In this research, we revealed the existence of strong temporal effects on pollutant–meteorology association, which can be fully supported by the 1-year data with four seasons (four complete time series with more than 90 records at 24 h scale and 720 records at 3 h scale). Meanwhile, the temporal variation of temporal effects on pollutant–meteorology association and its influencing factors should be further investigated in future studies, when the long-time-series data sets of 3 h meteorological data become available.

Based on CCM, we calculated the dominant meteorological factors for seasonal O3 (Table 1), PM2.5 (Table 2) and PM10 (Table 3) concentrations at the 3 and 24 h scales respectively. By comparing the extracted pollutant–meteorology association, we calculated the number of cities with the same meteorological factor at different temporal scales (Table 4). As shown in Table 4, the consistence between dominant meteorological factors for PM2.5, PM10 and O3 at two temporal scales varied significantly (ranging from 31.68 %–61.29 %), indicating the temporal scale played a large role in the analysis of pollutant–meteorology association. As can be seen from Tables 1, 2 and 3, the consistence between dominant meteorological factors extracted at 3 and 24 h in autumn and winter was higher than that in spring and summer. For example, temperature, precipitation etc. for O3, PM2.5 and PM10 were mostly more dominant in autumn and winter than in spring and summer. This phenomenon indirectly suggests that meteorological influences on airborne pollutants were stronger in autumn and winter, and thus the role of the dominant meteorological factor was highlighted.

As can be seen from Table 1, at the 3 h scale for O3, the number of cities with precipitation as the dominant influencing factor was largest in winter, with 43 cities, while the number of cities with temperature was largest in spring, summer and autumn, with 64 cities, 78 cities and 75 cities respectively. As one can see from Tables 2 and 3, for PM2.5 and PM10, the number of cities with temperature as the dominant meteorological factor was largest in all seasons. As a comparison, at the 24 h scale for O3, the number of cities with temperature as the dominant influencing factor was largest in spring, with 59 cities, and for PM2.5 and PM10, the number of cities with temperature as the dominant influencing factor was largest in autumn, with 61 and 55 cities respectively, which was consistent with previous studies (Wang et al., 2018; Yang et al., 2021), while the number of cities with precipitation was largest in winter, with 47, 35 and 36 cities respectively.

However, the consistence of dominant factors between two temporal scales remained less than 50 %. The study identified the dominant meteorological factors through CCM according to the p value. While the p value of the dominant meteorological factor was largest, it may be only slightly larger than the p value of other meteorological factors at the 24 h (3 h) scale and may be smaller than the p value of another factor, which led to the change of dominant factor, at the 3 h (24 h) scale. In this case, if we simply consider the difference between the dominant meteorological factor (with the largest p) at 3 and 24 h scales, the analysis was qualitative and not sufficient, which cannot comprehensively reveal the difference of pollutant–meteorology association at different temporal scales. Therefore, we further analysed the detailed p values for all meteorological factors acting on O3, PM2.5 and PM10 at two temporal scales to present a quantitative and comprehensive comparison.

The detailed distribution of influence of individual meteorological factors on O3, PM2.5 and PM10 concentrations is presented in Fig. 1. Generally, meteorological influences on airborne pollutants presented a consistent trend between the 3 and 24 h scales, characterised with a generally similar violin shape. According to Fig. 1, the violin shape and range of 3 h pollutant–meteorology is much sharper than the 24 h pollutant–meteorology, indicating that the 3 h temporal scale was more sensitive to revealing the variation of pollutant–meteorology interactions. As shown in Table 5, similarly to the number of dominant meteorological factors, the mean of calculated p values across China also proved that temperature exerted a much stronger influence on PM2.5, PM10 and O3 than other factors. Furthermore, according to the violin shape of different pollutants, we found that the pattern of PM2.5 between meteorology and PM10 between meteorology was generally consistent and largely different from the pattern of O3 meteorology, indicating that meteorological influences on particulate matters and gaseous pollutants were different. The major differences of pollutant–meteorology interactions at 3 and 24 h are explained in this section.

For all three airborne pollutants, temperature exerted the strongest influence across China in all seasons in terms of the largest mean p. High temperature promotes photochemical reactions and produces more PM2.5, PM10 and other precursors of secondary pollutants, leading to higher concentrations of PM2.5 and PM10. High temperature may also lead to increased evaporation loss of PM2.5 and PM10, including NO3- salt and other volatile or semi-volatile components, resulting in decreased concentrations of PM2.5 and PM10. For PM2.5 and PM10, the calculated influence of temperature at the 24 h scale was consistently larger than that at the 3 h scale. This may be attributed to the fact that the secondary reactions of the precursors of PM were less intensive (Chen et al., 2016, 2020) and thus the temperature variation within 24 h exerted a stronger influence than 3 h temperature variation. Meanwhile, the influence of temperature on O3 presented a notable seasonal pattern. For the relatively cold seasons of winter and spring, when O3 concentrations were relatively low, the influence of temperature at the 24 h scale was larger than that at the 3 h scale. For summer, when O3 concentrations were the highest, the influence of temperature at 3 h scale was much larger than that at the 24 h scale. This is mainly attributed to the fact that the high temperature in summer was the major trigger for quick reactions between precursors and high O3 concentrations. Therefore, short-term variations of temperature could strongly influence O3 concentrations in summer (Cheng et al., 2018, 2019).

For precipitation, since the distribution of precipitation in a day's time is not unified, and there may be no precipitation in many 3 h slots, the mean p of precipitation across China at the 3 h scale was weaker than that at the 24 h scale. As a comparison, at the 24 h scale the occurrence of precipitation was significantly enhanced and thus the influence of precipitation on airborne pollutants was much stronger. Across China, the precipitation intensity showed obvious seasonal variations, and most regions may have the maximum value in summer and minimum value in winter. The eastern region of China is affected by monsoons in summer and autumn, and there is a lot of precipitation. In winter, China receives less precipitation due to the influence of winter winds. Accordingly, the calculated p of summer precipitation for PM2.5, PM10 and O3 at 24 h scale was remarkably larger than that at 3 h scale.

Previous studies (Chen et al., 2017, 2018, 2020) proved that wind had a notable influence on PM. Similarly to precipitation, the daily distribution of wind is not unified, and there may be calm wind conditions in many 3 h slots. Therefore, the mean p of wind direction and wind speed on PM2.5 and PM10 at the 24 h scale was notably larger than that at the 3 h scale. Wind–O3 interactions presented notable seasonal patterns. In the less polluted spring and winter, the mean p of wind direction and wind speed at the 24 h scale was larger than that at the 3 h scale. In summer, when O3 concentrations were relatively high, the mean p of wind direction and wind speed at the 3 h scale was larger.

Atmospheric pressure mainly affects the transport and accumulation of pollutants by indirectly influencing other meteorological factors (e.g. wind and precipitation). Therefore, large uncertainties existed in the extracted pressure–pollutant causation. Generally, for PM2.5, PM10 and O3, the mean p of atmospheric pressure across China at the 3 h scale was weaker than that at the 24 h scale, except for summer, when the interactions between atmospheric pressure and other meteorological factors were strong.

All the locations of the mentioned regions have been marked in Fig. 2. As shown in Figs. 3, 4 and 5, the influence of meteorological factors on airborne pollutants has obvious seasonal variations and presented some regional similarity. The seasonal concentration of air pollutant data for each city is calculated using the average of hourly concentration data measured by all available local observation stations. For PM2.5 (Fig. 3) and PM10 (Fig. 4), the dominant meteorological factor for northeast China was mainly wind, especially the heavily polluted winter, while the dominant meteorological factor for the Yangtze River Delta was mainly precipitation at both the 3 and 24 h scales. The dominant meteorological factor for Shandong Peninsula in spring and autumn, for southern China in summer, for northern and coastal areas in autumn and for northeast China in winter is also consistent at different temporal scales. For O3 (Fig. 5), especially the heavily polluted summer, temperature presented a prevailing role across the nation and was the dominant role for most cities. This output was consistent with our previous studies (Chen et al., 2018, 2019a), suggesting that the general national trend of pollutant–meteorology association varied limitedly across temporal scales of research data, especially in those heavily polluted regions. Meanwhile, for those regions where the airborne pollution was not severe and homogeneous, the temporal issues of meteorological influences on PM were notable and thus the dominant meteorological factor in these regions presented notable differences at 3 and 24 h scales.

Based on the extracted pollutant–meteorology associations at the 3 h scale, which have rarely been discussed, we found some interesting differences between 3 and 24 h in some major regions across China. For the heavily polluted Beijing–Tianjin–Hebei region, the dominant meteorological factor for O3 in spring was temperature at the 3 h scale. Meanwhile, the dominant factor was wind speed at the 24 h scale. For PM2.5, the dominant factor for PM2.5 in spring was temperature at the 3 h scale and wind speed at the 24 h scale. The dominant meteorological factor for PM10 in summer was temperature at the 3 h scale and precipitation at the 24 h scale.

For the Yangtze River Delta, the dominant meteorological factor for O3 in spring was temperature at the 3 h scale and the combination of temperature and precipitation at the 24 h scale. In summer, the dominant meteorological factor for O3 was temperature at the 3 h scale and wind speed at the 24 h scale. The dominant factor of PM2.5 in spring was temperature at the 3 h scale and the combination of temperature and precipitation at the 24 h scale. The dominant factor of PM10 in spring was mainly temperature at the 3 h scale and wind speed at the 24 h scale. For the Pearl River Delta, the dominant meteorological factor for O3 in winter was temperature at the 3 h scale and precipitation at the 24 h scale.

For the Sichuan Basin, the dominant meteorological factor for O3 in all four seasons was temperature at the 3 h scale, while it was precipitation, atmospheric pressure and wind speed in summer, autumn and winter respectively at the 24 h scale. The dominant meteorological element for PM2.5 was temperature in all four seasons at the 3 h scale, while it was precipitation in summer and winter at the 24 h scale. The dominant meteorological element for PM10 in spring and winter was temperature at the 3 h scale, while it was atmospheric pressure for spring and winter at the 24 h scale. Compared with other regions, the unique basin terrain led to stronger temporal effects on extracted pollutant–meteorology associations.

Our previous studies (Chen et al., 2018, 2020) revealed that meteorological influences exerted a stronger influence on PM pollutants when PM concentration is higher. This might be the reason that the difference of PM–meteorology associations between 3 and 24 h was relatively small in the heavily polluted winter and large in less polluted spring. Meanwhile, we found that the role of wind speed and precipitation may be largely underestimated at the 3 h scale. Compared with the generally consistent pollutant–meteorology associations in these heavily polluted regions, the dominant factor for PM and O3 demonstrated significant variations in those coastal cities, such as Shenzhen, Zhuhai and Zhanjiang.