Figure 1 shows the geographic coordinates of multi-platform sites, including one ground-based lidar detecting site (denoted as a star), three air quality monitoring sites (circles) and four AERONET sites (triangles). The ground-based Raman–Mie lidar site is located at the lidar lab of Beijing Institute of Technology in Beijing, China. The detected pure rotational Raman and elastic returns are used to obtain the vertical characteristic of aerosols. The selected three air quality monitoring sites around the lidar site include Xizhimen north, Wanliu, and Guanyuan. The PM2.5 mass concentration is one of the variables to be monitored. The data collected from four AERONET sites, including Beijing site, Beijing_RADI site, Beijing_PKU site, and Beijing_CAMS site, are used to acquire the AOT value at the lidar site by using statistical calculation. The distances between the lidar site and other ones range from 2.63 to 7.59 km. Moreover, the periods of all the downloading PM2.5 mass concentration data and AOT data are the same as the detecting time, between 13 December 2016 and 11 January 2017, of ground-based lidar site.

To obtain the PM and AOT values in the ground-based lidar site accurately and reliably, three air quality sites and four AERONET sites (Fig. 1) are selected for collecting data. According to the distance information between the lidar site and the selected sites, the PM and AOT values at the lidar site are calculated with the following statistical equations: PM=∑i=1nGiPMi∑i=1nGi=1,n=3, AOT=∑i=1mQiAOTi∑i=1mQi=1,m=4, where PMi represents the PM value of the selected three air quality sites supplied by the Beijing Municipal Environmental Monitoring Center (BJMEMC); AOTi describes the AOT value of the four AERONET sites; Gi and Qi denote the normalized weight function which is inversely proportional to the distance between lidar site and the selected sites. According to the definition of AOT, it can be obtained by the integration of aerosol extinction coefficient over the entire column with the expression of ∫0zαa(z)dz′, where αa(z) is the aerosol extinction coefficient (AEC) which is retrieved from ground-based Raman–Mie lidar data with some robust inversion methods (Ji et al., 2017). As shown in Fig. 2, it is believed that the AOT value deduced from ground-based lidar data is reasonable and reliable due to the excellent Pearson correlation coefficient (+0.87) and R2 value (0.75). Besides, AOT is classified as vertical haze parameter because of its representative significance to pollutant concentration at the vertical column.

The Up-Vis is defined as the horizontal visibility at different altitudes, which is classified as a horizontal haze parameter. According to the Koschmieder's formula (Larson and Cass, 1989; Lee and Shang, 2016), the Up-Vis at a certain altitude is calculated with the following equation: Vz=-ln⁡A/bextz, where A is the limiting contrast threshold for the average human observer, with the common value of 0.02 (Middleton, 1951). bext is the total extinction coefficient. According to the research of Song et al. (2003), the visibility impairment mainly depends on the light scattering extinction by particles in bext.

According to the observation and forecasting level of haze (QX/T 113-2010) and the requirements for human health (Jarraud, 2008; Han et al., 2016), when the Up-Vis at a certain altitude is about 5 km based on Eq. (), the haze thickness (HT) can be defined as the value of this altitude. Therefore, HT reflects the main region of high-concentration pollution and can be classified as vertical haze parameter.

The height of ABL is affected by the underlying surface and can be retrieved by detecting the rapid drop-off in extinction or backscatter coefficient between the free troposphere and the mixing layer as shown in the following equation (Flamant et al., 1997; Sawyer and Li, 2013): hABL=max∂αaz∂z.

Tang et al. (2015) indicated the ABL represents the atmospheric diffusion capacity in vertical direction, so it can be classified as the vertical haze parameter.

Figure 4 plots the hourly variation of haze parameters and meteorological elements during the first haze episode shown in Fig. 3a. The meteorological elements include PM2.5 mass concentration supplied by BJMEMC, relative humidity (RH), temperature, wind direction (WD), and wind speed (WS) supplied by China Meteorological Administration (CMA). It is shown that the maximum Up-Vis (about 7.1, 12.4, and 15 km at the altitudes of 0.1, 0.3, and 0.5 km, respectively) and the maximum ABL height (about 0.9 km) were obtained at 06:00 on 22 December 2016, where the variation trend is in contrast to the PM2.5 mass concentration. However, the peak and valley values of HT and AOT, respectively, occurred at 21:00 on 21 December 2016 and at 06:00 on 22 December 2016, following the same trend as the PM2.5 mass concentration. Influenced by the effects of RH, the high RH enhanced the photochemical transformation of secondary aerosols that leads to a higher concentration of fine-mode particles, which exacerbates the atmospheric elements, for example, impairment of Up-Vis, turbulence in ABL, and increase in HT and AOT (Hennigan et al., 2008). According to the topographic feature of Beijing, a strong north wind would accelerate the diffusion of pollutants which gradually make the haze pollution better after 22 December 2016. The error bars indicate data uncertainty, which probably originated from signals fluctuation by atmospheric variability and the inaccurate calibration parameters of the inversion method.

Similar results can be found in the other haze episodes shown in Fig. 5. The Up-Vis and ABL have a negative correlation with the tendency of PM2.5 mass concentration. The Up-Vis reached peak values of about 5, 9.3, and 13.6 km at the altitudes of 0.1, 0.3, and 0.5 km, respectively, in the daytime on 2 January 2017, where the Up-Vis corresponded to the PM2.5 mass concentration of 58 µg m-3 and a smaller RH of 55 %. On the contrary, the maximum HT and AOT of about 0.8 km and about 3.6 were obtained at 02:00 on 4 January 2017, which corresponded to the PM2.5 mass concentration of 561 µg m-3 and a larger RH of 97 %. In addition, the continuous moderate pollution after 5 January 2017 could be attributed to the strong north wind with a maximum wind speed of 3 m s-1 in the nighttime of 4 January 2017 and the weak south wind with a mean wind speed of about 1.3 m s-1 on 6 January 2017 (Han et al., 2016; Zhao et al., 2013). A higher PM2.5 mass concentration led to the increase in AOT, which was accompanied by the decrease in Up-Vis, as derived by Dong et al. (2017) from a combination of the Moderate-Resolution Imaging Spectroradiometer (MODIS) and the Multi-angle Imaging SpectroRadiometer (MISR) across Guanzhong Plain. Additionally, the error bars indicate data uncertainty with the same origination as Fig. 4.

To compare and analyze the difference of haze parameters on haze days and non-haze days, Fig. 6 presents the daily variation of Up-Vis, ABL, HT, and AOT with the meteorological elements. The haze days are shown in the areas highlighted in grey in Fig. 6. The following phenomena are concluded from Fig. 6: (1) the minimum Up-Vis values were about 1.5, 2.5, and 4.2 km at the altitudes of 0.1, 0.3, and 0.5 km, respectively. The Up-Vis on non-haze days was about 3–5 times higher than that on haze days. (2) The height of ABL was about 0.5 km on haze days and ranged from 0.6 to 0.9 km on non-haze days. (3) The trends that contradicted to the Up-Vis and ABL could be found in the results of HT and AOT. By combining meteorological elements, a lower Up-Vis and higher HT can be measured when PM2.5 and RH values were higher and the wind blew from the south. When the prevailing wind came from the north and the RH value decreased, the diffusion of pollutants was accelerated, which improved the air quality and enhanced the Up-Vis. A high RH may favor the local contribution of humidity-related physicochemical processing in haze pollution, so the Up-Vis decreased on haze days, which is similar to the research from Tang et al. (2015). In addition, the error bars in Fig. 6 have the same meaning and origin as that in Fig. 4.

As shown in Fig. 7, the correlation between PM2.5 mass concentration and haze parameters was established based on the 201 statistical samples in Figs. 4 and 5, which describe the impact of near-ground particle concentration on haze parameters in the northwest of downtown Beijing. Figure 7a and b plot the exponential reduction of the ABL and Up-Vis values when PM2.5 mass concentration increased, with R2 values at about 0.73 (mean value of 0.76, 0.81, and 0.62) and 0.62, respectively. Moreover, owing to the location of detecting sites (located in the center of Beijing) and the different influence of human activities on Up-Vis at individual altitudes, the correlations between surface PM2.5 and Up-Vis at altitudes of 0.3 and 0.5 km (0.81 and 0.76, respectively) are much stronger than the correlation between surface PM2.5 and Up-Vis at an altitude of 0.1 km (0.62). In Fig. 7a, with the decreasing of PM2.5 mass concentration, the Up-Vis at the altitude of 0.1 km gradually increases, but the Up-Vis at the altitudes of 0.3 and 0.5 km increases much faster as shown in the inserted table. The exponential correlation between ABL height and PM2.5 mass concentration is similar to the studies of Zhao et al. (2017) as shown in Fig. 7b. From Fig. 7c and d, it can be observed that the HT and AOT values increased linearly with the growing PM2.5 mass concentration, with the R2 values at 0.75 and 0.84, respectively. With the accumulation of pollutants, the aerosol column concentration and the PM2.5 mass concentration would increase, which aggravates the light scattering and absorption.

As shown in Fig. 8, the vertical transport of particles is acquired by comparing hourly variations of PM2.5 mass concentration and Up-Vis at different altitudes in certain periods. In Fig. 8(1), as the PM2.5 mass concentration near the ground decreased, the Up-Vis at the altitude of 0.5 km increased 3 h later than that at the altitudes of 0.1 and 0.3 km. This indicates pollutants might ascend and prevent the improvement of Up-Vis at the altitude of 0.5 km. In Fig. 8(2), the Up-Vis at the altitude of 0.5 km increased rapidly, while the Up-Vis at the altitudes of 0.1 and 0.3 km increased slowly 4 h later. This demonstrates that the delayed diffusion might result from the descent of pollutants. And the descent of pollutants caused the slow reduction of near-ground PM2.5 mass concentration during this period. Therefore, the delayed variations of Up-Vis between high altitude and low altitude indirectly reveal the influence of vertical transport of pollutants on variation of haze parameters.

According to the 201 statistical samples mentioned above, the correlations between vertical haze parameters (ABL, HT and AOT) and horizontal haze parameters (Up-Vis) are plotted in Fig. 9 to analyze the two-dimensional characteristic of haze phenomenon. Figure 9a shows a positive exponential correlation between ABL and Up-Vis, with R2 values of 0.44, 0.58, and 0.46 at the altitudes of 0.1, 0.3, and 0.5 km, respectively. Because the ABL represents the atmospheric diffusion capacity in vertical direction indicated by Tang et al. (2015), the increasing ABL would be accompanied with the increase in Up-Vis. However, when the HT or AOT values increase, the Up-Vis would decrease exponentially as shown in Fig. 9b and c. Compared with the studies of Dong et al. (2017), the similar anticorrelation can be inferred between visibility and AOT. And the exponential changes in Up-Vis and AOT or HT could be attributed to the rapid accumulation of aerosol particles near the surface. Table 1 shows the statistical gradient of Up-Vis at different altitudes changing with the vertical haze parameters. It is found that the Up-Vis at an altitude of 0.3 km changed faster than that at altitudes of 0.1 and 0.5 km. Therefore, through the analysis of the correlation between vertical haze parameters (ABL, HT and AOT) and horizontal haze parameter (Up-Vis), the haze characteristics could be well investigated in two dimensions.

According to the observation and forecasting levels of haze (QX/T 113-2010) supplied by CMA, there are four forecasting levels of haze: slight pollution, mild pollution, moderate pollution, and severe pollution (CMA, 2010). Table 2 provides the standard range of horizontal visibility on the surface (H-Vis) for different haze levels. When slight pollution occurred with the H-Vis of 5–10 km, the corresponding PM2.5 mass concentration is less than 60±20 µg m-3, the Up-Vis at the altitudes of 0.1, 0.3, and 0.5 km is larger than 6.5±0.3, 9±0.5, and 14±1 km, respectively, and the ABL is higher than 0.8±0.03 km. When mild pollution occurred with the H-Vis of 3–5 km, the minimum Up-Vis decreased to 3.8±0.2, 5.1±0.2, and 7.2±0.3 km at the altitudes of 0.1, 0.3, and 0.5 km, respectively. While the ABL would also decline, with the minimum value of 0.57±0.03 km. However, the AOT would increase from 0.4±0.05 to 1.5±0.1. When the H-Vis value is between 2 and 3 km, the haze level is classified as moderate pollution. The PM2.5 mass concentration changes from 150±30 to 300±40 µg m-3. The Up-Vis would decrease from the minimum value of mild pollution to 2.6±0.1, 3.7±0.2, and 5.2±0.2 km at the altitudes of 0.1, 0.3, and 0.5 km, respectively. Simultaneously, the HT of between 0.3±0.03 and 0.48±0.03 km could be obtained. Once the H-Vis is lower than 2 km, severe pollution would occur, with the corresponding PM2.5 mass concentration higher than 300±40 µg m-3. The Up-Vis would decrease further based on the minimum value of moderate pollution, and the turbulent ABL height could range from 0.42±0.03 to 0.5±0.03 km. Moreover, the HT and AOT would further deteriorated to larger than 0.48±0.03 km and 2.1±0.2, respectively, as shown in Table 2.