The impacts of the atmospheric boundary layer on regional haze in North China

An intensive atmospheric boundary layer (ABL) experiment was conducted simultaneously at six stations arranged in a cross shape on the North China Plain (NCP) from 26 November to 26 December 2019. The impacts of the regional ABL structure on heavy haze pollution and the relationship between the ABL height and aerosol accumulation layer (AAL) depth were discussed. Bouts of downdrafts generate a persistent descending elevated inversion layer, helping the maintenance and exacerbation of haze pollution. Continuous weak wind layers contribute to the pollutants accumulation, and low-level jets promote the removal of air pollutants. The unique landform conditions of the NCP are reflected in its regional ABL structure and further affect the spatial distribution of haze pollution. Due to the drainage flow and strong downdrafts, the western stations near the mountains have a colder surface and warmer upper air masses, resulting in a more stable stratification and worse diffusion conditions; these stations also experience a thicker weak wind layer caused by increased friction. Thus, the spatial distribution of haze is heavier in the west and lighter in the east. The convective boundary layer (CBL) height declines evidently during haze episodes, usually lower than 560 m. Furthermore, as the vertical distribution of aerosols is mainly influenced by daytime thermal turbulence and maintained at night, it is appropriate to determine the CBL height using the AAL depth. However, the AAL depth is not consistent with the stable boundary layer height due to the influence of the residual layer at night.


INTRODUCTION
Frequent haze pollution events represent one of the most serious atmospheric environmental problems faced by China, as they result in poor air quality and low visibility [1][2][3] . Fine particulate matter, known as PM 2:5 (particulate matter with an aerodynamic diameter no greater than 2.5 μm), is the chief pollutant 4,5 . Haze pollution shows considerable seasonal variations and regional disparities. Seasonally, it is generally more serious in winter 6,7 . Spatially, the North China Plain (NCP), the Yangtze River Delta (YRD), the Pearl River Delta (PRD), and the Sichuan Basin (SB) have been recognized as four major haze regions in China [8][9][10][11] . The NCP has become the most polluted district in China 12 . And the effects of its unique topography and local circulation on haze pollution in the NCP have attracted wide attention of researchers [13][14][15][16][17][18][19] .
The formation mechanisms of long-lasting winter haze pollution events characterized by high PM 2:5 concentrations have been investigated from various perspectives and on different scales [20][21][22][23][24] . In general, persistent heavy haze events are associated with a high emission background 25,26 , adverse meteorological conditions 27-30 , regional transport [31][32][33] , and secondary aerosol formation [34][35][36] . In particular, the meteorological conditions in the atmospheric boundary layer (ABL), which determines the vertical transport of heat, water vapor and aerosols between the underlying surface and atmosphere, are crucial to haze dispersion 37 . Strong inversions and stagnant winds are favorable conditions for the accumulation of pollutants, and high humidity can contribute to the hygroscopic growth and secondary formation of aerosols 38,39 . The diurnal variation of the ABL can result in variations in the PM 2:5 concentration 40,41 . In the daytime ABL, known as the convective boundary layer (CBL), PM 2:5 can be mixed uniformly in a thick layer due to the active turbulent mixing 42 . While in the nighttime ABL, also called the stable boundary layer (SBL), high PM 2:5 concentrations are often observed near the surface due to the stable stratification and intermittent turbulence [43][44][45] . Moreover, pollutants in the residual layer can be mixed downward to the surface with the development of the ABL the next morning 16,46,47 . Regarding the dynamic structure, low-level jets (LLJs) and turbulent motions can modify the air quality by affecting transport and diffusion capabilities. LLJs can not only contribute to the advection of pollutants to less polluted areas 48 , but also improve air quality in the pollution dissipation stage by triggering turbulent mixing and transferring momentum downward 49,50 .
The atmospheric boundary layer height (ABLH) is an important parameter in air quality assessments that reflects the effects of turbulent mixing, convection and other physical processes in the ABL 51 . Studies have shown that the ABLH is a main meteorological driver of PM 2:5 variation 52 . There is a negative correlation between the ABLH and pollutant concentrations [53][54][55] . The ABLH in winter is lower than that in summer, which makes haze pollution form more easily in winter 56,57 . In addition, with the rapid development of ground-based remote sensing equipment, such as lidars and ceilometers, a number of studies have attempted to retrieve the ABLH based on the distributions of substances [58][59][60] . The theoretical basis of this approach is that aerosols are abundant in the ABL, but sharply decrease at the boundary layer top, while the free atmosphere is free of aerosols 61 .
With the increasing attention paid to the impacts of the ABL on haze pollution, many field experiments have been conducted. Atmospheric profiles have commonly been acquired by meteorological towers, tethered balloons, conventional radiosondes and surface-based remote sensing equipment 47,[62][63][64][65] . However, boundary layer observations are still scarce overall, the influence of the ABL structure on heavy haze pollution remains to be studied. And most studies were based on single-station observations, whereas joint observations of the spatial distribution of haze pollution and the regional ABL structure are lacking. In addition, the relationship between the aerosol accumulation layer (AAL) depth (see Section "Determination of the ABLH and AAL depth" for the definition) and ABLH needs to be further clarified. To investigate these topics, an intensive ABL field experiment was carried out at six stations in the NCP for a month during the winter of 2019. The six observation stations were arranged in the shape of a cross (Fig. 1), and regional profiles of atmospheric meteorological elements and PM 2:5 concentrations were collected by high-resolution GPS sounding. Details of the field experiment and data can be found in Section "Observation stations and instruments" and Section "Data acquisition and processing". Based on the observational data, the following three questions were studied: First, the characteristics of the ABL structure during persistent heavy haze pollution. Second, regional ABL structure and its impacts on spatial distribution of haze pollution. Third, the relationship between the ABLH and AAL depth.

RESULTS
Overview of fog-haze pollution during the observation period According to the National Environmental Protection Standards of China HJ 633-2012, the ambient air quality can be divided into six grades, namely excellent (level 1, AQI is between 0 and 50), good (level 2, AQI is between 51and 100), light pollution (level 3, AQI is between 101 and 150), moderate pollution (level 4, AQI is between 151 and 200), heavy pollution (level 5, AQI is between 201 and 300), and severe pollution (level 6, AQI is larger than 300), respectively. During the observation period, three serious air pollution events with PM 2:5 as the primary pollutant reached moderate or heavy pollution levels. As shown in Fig. 2, Case 1 ranges from 20:00 local time (LT) on 28 November to 20:00 LT on 1 December 2019, Case 2 is from 20:00 LT on 6 December to 8:00 LT on 11 December 2019, and Case 3 is from 14:00 LT 21 December to 8:00 LT 26 December 2019. The temporal variations of the surface meteorological elements observed at Renqiu station are also shown in Fig. 2. During these haze episodes, the diurnal variation of temperature (T) is weak. The specific humidity (q) is relatively higher in the pollution period but drops rapidly in the cleaning period. In hazy weather, the wind speed (WS) is mostly smaller than 2 ms −1 , which is favorable for the formation of haze pollution; while it increased obviously to~4 ms −1 during the cleaning period. The weather condition is relatively stable during the pollution period. As Fig. 2d depicts, the surface pressure (P) field changes slowly and has successive low pressures during heavy and long-lasting haze pollution, and this pressure pattern is consistent with the previous study 66 . Figure 3 illustrates a comparison of the pollution level and surface meteorological elements among Tuonan, Baoding, and Renqiu stations during the whole observation period. Figure 3a shows that Tuonan has the best air quality with excellent or good air quality accounting for~70%, while the air quality is the worst in Baoding with only 30% observations under clean weather and most frequent heavy pollution events. In brief, Baoding experiences the worst haze pollution, Renqiu follows, and Tuonan has the best air quality. There are significant differences in the surface meteorological elements among the different stations. Wind speeds smaller than 1 ms −1 account for 71%, 66%, and 55% of all wind speeds during the observation period at the Tuonan, Baoding, and Renqiu stations, respectively; these percentages suggest that the wind tends to be calmer in Tuonan but stronger in Renqiu. The proportions of temperatures less than 0°C are 71%, 46%, and 18% in Tuonan, Baoding, and Renqiu, respectively, indicating that Tuonan has the coldest surface, while Renqiu has the warmest. In addition, the daily temperature range in Tuonan is the largest among the three stations while that in Renqiu is the smallest. The specific humidity is relatively high at Baoding station, while it tends to be drier at Tuonan and Renqiu stations. Based on the above comparison, the wind speed increases from the western mountain area to the eastern plain, and the temperature has a similar trend. These features can be attributed to the influence of the mountains in western NCP. Due to increased friction near the mountains, the wind speeds are significantly weakened 6,37 . In addition, cold air masses slide down the mountains at night, forming cold air pools in the valley 67 . Because there is less water vapor transport from the southerly wind in Baoding than Renqiu and Tuonan, and Baoding has a denser population and advanced  industry than the other two areas 27,68 , thus the higher moisture at the Baoding station is more likely to be related to local anthropogenic emissions.
Impacts of the ABL structure on persistent heavy haze pollution Among all three haze pollution cases captured during the observation period, Case 2 arouses the greatest concern, as this persistent event was the most polluted. From 6 to 11 December 2019, this event lasted for more than 4 days, and the PM 2:5 concentration in the surface layer even exceeded 200 μg m −3 . As the pollution process and ABL structure are similar at six stations, the pattern of Baoding station is given here only. Figure 4a depicts the temporal variation of the vertical PM 2:5 concentration distribution, or in other words, the temporal variation of the AAL. As the strong southwest wind appeared and promoted the advection transport of pollutants on 6 December, the early AAL characterized by large thickness (~1000 m) but light pollution (PM 2:5 concentration smaller than 100 μg m −3 ) was formed. Then, in the accumulation stage of pollution, PM 2:5 was mainly concentrated in a shallow layer below 800 m. And after 8 December, the AAL depth showed a continuous declining trend and dropped to~200 m on 11 December, and the haze pollution became further aggravated. Finally, the pollution was rapidly removed by the northerly jet stream and the AAL disappeared on 11 December. Figure 4b shows that the variation of the AAL is closely related to the thermal ABL structure. From 8 to 11 December, there was a thick elevated inversion layer at relatively low altitudes all the time, and the bottom of the elevated inversion layer decreased gradually, corresponding to the decrease in the AAL depth. It is clear that fine particles were confined below the strong elevated inversion layer, and their vertical distribution changed with the regulation of the thermal structure. This is because the inversion layer exhibits stable stratification, which restricts vertical turbulent transport to a great extent. Therefore, it is difficult for pollutants to pass through the inversion layer. The persistent existence of inversions results in longlasting adverse vertical diffusion conditions, which is conducive to the accumulation of aerosols and water vapor. A decrease in the bottom height of the inversion layer further worsens the diffusion conditions, concentrating aerosols and water vapor in a shallower layer. The descending elevated inversion layer may be attributed to bouts of sinking motions. In this haze event, a trough was stable at low altitudes over the North China Plain and deepened with the intrusion of gusty cold air along its western flank, which caused constant sinking motions. Figure     play a key role in the maintenance and exacerbation of heavy haze pollution.
As shown in Fig. 4c, the AAL is also closely related to the dynamic structure of the ABL. In the transport stage, there is strong southwest wind throughout the ABL, making the PM 2:5 concentration gradually increase in the whole layer, and the AAL depth can reach 1000 m. In the accumulation stage, weak or calm winds (usually smaller than 2 ms −1 ) are dominant in the AAL. This dynamic condition, which implies the poor horizontal transport capacity of pollutants, also greatly contributes to the accumulation of PM 2:5 in local areas. The small wind layer, like the AAL, lies below the elevated inversion layer, and its formation is associated with the inversion layer. Due to the existence of the thick and strong elevated inversion layer, the turbulent transport is greatly inhibited. And the weak turbulent transport makes it difficult for the larger momentum in upper layer to be transported downward. As a consequence, the wind speed remains at low values beneath the elevated inversion layer, forming a small wind layer. Finally, haze pollution is cleared by a strong wind jet stream reaching the ground, which not only increases the horizontal transport capacity but also improves the vertical diffusion conditions by promoting the generation of mechanical turbulence. Therefore, heavy haze pollution is accompanied by weak winds, and the lowlevel jet is a key factor in the removal of air pollutants. Figure 4d depicts the humidity structure of the ABL, which also has an impact on haze pollution. Heavily polluted areas are consistent with areas characterized by high humidity. In the early stage of haze pollution, this configuration reflects the regional transport of pollutants and water vapor from southwestern areas. During the maintenance stage of haze pollution, the consistency indicates the synchronous accumulation of pollutants and water vapor in the lower atmosphere under poor diffusion conditions. The mitigation of haze pollution from 8 to 9 December might be attributed to the fog. In foggy weather, some aerosols can act as condensation nuclei and be converted into fog droplets, and some aerosols can be removed through wet scavenging 62,69 .
Spatial distribution of haze pollution and regional ABL structure Surrounded by mountains to the north and west and bounded by the sea to the east, the special geographical position of the NCP leads to significant differences in both the ABL structure and the spatial distribution of haze pollution over this region 12,15,70 . We have noticed that regional pollution pattern often reflects higher pollution levels in the western part of the NCP during the observation period. Figure 6a shows the regional spatial distribution of the PM 2:5 concentration at 14:00 LT on 30 November 2019. In terms of the pollution level, haze pollution was the heaviest at the Baoding and Dingzhou stations, with PM 2:5 concentrations exceeding 200 μg m −3 in the pollution center with a depth of 700 m. The Renqiu and Bazhou stations experienced the lightest haze pollution with the thinnest AAL, where the PM 2:5 concentration was less than 100 μg m −3 and the AAL was lower than 500 m. In addition, the pollution level was moderate at the Tuonan and Cangzhou stations, where the AAL was thick (~1000 m) in Cangzhou and thin (~500 m) in Tuonan. The corresponding regional thermal structure of the ABL is shown in Fig. 6b. The surface temperature increases from the west (Tuonan) to the east (Cangzhou). Closer to the mountains, the stations in the west are more influenced by nighttime drainage flow, resulting in the accumulation of cold air masses in the surface layer. As depicted in Fig. 6b, there is a strong and thick elevated inversion layer over the stations to the west (Tuonan, Baoding, and Dingzhou), while the stations in the east (Renqiu, Bazhou, and Cangzhou) do not exhibit this feature. This indicates that the warming effect induced by the downdrafts is stronger in areas near the mountains. As a consequence, stations located to the west have a colder surface and warmer upper air masses, which means a more stable stratification that can greatly suppress the vertical transport of air pollutants. This is one of the reasons why the western sites are more polluted than the eastern sites.
As for the dynamic structure of the ABL, Fig. 6c shows that the western sites (Tuonan, Baoding, and Dingzhou) possess a thicker layer (~500 m) with much calmer wind speeds (smaller than 2 ms −1 ). This is because of the increased friction near the mountains. Besides, this corresponds to the thermal structure, because the strong elevated inversion layer inhibits the downward transfer of momentum. As a result, the horizontal transport capacity of the stations in the west is poorer than that of the stations in the east, which is another reason for the observed spatial distribution of haze pollution.

ABLH and AAL depth
The ABLH, as a reflection of the layer dominated by turbulent motion, is a crucial parameter in air quality assessment. The ABLH was determined at 14:00 LT and 5:00 LT, corresponding to the time when the ABL was fully developed in the daytime and stabilized at night, respectively. As the CBL is usually formed in the daytime and the SBL is formed at night, we use the CBL and SBL below. The temporal variations of the average heights of six stations of the CBL and SBL during the observation period are shown in Fig. 7. The average CBL height is below 560 m during the three haze episodes, compared with 910 m during clear periods. The average SBL height is~280 m and 270 m during the haze episodes and clean periods, respectively. There is a significant decrease in the CBL height during haze pollution, which is associated with smaller sensible heat fluxes and may be attributed to cloudy weather and aerosol radiation effects, while the SBL height has little difference between haze and clean periods. As a consequence, it is mainly the suppression of CBL development that promotes the formation of haze pollution. Figure 8a shows a comparison between the ABLH and AAL depth. It can be seen that the consistency between the AAL depth and the ABLH is higher during the day than that at night. The nighttime AAL depth is obviously higher than the ABLH. As shown in Fig. 8b, we further compared the AAL depth at 20:00 LT and the CBL height on the same day. After rejecting the data points in the relatively clean atmosphere during the early stage of pollution, or in the nonstationary atmosphere state in the rapid cleaning period of pollution (most of the points in the lower right in Fig. 8b, there is a relatively good correlation between the nighttime AAL depth and the CBL height on the same day. The correlation coefficient is 0.74, which is significant at the significant level of 5%. Figure 9 gives an example that further illustrates the relationship between the AAL depth and the ABLH. This example indicates   that in the unstable CBL (at 14:00 LT), aerosols can be well mixed by vertical turbulent transport throughout the boundary layer, and the AAL corresponds well with the CBL. While in the SBL at night (20:00 and 23:00 LT), the stable layer is approximately one or two hundred meters thick near the ground. Due to the weak turbulent mixing in the stable layer, aerosols accumulate near the surface and have an increase in surface concentration. However, since the aerosols remain suspended in upper layer (known as the residual layer), the variation of AAL depth corresponds with the residual layer top at night. In other words, unlike the thermal structure, which collapses after sunset and rebuilds by surface radiation cooling at night, aerosols can remain suspended in the air and maintain their daytime vertical distribution in the residual layer at night. As a consequence, the evolution of the AAL depth is not comparable to the diurnal variation of the ABLH because the AAL depth is consistent with the CBL height due to sufficient turbulent mixing during the day, but suggests the presence of the residual layer at night. This feature of the vertical aerosol distribution makes it difficult to accurately retrieve the SBL height using lidars or ceilometers based on the distributions of substances 41,71,72 . In addition, considering only the effect of the ABL on the vertical diffusion of pollutants, the good consistency between the daytime ABLH and AAL depth occurs under the condition when the atmospheric motion is stationary and the turbulent mixing is sufficient that can make abundant pollutants from the ground distribute throughout the boundary layer. Therefore, using the daytime AAL depth retrieved by lidars to represent the CBL height also has preconditions.

DISCUSSION
From 26 November to 26 December 2019, an intensive field experiment was carried out simultaneously at six stations arranged in a cross shape in the North China Plain. Based on comprehensive observations, including both atmospheric profiles and surface meteorological elements, this study mainly focused on the following three questions. First, what are the impacts of the ABL structure on heavy haze pollution? Second, what are the characteristics of the spatial distribution of haze pollution and the regional ABL structure in this particular location of the NCP? Third, how does the AAL depth relate to the ABLH? The main results are as follows.
The meteorological elements and PM 2:5 concentration profiles indicate that the vertical distribution of pollutants is greatly influenced by the ABL structure. A persistent descending elevated inversion layer is crucial to the maintenance and exacerbation of heavy haze pollution. This stable layer traps aerosols beneath it by inhibiting vertical turbulent transport, and the decreasing bottom height forces aerosols to accumulate in a shallower layer, resulting in worsened air quality. This descending elevated inversion layer may be attributed to bouts of downdrafts generated by the intrusion of gusty cold air. With regard to the dynamic structure of the ABL, weak winds (speeds smaller than 2 ms −1 ) are dominant in the lower atmosphere during long-lasting haze pollution. The removal of pollutants is mainly due to the contribution of lowlevel jets which improve both the horizontal transport capacity and the vertical diffusion conditions. Furthermore, the aerosol accumulation layer corresponds to the water vapor-enriched layer, indicating the synchronous regional transport or local accumulation of both aerosols and water vapor.
The unique geographical location of the NCP is reflected in its particular regional ABL structure. Due to the nighttime drainage flow and warming effect induced by strong downdrafts, stations located in the west near the mountains have a colder surface and warmer upper air masses, resulting in a more stable stratification and worse diffusion conditions. Furthermore, due to the increased friction caused by the mountains, thicker layers with weaker winds also appear at the western stations. These differences in the ABL structure further contribute to the uneven spatial distribution of haze pollution, with higher pollution levels in the western areas near the mountains and less pollution toward the east.
Finally, the CBL height significantly decreases during haze episodes, with an average height lower than 560 m. In contrast, the SBL height experiences little variation between haze and clean periods, mostly within 200-300 m. This suggests that it is mainly the suppression of CBL development that promotes haze pollution. Moreover, the AAL depth is relatively consistent with the CBL height but much higher than the SBL height. However, high consistency is shown between the nighttime AAL depth and the CBL height on the same day. This finding reveals that the vertical distribution of aerosols mainly depends on daytime thermal turbulent mixing and is maintained at night. As a consequence, it is more suitable to determine the ABLH from the distributions of substances in the daytime, but this method is not applicable at night due to the impact of the residual layer.

METHODS Observation stations and instruments
The NCP, which is located in the northern part of eastern China, is surrounded by the Yanshan Mountains to the north, the Taihang Mountains to the west, and the Bohai Sea to the east (Fig. 1). As highaltitude terrain can block surface winds, a weak wind zone forms on the NCP 6,13 . Besides, the semienclosed terrain on the eastern leeward slope is influenced by remarkable downdrafts in winter 12 . Complex processes, such as mountain-plain breeze circulation, sea-land breeze circulation and the urban heat island effect [14][15][16][17] can affect the ABL structure in the NCP, which further affect the spatiotemporal distribution of air pollutants 18,19 . Some studies have found an inhomogeneous spatial distribution of pollution in the NCP 27,70,73,74 . To investigate the unique ABL structure in the NCP and better understand the influence of the ABL structure on regional haze pollution, an intensive field experiment was conducted from 26 November to 26 December 2019 at six observation stations in Hebei Province, China. As shown in Fig. 1, the six observation stations were organized in a cross shape centered on the Baoding station. Perpendicular to the Taihang Mountains, four stations were deployed from west to east, namely, Tuonan The instrumentation deployed at the observation sites is described as follows. Enhanced ground observations were arranged at the Tuonan, Baoding and Renqiu stations, and each site was equipped with a threedimensional sonic anemometer-thermometer to obtain turbulence data and meteorological factors in the surface layer. Radiosonde observations and surface pressure observations were carried out at all six stations. Detailed information on each site is summarized in Table 1.

Data acquisition and processing
The turbulence data and surface meteorological factors were detected by three-dimensional sonic anemometer-thermometer devices, including IGRASON (Campbell Scientific, Inc., USA) for Baoding and Renqiu stations and CSAT3 (Campell Scientific, Inc., USA) for Tuonan station. IGRASON integrates with a CO 2 =H 2 O gas analyzer which is absent from CSAT3, and therefore, there were no humidity observations at the Tuonan station. The original data were sampled at a frequency of 10 Hz and was averaged over an interval of 30 min.
The sounding data were obtained by a particulate sounding system, which comprises GPS radiosondes and portable particulate sensors. Detailed information on the sounding system has been described in Li Q. et al. 75 . The sounding data contained both meteorological elements (temperature, relative humidity, wind speed and wind direction) and PM 2 outliers from the original data and applied a moving average to the data. Considering the low ABLH in winter, we extracted the data from 0 to 2000 m and processed the data into a vertical resolution of 10 m.
The surface pressure data were collected by barometric pressure sensors (CS106, Campbell Scientific, Inc., USA). The observations were automatic and continuous with a temporal resolution of 10 min, and the original data were processed into averages with an interval of 30 min. The pressure at different heights was calculated based on the barometric height formula. Combined with the temperature and relative humidity observed by GPS sounding, the potential temperature and specific humidity were further calculated.
In addition to the data from our observations, we used the AQI data from the China National Envrionmental Monitoring Station. The hourly averaged AQI data were released in real-time and it can be downloaded from http://www.cnemc.cn/sssj/. Furthermore, the vertical velocity reanalysis data we used were downloaded from ERA5 (https://www.ecmwf.int/ en/forecasts/datasets/reanalysis-datasets/era5). The temporal resolution is 1 h and the horizontal resolution is 0.25°× 0.25°.

Determination of the ABLH and AAL depth
Because of differences in the thermodynamic properties and turbulent characteristics, the ABL structure is quite different between the daytime and nighttime. During the daytime, the CBL has an unstable stratification with active turbulence due to surface heating. While during the nighttime, the SBL characterized by a surface-based inversion layer is formed by surface radiative cooling, and intermittent turbulence often happens in it. The ABLH can be determined by the thermodynamic approach, that is, recognizing the boundary layer top according to the variation in the gradient of the potential temperature 76,77 . In the daytime, the potential temperature mixed nearly uniform in the ABL and has a large temperature gradient in the entrainment layer. We take the position of the entrainment layer as the CBL top. In the nighttime, the depth of the surface-based inversion layer is recognized as the height of SBL. Figure 10 is a schematic diagram of ABLH determination. We first calculate the potential temperature difference between 100 m and the surface to judge whether the boundary layer type is stable or unstable. If it is unstable, then we identify the location of entrainment layer by finding the peak height of potential temperature gradient greater than 10 K/km. If it is stable stratification, due to the potential temperature gradient decreasing upward from the ground, we identify the height where the potential temperature gradient is close to zero as the boundary layer top. As the average potential temperature gradient above 500 m is~5 K km −1 , we use 5 K km −1 as the threshold to find SBL top in practice. During the observation period, there was precipitation on 15 to 16 December, and thus, these two days were not considered.
The height determined from the distribution of substances essentially reflects the maximum vertical diffusion depth of aerosols, which is distinct from the height determined by meteorological elements 78,79 . To distinguish this height from the traditional boundary layer, which is derived from turbulent motion, we propose the aerosol accumulation layer to emphasize the properties of the vertical distribution of aerosols. According to the National Environmental Protection Standards of China, the air is polluted when PM 2:5 concentration is higher than 75 μg m −3 . Therefore, we define the AAL as the layer abundant in aerosols with PM 2:5 concentrations higher than 75 μg m −3 above the surface.

DATA AVAILABILITY
The AQI data used in this study are downloaded from http://www.cnemc.cn/sssj/. The reanalysis data used in this study are available from ERA5 (https://www.ecmwf.int/en/ forecasts/datasets/reanalysis-datasets/era5). The observational data used in this study are available from the corresponding author upon reasonable request (hsdq@pku. edu.cn).