We found that, during clean periods, mostly strong northwesterly winds occur whose velocity increases with height; during the HPEs, the southwesterly winds with dramatically decreased velocity were most frequent (Figs. 1–4a, b). Strong northerly winds and weak southerly winds closely correspond to the clean periods and the HPEs, respectively, because northwesterly winds, which are from less populated northern mountainous areas, carry unpolluted air masses while southerly winds carry polluted air masses from more populated and polluted southern industrial regions (Jia et al., 2008; Liu et al., 2013; Guo et al., 2014).

During the TSs with southerly winds, air temperature and moisture substantially increase compared with clean periods with northerly winds (Figs. 1–4b, c, d), which indicates the warm and humid southerly airflow transports more water vapor and heat into Beijing. During 15 rising processes (green lines), nearly no striking near-ground (< 250 m) moisture accumulation appears; no anomalous inversion appears except for brief weak inversion, which suggest that vertical variations in temperature and RH are unlike to primarily cause such rising. Nevertheless, weak inversion and more near-ground moisture favor growth.

If we assume that the primary cause of this rising is pollution accumulation due to local emissions, the rising needs to coincide with light (0.3–1.5 m s-1) or calm (0–0.2 m s-1) air observed during the later TSs instead of the slight (1.6–3.3 m s-1) or gentle (3.4–5.4 m s-1) breeze observed during the early TSs because weaker winds result in a stagnant condition, which is more favorable for local accumulation. However, the majority of later TSs with calm air do not exhibit such rising (Figs. 1–4a, b), which suggests local emissions under weak winds are likely conducive but not dominant with respect to rising.

Before rising processes during HPE1∼2, the urban PM2.5 mass concentration of Baoding (light gray lines), which is typically representative of pollution conditions in the south of Beijing, was much higher than in Beijing; the winds in Beijing rapidly shifted from northerly to southerly. Then the rising (green lines) occurred, consistently with southerly slight or gentle breezes in the BL (green boxes). The southerly air mass moved more than 288 km d-1 below 500 m (estimated from the measured wind speed), which is fast enough to transport pollutants to Beijing. Similar conditions appeared in eight of other nine HPEs with rising. Such processes indicate that southerly pollutant transport is primarily responsible for the rising, given the pollution transport pathway of the southwest wind belt determined by the unique geographic features of the North China Plain, with the Taihang Shan and the Yan Shan strengthening the southwest wind belt and leading to the convergence of pollutant transport in Beijing. (Su et al., 2004). Governed by this transport pathway, PM2.5 mass concentration increased by ∼ 400 µg m-3 from less than 35 µg m-3 in 10 h on 22 January 2013 when winds shifted from northerly to southerly with much higher PM2.5 concentrations in Baoding.

Pollutants transported from the south of Beijing primarily result in PM2.5 pollution formation in the urban area of Beijing, to which possible weak inversion and the near-surface moisture accumulation is conducive. Warm and humid airflow from the south transports more water vapor and pollutants to the North China Plain, which creates the requisite moisture and pollution accumulation conditions for subsequently cumulative explosive growth.

Anomalous inversion occurs during 10 of 12 HPEs (Figs. 1–4a, c). The factors that cause inversion in Beijing include topography, advection and radiation. With the Taihang Shan and the Yan Shan lying north of Beijing, a cold air mass flows down into the urban area of Beijing from the mountain peaks, which occasionally causes topography inversion; advection inversion occurs when a warm and less dense air mass moves over a cold and dense air mass. However, during most cumulative stages, the anomalous inversion appears with slight or calm winds, which suggests that the movement of air masses is not striking, so the contribution of topography and advection to such inversion is limited. The ground emits long-wave radiation at night to reduce near-ground temperature to facilitate inversion occasionally. However, almost no anomalous inversion occurs without pre-existing high PM2.5 mass concentration in the WPP (Figs. 1–4), which suggests that the ground radiation is likely conducive to weak/normal inversion but not dominant with respect to anomalous inversion.

The anomalous inversion noted is preceded by existing relatively high PM2.5 levels generally established by the rising processes. Before the cumulative explosive growth, existing aerosols are concentrated below 500 m (Fig. 5). These low-layer aerosols backscatter amounts of radiation to space (J. Wang et al., 2014; Gao et al., 2015) and cause a significant reduction in radiation reaching the ground, which further reduces near-ground temperature. These findings indicate that anomalous inversion is primarily due to the radiation cooling effect of preexisting aerosols. Below the inversion, near-ground temperature reduction cools down plumes or thermals of originally warm surface air to decrease thermal turbulence; observed weakened vertical shear of horizontal winds (Figs. 1–4b) produces less vorticity to reduce mechanical turbulence, which further strengthens the existing inversion.

Anomalous inversion traps pollution-laden air beneath it due to its strong static stability (Wallace and Hobbs, 2006). It facilitates pollutant accumulation by suppressing vertical air mixing and reducing BL height. During the cumulative explosive growth with anomalous inversion in the HPE10, the turbulent diffusion coefficient rapidly decreases from 100 to 50 m2 s-1 (model output of CUACE/Chem, the mesoscale China Meteorological Administration (CMA) Unified Atmospheric Chemistry modeling system, Hong Wang, personal communication, 2016), and similar conditions of turbulent diffusion have been modeled in another pollution episode in Beijing (Wang et al., 2015a, b); the BL height decreases from ∼ 500 m in the early morning, to ∼ 350 m at noon even to ∼ 250 m at night (Fig. 5), which coincide with the increase of PM2.5 from ∼ 200 to ∼ 450 µg m-3 (Fig. 4a). The striking layered structure in the BL occurs at the height of ∼ 300 m on 20 December 2016 (Fig. 5), which is consistent with the lower edge of anomalous inversion (Fig. 4), which confirms the strong inhibition of anomalous inversion. Additionally, a short cold air mass invades the northern urban area of Beijing in the early morning on 20 December 2016. The enhanced movement increases the BL height and reduces the PM2.5 mass concentration in part of the northern urban area (Fig. 5), which slightly reduces the urban mean mass concentration of PM2.5 in the early morning of that day (Fig. 4a). However, the anomalous inversion rapidly restores its original structure to facilitate pollutant accumulation.

The occurrence of anomalous inversion in nine HPEs coincides with cumulative explosive growth of PM2.5 levels (F1 ∼ 4a, c), which confirms the suppression of anomalous inversion to pollutants. Note that no cumulative explosive growth of PM2.5 levels appears in HPE3 despite anomalous inversion, partly because the height of the lowest inversion layer in HPE3 (∼ 750 m) is much higher than that in the nine HPEs (∼ 250 m), which suggests that near-ground inversion is more favorable for pollutant accumulation.

During clean periods, the moisture is evenly distributed in the BL with RH of less than 40 %, while during the HPEs, RH is over 60 % (even 80 %) in the lower or upper BL (Figs. 1–4c, d). During the HPEs, in the absence of temperature inversion, moisture vertically distributes in the BL, and the RH in the upper BL is occasionally higher than that of the near-ground surface; in the presence of weak inversion, the lower edge of the inversion layer is in approximate agreement with the RH contour of 60 %. In the presence of anomalous inversion (red boxes in Figs. 1–4c) in the BL, the lower edge of the strong inversion layer frequently coincides with an RH contour of 80 % (red boxes in Figs. 1–4d), which is observed in most cumulative explosive growth processes.

The relation of vertical temperature and RH previously noted indicates that anomalous inversion results in appreciable near-surface moisture accumulation by suppressing the vertical mixing of the water vapor (Wallace and Hobbs, 2006). The vertical diffusion of the near-surface water vapor as the anomalous inversion disappeared on 1 December 2016, 26 December 2016 and 5 January 2017 confirms the cited research outcome. Note that the mentioned near-ground temperature reduction caused by cooling effects of aerosols is also conducive to moisture accumulation by decreasing near-ground saturation vapor pressure to increase RH.

Strongly absorbent aerosol particles absorb and grow when additional water vapor appears in the air (L. Zhang et al., 2015). The mass concentrations of organic aerosols, sulfate, nitrate and ammonium rapidly increase with RH (Fig. S1 in the Supplement). After moisture absorption in North China, aerosol particle size increases by 20–60 % (Pan et al., 2009) and aerosol direct radiative forcing increases by ∼ 50 % (L. Zhang et al., 2015). As a key component of atmospheric aerosols, aerosol water serves as a medium that enables aqueous-phase reactions (Pilinis et al., 1989; Seinfeld and Pandis, 1986; Ervens et al., 2011). For example, aerosol water serves as a reactor in which alkaline aerosol components trap SO2, which is then oxidized by NO2 to form sulfate in northern China (Cheng et al., 2016). The ratio of SO2 to SO42- ranges from less than 0.1 at RH< 20 % to 1.1 at RH > 90 %, exhibiting an exponential increase with RH (Wang et al., 2016). In addition, high RH facilitates heterogeneous chemical processes to aggravate air pollution (Zhu et al., 2011). For example, the net reaction probability of HNO3 uptake on CaCO3 particles was found to increase with relative humidity from ∼ 0.003 at 10 to 0.21 at 80 % (Liu et al., 2008).

The stable atmospheric stratification characteristic of southerly light or calm winds, anomalous inversion, and near-ground (< 250 m) moisture accumulation (RH > 80 %) dominates the cumulative explosive growth of PM2.5.

During the HPEs, nearly all 10 cumulative explosive growth processes (Figs. 1–4) occur concurrently with stable atmospheric stratification primarily characterized by southerly light or calm winds, near-ground anomalous inversion, and cumulative moisture (RH > 80 %). The weak southerly winds, increased with height, are conducive to the growth because relatively strong southerly winds in the upper BL (∼ 1000 m) transport pollutants from the south of Beijing, while low-level (∼ 250 m) southerly light or calm winds limiting the invasion of northerly cold winds facilitate local pollution accumulation by minimizing horizontal pollutant diffusion. The anomalous inversion facilitates vertical pollutant accumulation by suppressing convection activities. During the cumulative growth process in HPE10, the turbulent diffusion coefficient rapidly decreases from 100 to 50 m2 s-1 and the BL height decreases from 500 to ∼ 250 m, which is extremely favorable for pollutant accumulation. The additional suppression of vertical mixing of water by inversion and the decreased saturation vapor pressure previously noted cause near-surface moisture accumulation (RH > 80 %). This accumulated moisture facilitates secondary aerosol formation in liquid-phase and heterogeneous reactions to increase PM2.5 levels.

It is likely that it is primarily merely weak southerly winds or near-ground anomalous inversion that can cause cumulative explosive growth. However, the growth does not occur in the polluted process from 4 to 15 December 2015 with weak southerly winds, which indicates that weak southerly winds do not suffice to cause cumulative explosive growth in the absence of anomalous inversion; even with anomalous inversion, no explosive growth appeared on 14 and 24 January 2013, which suggests that anomalous inversion cannot cause explosive growth without weak southerly winds. Therefore, cumulative explosive growth in CSs primarily resulted from the joint effects of southerly light or calm winds, near-ground anomalous inversion and moisture accumulation.

Note that the cumulative explosive growth at 20:00 BJT on 3 January was accompanied by a southerly gentle breeze (3.4–5.4 m s-1), which suggests that low-level southerly pollutant transport occasionally exerts an important impact on growth, with anomalous inversion and near-ground moisture accumulation.

Established from cumulative explosive growth, exceedingly high PM2.5 levels further decrease the near-ground temperature by reflecting and scattering more solar radiation, which strengthens the existing anomalous inversion and subsequently results in additional pollutant accumulation until the next synoptic process occurs. The near-surface temperature decreased from 3∘C at 20:00 BJT on 19 December to -3∘C at 08:00 BJT on 20 December after elevated ground PM2.5 levels (Fig. 4d). Then, it remained at ∼ -1∘C, with PM2.5 of more than 400 µg m-3 until northerly strong and clean winds blew the pollution away on 22 December. Similar processes also occurred in the CSs of other HPEs, which confirms the outcome.

The explosive growth of PM2.5 appears in HPE4-5 without inversion and near-ground moisture accumulation (Fig. 2), which suggests that stable atmospheric stratification noted previously does not primarily cause the growth. Weak winds in convergent explosive growth processes, particularly the process in HPE5, eliminate the likely contributions of southerly transport pollution. A comparison of surface wind distributions in the North China Plain before (Fig. 6a, d) and during (Fig. 6b, c, d, e) the convergent explosive growth processes in HPE4-5 shows that the urban area of Beijing is dominated by northerly winds before the growth, while is characterized by local air convergence during the processes, which suggests that the persistent local convergence is conducive to the explosive growth by causing pollutants to further accumulate locally. The convergent explosive growth in HPE6-7 with air convergence (Fig. S2) also confirms the outcome.