The CALIPSO ground-based lidar was used for calculation of BLHs over Wuhan, a megacity close to the Han and the Yangtze rivers. Wuhan is one of the most densely populated and industrialised region over central China (B. Liu et al., 2018b; L. Liu et al., 2018; Zhang et al., 2017). In the Wuhan area, the ground-based lidar stations are located at the State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University (30∘32′ N, 114∘21′ E) (Liu et al., 2017). Figure 1 shows the geographic distributions of the ground-based lidar. The black point represents the ground-based lidar. The black line represents the track of CALIPSO satellite. About matching principles of ground-based and space-borne lidar, the distance between CALIPSO and ground-based lidar stations is within 50 km. Meanwhile, the ground-based lidar data were obtained within 30 min of CALIPSO overpass times.

A ground-based lidar system was used for the detection of the atmospheric vertical profiles in Wuhan (Wei et al., 2015). The lidar system uses a pulsed Nd:YAG laser with 532 nm wavelength. The pulse rate of the laser was 20 Hz, and the laser energy was 150 mJ. The vertical resolution of the system was 3.75 m, and the acquisition frequency of the system was 20 Hz. Additional details of this lidar system can be found in previous studies. Given that the lidar signal is susceptible to the noise of background light during daytime, the lidar system was employed at night from 19:00 to 07:00 local time (LT). The ideal profile fitting method proposed by Steyn et al. (1999) is an effective method for delineating stable boundary layers. As this method can be successfully used for obtaining the BLH in ground-based lidar research, an ideal profile fitting method was used. The lidar data were collected from January 2013 to December 2017. After matching the CALIPSO data, the valid number of the ground-based lidar data was 21 cases.

The CALIPSO satellite is the first space-borne lidar optimised for aerosol and cloud profiling, which has a 532 nm channel (parallel and perpendicular polarisation) and a 1064 nm channel (Liu et al., 2009). This satellite can provide the total attenuated backscatter coefficient 532 and attenuated backscatter coefficient 1064 with a horizontal resolution of 1/3 km and vertical resolution of 30 m. Attenuated backscatter data (Level 1B) were used for testing the proposed algorithm. The cycle time of CALIPSO across the central China region is 16 days, and the crossing time of the satellite in Wuhan is 13:10 and 02:10 LT. The nighttime data have a higher SNR relative to daytime data (Winker et al., 2009; Guo et al., 2016b). The nighttime data were employed for this analysis for the matching of the ground-based data, and cases with cloud and dust were removed in this study. The data collection time was from January 2013 to December 2017. During this time, the total number of CALIPSO crossing Wuhan was 93. After removing the cloud cases, there were 49 valid samples.

Previous studies reported that the different particles are distributed in different vertical heights (B. Liu et al., 2018c; Sugimto et al., 2002). Most of the particles above the boundary layer are molecular particles, and the particles below the boundary layer are mainly aerosol particles, as shown in Fig. 2a and c, respectively. Therefore, we proposed a dual-wavelength algorithm that determines BLH on the basis of two-dimensional graphical distribution. The total attenuated backscatter coefficient 532 (TAB532) and attenuated backscatter coefficient 1064 (AB1064) were used to construct the two-dimensional graphical distribution. The specific steps are as follows:

Firstly, the TAB532 and AB1064 were employed for the construction of the sample sequence X(z). As shown in Fig. 2b and d, the TAB532 and AB1064 represent the aerosol vertical profile at 532 and 1064 wavelength measured by CALIPSO, respectively. The X(z) can be expressed as follows: X(z)=TAB532(z),AB1064(z), where z stands for the altitude of sample points; X(z) represents the coordinates of the sample point at the altitude of z; TAB532(z) and AB1064(z) represent the total attenuated backscatter (532 nm) and attenuated backscatter (1064 nm) value of the sample point at the altitude of z, respectively.

The sample sequence X(z) is shown in Fig. 3a. The colour bar is the altitude of sample points. The figure shows that TAB532 and AB1064 of blue points (the particles below the boundary layer) were larger than those of the red points (the particles above the boundary layer). According to this two-dimensional distribution, the sample sequence X(z) can be divided into two categories.

The k-means method was used for the classification of the sample sequence. Two centroid points (u1, u2) were randomly selected from the sample sequence. For each sample point of sample sequence X(z), the cluster C belonging to it is calculated as follows: c(z)=arg⁡min⁡jX(z)-uj2, where C(z) represents the cluster of sample point at the altitude of z, and uj is the centroid of cluster j (u1 or u2). For each cluster j, the centroid uj is recalculated as follows: uj=∑i=1m1c(i)=jx(i)∑i=1m1c(i)=j. Equations (3) and (4) are repeated until the centroids (u1 and u2) converge. The sample sequence is divided into two categories after the convergence. As shown in Fig. 3b, cluster2 (blue points) indicates the aerosol particles below the boundary layer, and cluster1 (red points) is the molecular particles above the boundary layer. Black cross represents centroid points. Meanwhile, the category sequence f(z), which changes with height, can be obtained and expressed as follows: f(z)=1,z∈cluster12,z∈cluster2, where f(z) is the category of sample point at the altitude of z. The noise points would affect the classification results due to the large noise of satellite data. Therefore, the noise points on the category sequence must be eliminated. The noise point was determined by comparing two points near the point. If the two points above and below this point belong to the same class, then this point should also belong to this category. The noise point can be filtered by f(z)=f(z-m),if:f(z-m)=f(z+m), where m represents the multiple of the vertical resolution, and the different values can be selected at different noise levels. When the horizontal smoothing number is small and the signal noise is large, the value of m can be set as 2; when the horizontal smoothing number is large, the value of m can be set as 1. According to the noise removal principle, the the category of noise point was judged as the cluster which is the same as the neighbouring particles. Hence, the noise points were removed, and the new category sequence F(z) was obtained as follows: F(z)=1,z>BLH2,z<BLH, where F(z) represents the category of the sample point at the altitude of z. BLH indicates the BLH result. Figure 3c shows the category sequence F(z), which contains the height information and shows evident variation at the top of boundary layer. Therefore, the maximum gradient of the category sequence F(z) is the top point of boundary layer. The BLH can be calculated by searching the maximum gradient, which can be expressed as follows: BLH=dF(z)max⁡. Following this process, the BLH was obtained based on the two-dimensional distribution of particles.

Figure 4 shows the flow chart of the GDM algorithm. Four calculation steps are available: establishing the sample sequence, particle clustering, filtering noise points, and maximum gradient searching. The error of input parameters is the main factor affecting the accuracy of the algorithm because these steps are quantitative calculations. According to the official description, the uncertainty of backscatter coefficient was 20 %–30 % (Winker et al., 2009). The total attenuated backscatter at 532 nm wavelength and the attenuated backscatter at 1064 nm wavelength were measured from CALIPSO. Therefore, the error of input parameters was 20 %–30 %. The error of the BLHs derived by the GDM algorithm is approximately 20 %–30 %. In addition, it needs to be noted that this method cannot be applied to low cloud and dust cases, because the boundary of cloud or dust would be misclassified to BLH. In addition, due to the effect of the nocturnal residual layer, the top of residual layer would be identified as the BLH by lidar system in some cases.

Figure 5 shows the case study of CALIPSO data with different horizontal smoothing numbers on 4 October 2013 over Wuhan area. Figure 5a, b, c and d represent the vertical profile of TAB532 derived from CALIPSO profile with a horizontal smoothing number of 1, 3, 15 and 30, respectively, and their BLH result was 1020, 980, 980 and 980 m, respectively. Figure 5a shows the vertical profile of TAB532 with a horizontal smoothing number of 1, in which the noise of satellite data was large. Such noise produced discrete sample sequence distribution. However, the category sequence and the BLH result (1010 m) can still be obtained. As shown in Fig. 5b, c and d, the noise of satellite data was reduced with the increase in horizontal smoothing number. Moreover, the vertical profile of TAB532 derived from CALIPSO profile was gradually becoming smooth. Such transformation resulted in significantly compact distribution of sample sequences (Fig. 5d), which were conducive to the classification of sample points. The category sequence was easily obtained from the classification calculation, and the result of the BLH converged to 980 m. In this case, the GDM algorithm can obtain the BLH result under different horizontal smoothing numbers.

Figure 6 shows the case study of CALIPSO data with different horizontal smoothing numbers on 12 February 2015 over Wuhan area. The BLH result of Fig. 6a, b, c and d was 532, 1280, 1370 and 1370 m, respectively. As shown in Fig. 6a, when the horizontal smoothing number was 1, the high noise of CALIPSO mixed together the sample points at different heights. In this condition, the category sequence cannot accurately distinguish between molecular and aerosol particles. Therefore, an inaccurate BLH result was obtained under this condition. When the horizontal smoothing number was added to 3 (Fig. 6b), the distribution of sample sequences significantly improved, and the obtained BLH result was 1280 m. Figure 5c and d show the vertical profile of TAB532 with the horizontal smoothing number of 15 and 30, respectively, in which the distribution of sample sequences gradually became compact. The result of the BLH converged to 1370 m. This result indicates that the GDM algorithm cannot be applied to the data with horizontal smoothing number of 1 in this case, but it can provide a relatively reliable result when the horizontal smoothing number was greater than 3.

The relationship between the horizontal smoothing number and BLH was investigated to determine the convergence of the BLH results. Figure 7 shows the relationship between the horizontal smoothing number and BLH under different cases. Figure 7a shows the case study on 4 October 2013. The result of the BLH converges to 980 m when the horizontal smoothing number was greater than 2. Figure 7b shows the case study on 12 February 2015. The result of the BLH converged to 980 m when the horizontal smoothing number was greater than 4. These results indicate that the PDM algorithm was not applied to the satellite data when the horizontal smoothing number was extremely small. However, this algorithm can provide a reliable result when the horizontal smoothing number is greater than 5.

In this section, we compare the results of BLH obtained by CALIPSO data with those retrieved by the ground-based lidar to verify the stability of the algorithm. The number of the ground-based lidar data matching CALIPSO data was 21. The results of BLH calculated by the MSD method were used as a reference.

Figure 8a and c show the total attenuated backscatter at 532 nm plot from CALIPSO on 7 October 2014 under the horizontal smoothing number 15 and 9, respectively. The black and blue line represent the BLH results calculated by GDM algorithm and MSD method, respectively. The red circle stands for the BLH result from ground-based lidar. Figure 8b shows the corresponding vertical profile of TAB532 derived from CALIPSO profile over Wuhan area under the horizontal smoothing number 15. The BLH results calculated by GDM algorithm, MSD method and ground-based lidar were 1220, 980 and 1250 m, respectively. Figure 8b shows the corresponding vertical profile of TAB532 under the horizontal smoothing number 9. The BLH results calculated by GDM algorithm, MSD method and ground-based lidar were 1220, 770 and 1250 m, respectively.

Figure 9 shows the correlation coefficients between the BLH derived from CALIPSO and ground-based lidar under the horizontal smoothing numbers of 1, 3, 6, 9, 12 and 15. The red and blue points represent the BLH calculated by GDM algorithm and MSD method, respectively. Figure 9a, b and c show the comparison of BLH between CALIPSO and lidar under the horizontal smoothing number of 1, 3 and 6. The correlation coefficients between the BLH derived by GDM algorithm and ground-based lidar were 0.12, 0.14 and 0.47, respectively. Meanwhile, the correlation coefficients between the BLH derived by MSD method and ground-based lidar were 0.1, 0.27 and 0.33. Figure 9d, e and f show the comparison of BLH between CALIPSO and lidar under the horizontal smoothing number of 9, 12 and 15. The correlation coefficients between the BLH derived by GDM algorithm and lidar measurements were both 0.72, and the correlation coefficients between the BLH derived by MSD method and lidar measurements were 0.54, 0.62 and 0.7, respectively. These results indicate that the performance of GDM algorithm was similar to the MSD method when the horizontal smoothing number was large. When the horizontal smoothing number was 9, the performance of GDM algorithm was superior to the MSD method. Moreover, the GDM algorithm and MSD method show a poor performance when the horizontal smoothing number was small.