The weather classification data were derived from the ERA-Interim data from 2014–2017. ERA-Interim (0.125∘ × 0.125∘) is a new reanalysis data from the ECMWF (European Centre for Medium-Range Weather Forecasts) after the ERA40, with 60 vertical layers, and partially overlaps with the ERA40 in time. However, significant progress has been made in data processing, for example, from the three-dimensional assimilation system (3D-Var) to the four-dimensional assimilation system (4D-Var). There are four soil moisture layers with the depth of 7, 28, 100, and 255 cm, respectively. The model contains 20 vegetation types, and the land surface parameters change with the change of vegetation types (https://apps.ecmwf.int/datasets/, last access: 7 June 2021).

The 850 hPa geopotential height field (30–50∘ N, 110–128∘ E) of ERA-Interim was used to classify the weather system. The meteorological elements at 850 hPa interact with the meteorological elements in the boundary layer. At the same time, the 850 hPa is evidently influenced by the free atmosphere, especially in the Beijing area, which can be regarded as the transition layer between local thermal circulation (valley wind, sea–land wind, and mountain–plain wind ) and the free atmosphere. In addition, the hourly relative humidity, visibility, and wind speed observed at the Beijing observatory (39.93∘ N, 116.28∘ E) were used in this study.

A 12-channel (5 water channels and 7 oxygen channels) microwave radiometer (Radiometrics, Romeoville, IL, USA) was used to measure the hourly relative humidity and temperature profile in the atmosphere. The microwave radiometer was installed in the Beijing observatory (39.93∘ N, 116.28∘ E) and was calibrated every 3 months. The wind profiles, including the wind speed and direction between 100 and 5000 m, are measured at the same station by a wind profiler. The wind profiler radar provides a set of profile data every 6 min at a detection height of ∼ 12–16 km, and hourly data were used in this study. In data analysis, Beijing local time (China standard time, CST) was used.

Hourly PM2.5 concentrations at 12 national stations and the daily air quality index (AQI) in the Beijing are available from http://zx.bjmemc.com.cn/getAqiList.shtml?timestamp=1621574187545 (last access: 7 June 2021). Surface PM2.5 mass concentrations were measured by the tapered element oscillating microbalance method. The measurements were calibrated and quality controlled according to the Chinese environmental protection standard (HJ 618-2011).

As this study focuses on episodes of heavy haze pollution, we first defined the criteria. Haze is defined by the relative humidity and visibility. Considering that haze pollution mainly refers to reduced visibility caused by fine particulate matter, as well as taking into account the effects of the pollution levels and duration, the screening criteria for heavy haze pollution were still based on the AQI, PM2.5 concentration, and the duration of low visibility. The specific criteria of a haze pollution event can be defined as follows: the AQI reaches a moderate pollution level (AQI ≥ 150) for more than or equal to 3 d in which at least 1 d reaches the heavy pollution level (AQI > 200). The primary pollutant is PM2.5 in the Beijing area. As defined by the AQI, the 24 h average concentration of PM2.5 must be above 115 µgm-3 for more than 3 consecutive days and above 150 µgm-3 for at least 1 d. At the same time, the accumulated time of horizontal visibility, that is, less than 5 km, has a duration of at least 12 h each day at the Beijing observatory station.

Based on these criteria, 32 events (125 d) were screened for heavy haze pollution in Beijing between 2014 and 2016. Eight events occurred in spring and summer while 24 events were concentrated in autumn and winter, with 32 events accounting for 75 % of the events that occurred during the study period (2014–2016). We collected ground-based routine meteorological observation data in North China: L-band radar second-order sounding data (including wind, temperature, and humidity), wind profile data, ceilometer data, and tower data during these events.

The 925 hPa geopotential height field is affected by both synoptic and local circulations, which can simultaneously reflect the variation characteristics of the weather system and boundary layer. Thus, the 925 hPa geopotential heights of all pollution events were analyzed in this study by using the 6 h ERA-Interim reanalysis data. With 500 samples (four times each day in 125 d), the rotated empirical orthogonal function (REOF) was used to determine which mode the pollution events belong to according to the characteristic values of the different pollution events (Paegle and Mo, 2002; Li et al., 2009). Since Lorenz (1956) introduced empirical orthogonal function (EOF) analysis to atmospheric science, this simple and effective method has been widely used in atmospheric, oceanic, and climatic studies. The essence of EOF analysis is to identify and extract the spatiotemporal modes that are ordered in terms of their representations of data variance (Lian and Chen, 2012). In the empirical orthogonal function (EOF) analysis, the first few main components are the focus of the analysis element variance, such that the EOF method can highlight the entire correlation structure of the analysis element. However, the local correlation structure is not sufficient, which is a defect of the pollution weather classification based on the EOF. The spatial patterns (EOFs) and the temporal coefficients of these modes are orthogonal. This orthogonality has the advantage of separating unrelated patterns, but it sometimes leads to the complexity of spatial structure and the difficulty of physical interpretation (Hannachi, 2007). Based on the EOF analysis, the REOF transforms the load characteristic vector field into a maximum rotation variance, as a result of which each point in the rotation space vector field is only highly correlated with one or a few rotation time coefficients. Previous studies have shown that REOF analysis can avoid non-physical dipole-like EOF analysis patterns, which often occur when known dominant patterns have the same symbols in the region (Dommenget and Latif, 2002). REOF analysis outperforms EOF analysis in reconstructing spatially overlapped modes, and this superiority is stable, which does not change or decline with the number of modes, the spatial scale of the signal, and the degree of rotation (Lian and Chen, 2012). Thus, the high load value areas are concentrated in smaller areas, while the remaining areas are relatively small and nearly 0, highlighting the pattern and characteristics of the abnormal distribution of elements (Paegle and Mo, 2002; Chen et al., 2003); the classification of heavy pollution weather types based on this method is more consistent with the requirements of this study. Pollution weather types were classified by the REOF method to analyze the differences in the structures of the pollution boundary layer.

In this study, the 925 hPa geopotential height was used to classify the pollution weather types into four categories with the REOF method, as shown in Fig. 1: (a) type 1, that is, influenced by southerly winds at the rear of the high-pressure system; (b) type 2, that is, influenced by easterly winds at the bottom of the high-pressure system; (c) type 3, that is, a weak downdraft effect in the high-pressure system; and (d) type 4: no significant weather system. In this study, we observed 125 d of heavy polluted weather. Among these days, type 1, type 2, type 3, and type 4 had 67, 27, 21, and 10 d, respectively (Fig. 2), where the four weather types accounted for 53.6 %, 21.6 %, 16.8 %, and 8.0 % of the total sampled weather event days, respectively. The total interpretation variance of the four types for all events was 97.8 %, while the independent interpretation variance was 43.69 %, 33.68 %, 16.51 %, and 3.92 %, respectively (Fig. 2). This indicates that an objective weather classification can effectively obtain the main feature information of the pollution weather types.

As shown in Fig. 1, the Beijing area is located toward the west of the high-pressure system that has its center located in the sea. The low-pressure system is located in the northern Hebei province for type 1, where southerly winds control the 925 hPa, which is favorable for the regional transportation of pollutants. Type 1 is similar to the results of pattern 2 and patter 4 by Zhang et al. (2016) accompanied by regional transmission characteristics. Type 1 is also similar to the results of type 1 by Miao et al. (2017), with southerly winds throughout the layer. When type 2 appears, the Beijing area is located at the bottom of the high-pressure system in Northeast or North China. In the plain area, the sea level pressure in the eastern part of Beijing is higher than that in the central Beijing area, such that there is an evident pressure gradient. Due to pressure-gradient forcing, the boundary layer appears within the easterly wind component while the easterly wind speed is smaller, which leads to pollutant convergence into the plains along the Taihang Mountains. When type 3 appears, the high-pressure center is located in the middle of Mongolia, where Beijing is in the front of the weak high-pressure system, with a northwest current at 925 hPa. However, the wind speed is lower than that affected by strong cold air, because of which it is difficult to penetrate the lower layer of the boundary layer and the wind can only exist in the upper atmosphere of the boundary layer. When type 4 appears, western Mongolia is a high-pressure region and southern Hebei province is a low-pressure area, where there is only a low-pressure system with a smaller spatial and temporal scale. The synoptic-scale low-pressure system is already located over the sea in the eastern Jianghuai region, showing that the high and low pressures corresponding to the synoptic-scale system are far from the Beijing area, which results in a weak synoptic-scale pressure gradient in Beijing and the surrounding areas (Fig. 1d). Most areas in North China do not have strong weather systems, and the average wind speed in the boundary layer is smaller, which is favorable to the formation and maintenance of the local circulation considering the topography in the Beijing area (Fig. 1i). The wind speed of type 4 in the lower boundary layer is more difficult to regulate via the evolution of the wind field based on the effect of descending momentum. Therefore, the dynamic pollutant process in the boundary layer in type 4 is more related to the local circulation.

The vertical structure of the atmosphere is very important for the formation and evolution of extreme haze events. The vertical thermal and dynamic structures of four weather types are investigated in three-dimensional view. Figures 3 to 6 presented the vertical distribution of temperature, wind, and RH, respectively. The temperature in Fig. 3 and vertical speed profiles in Fig. 5 are averaged for each weather type by using the 6 h ERA-Interim reanalysis data, respectively. The hourly mean wind profiles in Fig. 4 are observed at the Beijing observatory, and the hourly mean relative humidity in Fig. 6 is measured with a microwave radiometer at the same site. According to the classification of weather type, the spatiotemporal average analysis of the observed data is carried out. To classify the pollutant regimes according to the various meteorological features, we summarized relevant thermodynamic and dynamic parameters in Table S1.

Figure 3 shows that the strong inversion is located at 800–900 hPa for type 1. In type 2, easterly winds with low temperatures influence the temperatures below 800 hPa, where a cooling layer appears at 900 hPa, with the height of inversion between 700 and 800 hPa. The inversion height for type 3 is the lowest among the four types due to the sinking motion, where the inversion is mainly below 900 hPa, which causes a rapid decline in the atmospheric capacity. The atmospheric structure is also relatively stable in type 4, whose inversion structure is similar to type 2. However, the inversion intensity (0.4 ∘C) in type 4 is weaker than that in type 2 (0.7 ∘C), and the wind speed is also small in type 4.

As shown in Fig. 4, the basic flow is the southerly wind below 2000 m in type 1, where a southwest wind appears from 500–2000 m. The south wind is below 500 m between 04:00 and 20:00 CST, and the easterly wind appears at other times. The south wind speed below 500 m is 4–6 ms-1, which is higher than the easterly wind (2–4 ms-1). In type 2, the basic flow above 1000 m is westerly wind, where the layer between 500 and 1000 m is a weak wind layer. We note that the wind velocity in this layer is the smallest when there is an increase in the easterly component below 500 m. This indicates that the weak wind layer is the wind shear transition layer between the westerly wind above 500 m and the easterly wind below 500 m. The easterly and westerly winds cancel each other out at this height and form a small wind velocity layer. From 04:00 to 20:00 CST, southerly winds appear below 500 m while we observe the appearance of easterly winds at other times. The space–time structure of the wind field below 500 m was similar to that of type 1, but the southerly wind speed was lower than in case of type 1. In type 3, the wind above 500 m originates from the northwest from 04:00 to 14:00 CST. At altitudes below 500 m, the wind is southerly during these hours and northerly at other times. Whether it is southerly or northerly, the wind speed is smaller. Mountain–plain wind in the Beijing area causes this diurnal and nocturnal circulation of the wind field. In type 3, the wind velocity below 500 m is less than that of type 1 and type 2 because the basic flow is northerly, where northerly wind is superposed onto the plain wind (southerly), which may weaken the southerly wind speed. The observed data are the superposition results of two-scale wind fields (i.e., local circulation and synoptic airflow). Westerly or weak northerly winds above 1000 m in type 4 control the atmosphere, where the wind velocity below 1000 m is significantly weak. For the majority of the time, the wind velocity is less than 4 ms-1, but the mountain–plain diurnal cycle wind can still be observed from the diurnal variation in the wind direction. From 08:00 to 18:00 CST, the wind is southerly while mainly northerly at night. Weak wind speeds last for a long period in the boundary layer of type 4, because of which the local thermal and dynamic conditions can become the main factors that affect the spatiotemporal distribution of haze pollutants in Beijing.

Figure 5 shows that, above 700 hPa, type 1, type 2, and type 4 are ascending movements. The maximum of the synoptic-scale ascending movement appears in 900–950 hPa. With an increase in height, the intensity of the ascending movement gradually weakens, whereas in type 3, below 750 hPa can be characterized as a sinking movement. The intensity of the sinking movement increases gradually with decreasing pressure, where the maximum of the sinking movement appears at 900–950 hPa. The intensity of the subsidence movement from this layer at 900–950 hPa to the ground decreases a second time. Therefore, the sinking movement affects the inversion layer of type 3, where the height of the inversion layer is the lowest of all types, resulting in type 3 characterized by the smallest atmospheric capacity among the four types.

Based on Fig. 6, the relative humidity profiles for the four weather types have both similarities and differences in their space–time structures. The similarities in the four types are the increased and decreased relative humidity below 1000 m during the night and day, respectively, with a reverse in the relative humidity appearing at an altitude about 500 m during the day. The relative humidity of the surface layer decreases daily from 10:00 to 20:00 CST with an increase in the solar radiation. The thickness of the dry layer in the surface layer increases continuously, reaching its maximum height at ca. 14:00 or 15:00 CST every day, but the maximum height of the dry layer does not exceed 500 m. The top of the dry layer is the reverse of the relative humidity layer. Above 1000 m, the relative humidity of the other three types, except type 2, decreases significantly during the day. However, the relative humidity increased evidently in type 4 above 2000 m. As mentioned in Sect. 3.1, in type 4, Beijing is located between a high pressure and a low pressure and in the front of the weak frontal zone. Stratus clouds with high stability are located in the front of the weak frontal zone above 2000 m, so relative humidity above 2000 m is higher.

The difference in the relative humidity field among the four types can be summarized as follows. The average relative humidity below 1000 m is higher than that above 1000 m. The inverse relative humidity structure appears below 500 m in type 2 and type 3 from 00:00 to 05:00 CST, with a maximum relative humidity center of more than 90 %. Above 500 m, the relative humidity also increases from 05:00 to 12:00 CST. The relative humidity structures of type 1, type 2, and type 3 all contain a baroclinic structure from lower to higher levels, where the baroclinic structure in type 2 is more evident because the basic flow in type 2 is westerly, which reflects the baroclinic characteristics of the atmosphere in the mid–high latitudes of East Asia. The basic flow is generally westerly in this area, where type 1 and type 3 are more typical of the disturbances in the northerly and southerly wind in the westerlies, which is the fluctuation feature of the basic flow (Fig. 6). The relative humidity profile in the pollution boundary layer formed under the condition of wave–current interaction in the atmosphere.

Type 2 has strong westerly characteristics below 3000 m (Fig. 4), which reflects more baroclinic characteristics in the atmospheric vertical structure for the westerlies. Based on the analysis of the wind field, type 4 is characterized by an average wind speed that is the weakest among the four types. Three important factors determine the baroclinicity, that is, the density gradient, the pressure gradient, and the intersection angle between the density surface and pressure surface. This may be an important factor for why the relative humidity field has more barotropic characteristics. From the analysis of the baroclinic and barotropic characteristics, we can observe that the weather systems of type 1, type 2, and type 3 have a significant influence on the accumulation and transport of pollutants in the Beijing area. The mountain–plain wind in type 4 can occur due to weakening in the weather system (Fig. 4).

Based on the characteristics of the circulation field and the vertical thermodynamic structure for the four weather types, we established conceptual models of the boundary layer structure under the influence of the four pollution weather types. Because the vertical axes are different for the wind profile and temperature profile, we chose the pressure axis, which is widely used in meteorology, to make conceptual model. In the Beijing area, 700, 850, and 925 hPa layers are generally located at a height of about 3000, 1500, and 800 m, The four types are as follows: (a) type 1 – southerly transport, (b) type 2 – easterly convergence, (c) type 3 – sinking compression, and (d) type 4 – local accumulation (Fig. 7). When type 1 appears, the Beijing area is located at the rear of the high-pressure system, consistent with southerly winds throughout the atmosphere (Figs. 1e and 4), and multilayer inversion occurs in the boundary layer (Fig. 3). Under the influence of a southerly wind, haze pollutants accumulate in front of the Yan and Taihang Mountains. The air pollutants in the Hebei region have evident regional transport features (Fig. 1). When type 2 appears, the Beijing area is located at the bottom of the high-pressure system, where the air above 850 hPa (about 1500 m in Beijing) is a westerly wind, with easterly winds below 850 hPa. Under the influence of easterly winds below 850 hPa, haze pollutants tend to accumulate in front of the Taihang Mountains. The cross-mountain air mass flows from west to east, preventing the further dispersion of air pollutants in front of the Taihang Mountains. When type 3 appears, a weak high-pressure system controls the Beijing area. A weak subsidence northwest flow influences the atmosphere above 850 hPa, which further compresses the capacity of the atmosphere to absorb pollutants in the boundary layer. The southerly wind at 850 hPa is favorable for pollutant transportation in the region and accumulation in front of the Yan and Taihang Mountains. The atmospheric vertical structure in the high-level northwest wind and low-level southward wind provides excellent conditions for the stability of atmospheric stratification with respect to dynamic conditions and a thermal structure. The 850 hPa southerly winds favor regional pollutant transport and their accumulation in the area along the Yan and Taihang Mountains. The atmospheric vertical structure of the high-level northwest wind and low-level southerly wind provides excellent conditions for stratification stability in terms of dynamic–thermal structures because southerly wind at 850 hPa is warm advection, where advection inversion can form in the boundary layer, while weak subsidence above 850 hPa can cause subsidence inversion. These two inversion mechanisms are coupled at the interface between the northwest wind and southerly wind, resulting in stable atmospheric stratification. When type 4 appears, there is often no evident synoptic-scale system surrounding Beijing, with a weak pressure gradient above 850 hPa. Therefore, the average wind speed is weak. The most important local circulation in Beijing, that is, the mountain–plain wind, begins to form in the boundary layer and plays an important role in the spatial and temporal distribution of atmospheric pollutants, with the wind direction continuously shifting from the south to the north. The air pollutants accumulate near the terrain convergence line formed by the mountain–plain wind. The terrain convergence line also swings from north to south, such that air pollution in the Beijing area often appears as a “different sky” relative to a clean sky in the north and a polluted sky in the south.