*3.2. Classification of PM*2.5 *Growth Periods in Central and Eastern China form 2013 to 2020*

To explore the growth mechanism of PM2.5 in autumn and winter, the data of PM2.5 growth periods (GP, hourly growth rate > 0) from 2013 to 2020 were selected year by year. Unless otherwise specified, the following research only focuses on the hourly growth rate

greater than 0, that is, the data during the positive GP. The hourly growth rate of PM2.5 (unit: μg m<sup>−</sup>3/h) is expressed as +ΔPM2.5. Figure 3 shows the statistical value of +ΔPM2.5 at different representative stations in autumn and winter year by year. Similar to the average PM2.5 concentration, with the Huai River as the boundary, the +ΔPM2.5 of the representative station in the southerly latitude area is lower than that of the northerly latitude station (autumn and winter). In terms of average value, the mean range of +ΔPM2.5 north of the Huai River is 10.7–40.9 μg m<sup>−</sup>3/h between 2013 to 2017 (on the left side of the dotted line). Among them, the maximum value of 40.9 μg m<sup>−</sup>3/h appeared in the Harbin (Northeast China) in 2013. Except for Shijiazhuang and Changchun, the average +ΔPM2.5 of 12 of the 14 sites (north of Huai river) in 2015–2016 was lower than that in 2013 and 2014. However, the +ΔPM2.5 of eight sites rebounded in 2016 comparing to 2015. After 2017, +ΔPM2.5 has a stepwise decline. Except for Linfen (Fenwei) and Harbin (Northeast China), whose +ΔPM2.5 is 27.2 and 21.5 μg m<sup>−</sup>3/h, respectively, all other stations decreased by less than 19 μg m<sup>−</sup>3/h. Especially in 2021, the maximum value of +ΔPM2.5 is only 15.3 μg m<sup>−</sup>3/h with a relatively concentrated distribution range of each site between 15.3 μg m<sup>−</sup>3/h and 9.4 μg m<sup>−</sup>3/h. For the representative stations south of the Huai River (on the right side of the dotted line), the average of +ΔPM2.5 is less than 20 μg m<sup>−</sup>3/h except for Hefei in 2013, which was 21.6 μg m<sup>−</sup>3/h. After 2017, all stations of +ΔPM2.5 educe to within 15 μg m<sup>−</sup>3/h and within 10 μg m<sup>−</sup>3/h in 2020.

The statistical results of the 25th, 50th, and 75th percentiles of +ΔPM2.5 are similar to the average overall. The distribution value of +ΔPM2.5 in the north of the Huai River is lower than that in the south of the Huai River, and the +ΔPM2.5 after 2017 also showed a significant decreasing trend compared with that before 2017. In the statistical results, the value of the 50th (median value) of the +ΔPM2.5 is significantly lower than that of the average, indicating that values greater than the 50th deviate are higher than those less than the 50th.

The PM2.5 concentration before the start of growth is classified with 75 μg m−<sup>3</sup> as the boundary, divided into clean and pollution, of which pollution is further divided into light (75–115 μg m<sup>−</sup>3), moderate (115–150 μg m<sup>−</sup>3), and heavy pollution (>150 μg m<sup>−</sup>3). The +ΔPM2.5 is compared based on the PM2.5 background mass concentration (clean, lightly polluted, moderately polluted, and severely polluted) before the start of the growth. At the same time, the proportions of pollution background, as well as the proportions of light, moderate, and severe pollution (under pollution background) before the start of growth, are shown in Figure 4. Still using the Huai River as the division, the proportion of PM2.5 growth occurring in the pollution background in south of the Huai River is significantly lower than that of the sites north of the Huai River. Among the representative stations in the Pearl River Delta, only 7–8% of PM2.5 growth occurred in pollution. Among other representative stations south of the Huai River, the highest probability of PM2.5 growth occurring in the pollution is Wuhan (42.0%), followed by Nanjing (40.0%) and Changsha (40.1%). Other sites are all below 40%. For the 14 representative stations north of the Huai River, the proportion of the PM2.5 increase in pollution is higher than 33%, and 78.6% of the stations are higher than 40%. For the stations of Shijiazhuang and Xingtai, in particular, the proportion of pollution background is as high as 55.5% and 56.8%, respectively. Further classifying pollution into light, moderate, severely pollution, as indicated in Figure 4, in the pollution background, the sites south of the Huai River are dominated by light pollution, with the lowest being 55% (Hefei) and an average of 71.2%. In contrast, more than 50% of the PM2.5 growth occurs in moderate and heavy pollution in the pollution background of the stations north of the Huai River. It is noteworthy that the proportion of heavy pollution is significantly higher than that of moderate, especially for Shijiazhuang and Xingtai, where the proportion of the PM2.5 growth occurs in heavy pollution (53.7% and 48.0%, respectively) once the light pollution is exceeded.

The average of +ΔPM2.5 corresponding to clean, light pollution, moderate pollution, and heavy pollution background was calculated before growth in GP (Figure 4 below). It can be seen from Figure 4 that, among all representative stations, the average of +ΔPM2.5

corresponding to the clean background before GP is the lowest, followed by light, moderate, and heavy pollution. Among them, the average of +ΔPM2.5 under a clean background generally less than 15 μg m−<sup>3</sup> and the increase value is generally under 10 μg m−<sup>3</sup> h−<sup>1</sup> in most areas south of the Huai River. Under the background of light pollution, the distribution range of the average +ΔPM2.5 at stations north of the Huai River is between 11.2 μg m−<sup>3</sup> h−<sup>1</sup> and 24 μg m−<sup>3</sup> h<sup>−</sup>1, with an average of 16.1 μg m−<sup>3</sup> h<sup>−</sup>1. South of the Huai River is slightly lower, with an average of 10.2 μg m−<sup>3</sup> h−<sup>1</sup> of +ΔPM2.5 under a light pollution background. Under moderate and severe backgrounds, the average +ΔPM2.5 at stations north of the Huai River were 19.0 μg m−<sup>3</sup> h−<sup>1</sup> and 26.6 μg m−<sup>3</sup> h<sup>−</sup>1, respectively. The average +ΔPM2.5 south of the Huai River (moderate: 12.3 μg m−<sup>3</sup> h<sup>−</sup>1, severe: 15.1 μg m−<sup>3</sup> h<sup>−</sup>1) is significantly lower than that in the north of the Huai River, but still higher than the average +ΔPM2.5 under the background of clean and light pollution of the site. Therefore, in each regional representative site, the background concentration of PM2.5 before GP has an important impact on the PM2.5 growth rate. Overall, a higher degree of air pollution before the growth leads to a faster average growth rate of the PM2.5.

The PM2.5 shows different growth rates during GP (+ΔPM2.5 > 0). According to the value of +ΔPM2.5, we divided GP into three categories as slow growth (SLG), rapid growth (RAG), and explosive growth (EXG). The atmosphere aerosol background concentration and the growth rate of PM2.5 both show obvious regional and inter-annual differences (Figures 2–4). We define the average annual +ΔPM2.5 from 2013 to 2020 as the threshold Ak,year (K represents the region) for determining the type of growth (SLG, RAG, or EXG) of the stations in that year. Figure 3a shows the value of Ak,year. Slow growth (SLGk, year), defined as the +ΔPM2.5, is less than Ak, i.e., SLGk, year < Ak,year; the interval of rapid growth (RAGk, year) is between 1 and 2 times of Ak,year, i.e., Ak,year ≤ RAGk, year ≤ 2\* Ak,year; and the +ΔPM2.5 of explosive growth (EXGk, year) is more than double that of the threshold, i.e., EXGk, year > 2\* Ak,year.

**Figure 4.** The average growth rate of PM2.5 (+ΔPM2.5) at each representative station during clean, light pollution, moderate pollution and heavy pollution before growth (**below**) and the proportion of PM2.5 above 75 μg m−<sup>3</sup> before the growth and the proportion of light, moderate, and heavy pollution (**upper**).

Since the +ΔPM2.5 in GP is closely related to the initial PM2.5 concentration, there should be a certain PM2.5 concentration threshold to judge the rapid or even explosive growth of PM2.5. Zhong et al. [13] found that, when PM2.5 reached a certain threshold, the positive feedback from aerosols to near-ground radiative cooling to anomalous inversion is effectively triggered, which subsequently results in explosive rising of PM2.5. In each representative station, the proportion of EXG in GP is 6.2–13.8%, with an average of 10.3% (Figure 5). Among them, the EXG of Tangshan (Beijing-Tianjin-Hebei and surrounding areas) accounted for more than 20% of the GP, which was the highest among all representative stations. Although the proportion of the EXG is lower than the RAG and the SLG, the EXG played a vital role in the occurrence and development of the heavy pollution process. It is necessary to quantify the relevant threshold of the EXG.

Figure 5 presents the average PM2.5 concentration thresholds before EXG in representative stations in each region during autumn and winter from 2013 to 2020. The statistical value of the lower quartile (25th) of PM2.5 before EXG can be used as the reference threshold of PM2.5 concentration for EXG, and the upper quartile (75th) characterizes that exceeding this critical value is extremely prone to EXG [13,27]. In the relatively heavily polluted stations north of the Huai River, the average PM2.5 threshold before the EXG is 70.8 μg m<sup>−</sup>3. Among them, the threshold in Beijing is 68.3 μg m<sup>−</sup>3, which is slightly lower than the strict threshold (71 μg m<sup>−</sup>3) proposed by Zhong et al. [13] for the EXG of PM2.5 in Beijing. The stations with the highest EXG threshold is Shijiazhuang (91.0 μg m<sup>−</sup>3), followed by Harbin (89.1 μg m<sup>−</sup>3) and Zhengzhou (88.9 μg m<sup>−</sup>3). Although the PM2.5 concentration threshold is the highest, the probability of EXG in these three cities (Shijiazhuang, Harbin and Zhengzhou) is still higher than the average proportion in the north of the Huai River (11.5%). For the area south of the Huai River, air pollution is relatively light, but at the same time, the threshold for PM2.5 explosive growth is relatively low, and a more stringent threshold also puts forward stricter requirements for atmospheric environmental governance. The upper quartile of the initial PM2.5 mass concentration values is much higher than the lower quartile (threshold) with the distribution interval from 156 μg m−<sup>3</sup> to 277 μg m−<sup>3</sup> for the

area north of the Huai River. Beijing's upper quartile value is 156 μg m<sup>−</sup>3, which indicates that an explosive growth of PM2.5 will likely occur once it is higher than this value.

As a comparison, the statistical values of SLG and RAG are lower than that of EXG, while the relevant thresholds can also be used as a stage indicator of prevention and control measures.

**Figure 5.** Thresholds for slow growth (SLG), rapid growth (RAG), and explosive growth (EXG) of each region and its representative stations, and the fraction of three growth methods. The dot is the average; the vertical line is the 10th percentile (**bottom**) and the 90th percentile (**top**); and the horizontal line is the 25th, 50th, and 75th percentile from top to bottom (the picture below is the same).
