Two-wavelength Lidar inversion algorithm for

Journal of Quantitative Spectroscopy & Radiative Transfer 206 (2018) 117–124

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Two-wavelength Lidar inversion algorithm for determining planetary boundary layer height Boming Liu a, Yingying Ma a,b,∗, Wei Gong a,b, Yang Jian c, Zhang Ming a a

State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing (LIESMARS), Wuhan University, Wuhan 430079, China Collaborative Innovation Center for Geospatial Technology, Wuhan 430079, China c Faculty of Information Engineering, China University of Geosciences, Wuhan, Hubei 430074, China b

a r t i c l e

i n f o

Article history: Received 8 September 2017 Revised 7 November 2017 Accepted 7 November 2017 Available online 8 November 2017 Keywords: Lidar Aerosol Color ratio Depolarization ratio Planetary boundary layer

a b s t r a c t This study proposes a two-wavelength Lidar inversion algorithm to determine the boundary layer height (BLH) based on the particles clustering. Color ratio and depolarization ratio are used to analyze the particle distribution, based on which the proposed algorithm can overcome the effects of complex aerosol layers to calculate the BLH. The algorithm is used to determine the top of the boundary layer under different mixing state. Experimental results demonstrate that the proposed algorithm can determine the top of the boundary layer even in a complex case. Moreover, it can better deal with the weak convection conditions. Finally, experimental data from June 2015 to December 2015 were used to verify the reliability of the proposed algorithm. The correlation between the results of the proposed algorithm and the manual method is R2 = 0.89 with a RMSE of 131 m and mean bias of 49 m; the correlation between the results of the ideal profile fitting method and the manual method is R2 = 0.64 with a RMSE of 270 m and a mean bias of 165 m; and the correlation between the results of the wavelet covariance transform method and manual method is R2 = 0.76, with a RMSE of 196 m and mean bias of 23 m. These findings indicate that the proposed algorithm has better reliability and stability than traditional algorithms. © 2017 Elsevier Ltd. All rights reserved.

1. Introduction The planetary boundary layer (PBL) is the layer of the Earth’s surface atmosphere, which is directly influenced human activity, and by surface atmospheric conditions [21]. The PBL has a considerable impact on local and regional environmental health and is important in weather forecasting model [19]. The heating process of solar radiation for the surface is also achieved through PBL dynamics. Furthermore, atmospheric activity in the PBL will affect cloud nuclei propagation and pollutant dispersion [6]. Therefore, the PBL is extremely significant for environmental health and human activities. It is also essential for conducting continuous observation of the boundary layer height (BLH) with accurate means of detection. The vertical structure of the atmospheric boundary layer includes the near-surface layer, mixed layer and entrainment layer [21]. Aerosol particles are abundant within the boundary layer. Moreover, there is free atmosphere with mostly atmospheric molecules and few aerosol particles above the boundary layer. Currently, a variety of remote sensing detection technologies are used ∗

Corresponding author. E-mail address: [email protected] (Y. Ma).

https://doi.org/10.1016/j.jqsrt.2017.11.008 0022-4073/© 2017 Elsevier Ltd. All rights reserved.

for boundary layer observation, including acoustic (sonic detection and ranging), optical (Lidar, ceilometers) and electromagnetic (radiosondes, Doppler radar) remote sensing [22]. Radiosonde is the most common measurement technique used for thermodynamic profiles. Radiosonde data can be used to determine BLH based on the vertical profiles of meteorological parameters [27]. However, the spatial resolution of this method is very low. The Lidar system has become a major means in the study of the boundary layer because of its active remote sensing equipment, which have a high temporal and spatial resolution. It can be used to investigate the evolution, optical and physical properties of the main components of the atmosphere [5,15,18]. Traditional Lidar algorithms depend on the aerosol concentration to calculate BLH. The maximum gradient position is regarded as the BLH. The Lidar algorithm for retrieving the BLH mainly includes the gradient method [11], wavelet covariance transform (WCT) method [2], and ideal profile fitting method [12]. The gradient method defines the maximum gradient position of the aerosol profile as the top of the boundary layer. WCT method can reduce the impact of noise because the operator can choose an appropriate base function and set an appropriate threshold. The ideal profile fitting method, developed by Steyn et al. [23], is an effective method for delineating well-mixed boundary layers. These methods are based on the single wavelength Lidar signal to

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calculate BLH. This means that those methods detect the BLH using aerosols as tracers, and that BLH is inferred from the aerosol concentration profile [1,5,13]. However, when the vertical distribution of aerosols becomes nonuniform or is affected by multi-layer aerosols, determining BLH accurately using these Lidar algorithms becomes difficult [24,25]. Therefore, more robust and effective algorithms are needed to alleviate this problem. In recent years, the multi-wavelength Lidar has been widely used in atmospheric research. Aerosol color ratio and depolarization ratio can be obtained through dual-wavelength information. Sugimoto [20] investigated dust and anthropogenic aerosol plumes by using two-wavelength polarization Lidar, and showed that the properties of atmospheric particles differ at different heights. Burton [3] indicated that different types of aerosols have different color ratio and depolarization ratio. Groß [10] classified aerosols based on airborne high spectral resolution Lidar observations, and found that the same aerosol type can be together in a cluster. Lu [17] analyzed the atmospheric vertical characteristics based on a two-wavelength Lidar inversion algorithm. The multi-wavelength information can reduce the parameters of the hypothesis in atmospheric studies. For this reason, multi-wavelength information can be used to calculate BLH. In the current research, we proposed a two-wavelength Lidar inversion algorithm to determine BLH based on the particle distribution. The algorithm is called the particle distribution method (PDM) in following text. The aerosol color ratio and depolarization ratio were used to establish the particle distribution, which were then used to retrieve BLH. Next, the algorithm was used to determine the BLH under different boundary layer mixing state. Experimental results demonstrate that the PDM algorithm is more stable in determining the BLH compared with traditional methods. In particular, it can identify the boundary layer accurately under weak convection condition where the traditional methods cannot be applied. Finally, experimental data from June 2015 to December 2015 verified the stability of the algorithm. The results indicate that the new method not only possesses better feasibility than traditional methods, but also maintains comparable stability. 2. Instrumentation The two-wavelength polarization Lidar system used in this study is located at Wuhan University (114°21 E, 30°32 N), China, on the roof of the Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing. The instrument is positioned 39 m above sea level and is surrounded by buildings [26]. The twowavelength polarization Lidar system consists of a laser transmitter system, a receiving telescope, and data acquisition and processing sub-systems. The Lidar transmitter functions at 532 and 355 nm with the aid of a ND: YAG pulse laser. The signals are detected by the photomultiplier tubes (PMTs) and are fed into an amplifier. The outputs of the amplifier are connected to a PC-based data acquisition system. The system provides a backscatter signal with a temporal resolution higher than 1 s and a vertical spatial resolution higher than 7.5 m. In terms of instrument calibration, the channel gain constant is measured every day before signal acquisition begin. We cover the receiving telescope and construct the system in normal working conditions. When the system is in a stable working state after five minutes, the data collected by Licel are used as the channel gain constant. Then, the acquired signal subtracts the gain constant to correct the acquired signal. The 45°-calibration with a polarizing sheet filter was applied to calibrate the depolarization channels under a cloudless weather condition [9]. A polarizing sheet filter was placed before the polarizing prism when calibrate the depolarization channels. According to rotate the angle of polarizing sheet filter, the polarizing signal from the parallel (//) or perpendicular (⊥) channel could be obtained. The ratio of the sig-

Fig. 1. Scatter plots of color ratio and depolarization ratio on 7 December 2015. The color bar represents the altitude information. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

nal intensity of the parallel and perpendicular channel is the calibrated constant of the depolarization channel. Additional details can be seen in a previous study [16]. Experimental data acquired from the Wuhan University ground-based Lidar system from June 2015 to December 2015 tested the proposed algorithm. 3. Methodology 3.1. Theory The development of Lidar system provided the more wavelength information in the study of the boundary layer. Sugimoto’s [20] research shows that atmospheric particles at different heights have different color ratio and depolarization ratio. Our previous research indicates that particles with large color ratio are distributed in the near ground (below 2 km); the distribution of the depolarization ratio is uniform over the vertical structure [16]. Fig. 1 shows the relationship between color ratio and depolarization ratio. The color bar represents the altitude. The distribution shows that different particles are distributed in different areas. Most of the particles in the upper atmosphere (above 1500 m) are molecular particles, and are therefore concentrated in the red area with a low color ratio. However, atmospheric particles near the ground (below 10 0 0 m) are mainly aerosol particles, and are concentrated in the black area, with a high color ratio. Similar particles gather together. Therefore, we aimed to determine the top of the boundary layer based on the particles distribution. 3.2. Method An algorithm based on the particles distribution was proposed to calculate the top of the boundary layer. Fig. 2 shows the flowchart of the PDM algorithm. First, the color ratio and the depolarization ratio are used to form the sample sequence x(i). Second, according to the clustering algorithm, the sample sequence is divided into two categories. The categories sequence f(i) is then used to calculate the BLH. Finally, the centroid of the cluster is employed to confirm the threshold value that will be used to filter the point of error. The more detailed procedure is as follows: The single channel Lidar equation can be written as ([7,8]; 1984):

P (i ) = C P0 i−2 [β m(i ) + β a(i )] exp[−2



0

i

[α m(i ) + α a(i )]di]

(1)

where i is the altitude, P(i) represents the received Lidar signal, C is a channel calibration constant, P0 is an output pulse energy, β m (i)

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into two categories. Cluster 1 is the molecular class above the boundary layer, cluster 2 is the aerosol particles below the boundary layer. Moreover, the categories sequence f(i), which changed with height, could be obtained. It can be written as:



f (i ) =

1, 2,

i > BLH point i < BLH point

(6)

where f(i) represents the category of the sample point i. BLHpoint is the sample point at the top of the boundary layer. The f(i) is changed with height, and it has obvious change at the top of boundary layer. Therefore, the maximum gradient in the categories sequence f(i) is the height of the boundary layer. The BLHpoint can be obtained based on the categories sequence f(i), which can be written as:

BLHpoint = |d[ f (i )]|max

Fig. 2. Flowchart of the PDM algorithm based on particles clustering.

and β α (i) are the backscattering coefficient of the aerosols and molecules at slant range i respectively, α m (i) and α α (i) are respectively the extinction cross sections of the aerosols and molecules at range i. On the basis of the Lidar equation, we can obtain the backscattering coefficients (β 532 and β 355 ) of 532 and 355 nm channel; these backscattering coefficients are used to calculate the depolarization ratio and color ratio. Color ratio is the ratio of backscattering coefficients at 355 and 532 nm channel. Depolarization ratio is the ratio of the backscattering coefficients at 532 nm parallel (//) and 532 nm perpendicular (⊥) channel, respectively. The depolarization ratio and color ratio are expressed as follows [16,22]:



DR(i ) = k1 · ββ532 ⊥((ii))

CR(i ) = k2 ·

532//

β532// (i )+β532⊥ (i ) β355 (i )

(2)

where β 355 , β 532  and β 532⊥ represent the 355 nm, 532 nm parallel and 532 nm perpendicular channel backscattering coefficient respectively; k1 and k2 are the ratio of the channel constant. The color ratio and the depolarization ratio are used to form the sample sequence x(i):

[x(i )] = [(DR(i ), CR(i ))]

(3)

where x(i) represent feature value of the sample point i; CR(i) and DR(i) represents the color ratio and depolarization ratio value of the sample point i, respectively. The x(i) can be understood as the coordinates of the sample point in the two-dimensional picture. Randomly select two centroids from the sample sequence as u1 , u2 . For each sample point x(i), calculate the cluster C where it should belong to [14]:



2

c (i ) = arg min x(i ) − u j  j

uj =

i=1

thr = (u1 +u2 )/2

(8)

where u1 and u2 represent the centroid of cluster 1 and 2, respectively. thr represents the mean value of the two centroids. When the number of BLHpoint is greater than 1, each BLHpoint is compared with the threshold, and the closest point to the threshold is the final BLHpoint . Finally, the BLH can be determined. 3.3. Error analysis Errors in BLH retrieved from the two-wavelength Lidar inversion algorithm are due to the variability of the depolarization ratio and the color ratios. Since the depolarization ratio and color ratio is obtained from Eq. (2), errors on the backscattering coefficients will affect the variability of the depolarization ratio and color ratios. When calculated the backscattering coefficients from the Eq. (1), it need to assume the Lidar ratio. Therefore, the errors affecting the backscattering coefficients are mainly the results of the error in Lidar ratio. Liu et al. [16] noted that the standard deviation of our assumed Lidar ratio is approximately 10–20%. Moreover, according to the error estimation described in the Freudenthaler’s paper (2009), there is approximately 5% error in our Lidar calibration of the depolarization channels. Therefore, the uncertainty for the BLH result calculated by the two-wavelength Lidar inversion algorithm is approximately 15–25%. 4. Results and discussion

1{c (i ) = j}x(i )

i=1 m 

where BLHpoint denotes the sample point at the top of the boundary layer. With this method, the primary boundary layer height was determined based on the clustering. The aerosol layers change constantly and cannot be maintained in a well-mixed state because of the complexity of atmospheric motion. Consequently, large differences between different aerosol layers occur as well. These factors may lead the algorithm to identify the junction point of the aerosol layer as the top of the boundary layer, and reduce the robustness of the algorithm. To account for this problem, the threshold method is used to filter the error points and produce results that are more accurate. We define thr as the threshold value. The equation can be expressed as:

(4)

where C(i) represent the cluster of sample point i, and uj is the centroid of cluster j (u1 or u2 ). For each cluster j, recalculate the centroid uj : m 

(7)

To verify the performance of the PDM algorithm, three different cases were tested. Moreover, the experimental data from June 2015 to December 2015 are used to assess the stability of the proposed algorithm.

(5) 1{c (i ) = j}

Repeat the Eqs. (3) and (4) until the centroid (u1 and u2 ) convergence. After the convergence, the sample sequence is divided

4.1. Case study Fig. 3 shows the case detection of the PDM algorithm under the weak convection condition at 01:00 (LT) on 8 December 2015. The

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Fig. 3. Case study under the weak convection condition at 01:00 (LT) on 8 December 2015. (a) Scatter plots of color ratio and depolarization ratio. The color bar shows the altitude of sample point. (b) Classification results. The red and blue point represent the cluster 1 and 2, respectively. The black fork represents the centroid of the cluster. (c) The sequence of category. (d) The result of the case analysis. The red line and blue line represent the boundary layer and backscatter signal, respectively. The orange circle represents the result of BLH. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

weak convection of the atmosphere can lead to nonuniform mixing of aerosols. Multiple aerosol layers would be affecting the inversion of the BLH. Fig. 3(a) shows the scatter plots of color ratio and depolarization ratio with altitude information. The distribution of particles is relatively discrete. Fig. 3(b) shows the clustering results. The sample points are divided in two cluster: the cluster 1 with small CR and DR, the cluster 2 with large CR and DR. The black fork represents the centroid of the cluster. Fig. 3(c) shows the sequence of category that changed with altitude. The orange line represents the junction of different cluster. Fig. 3(d) shows the result of BLH retrieved by PDM algorithm, and the BLH is about 1050 m. The red line and blue line represent the boundary layer and backscatter signal, respectively. In this case, aerosol concentration is nonuniform in the vertical direction. Owing to the drastic changes in aerosol concentration, the cluster 2 is not very close, as shown in Fig. 3(b). The result of the clustering algorithm indicates three junctions in the sequence of category at altitude of 517.5 m, 547.5 m and 1050 m. After the threshold value identifying, the altitude of 517.5 m and 547.5 m are regarded as the bases of the thin aerosol layer, and the BLH result shows an altitude of 1050 m. Fig. 4 shows the case study of the PDM algorithm under the strong convection condition at 03:00 (LT) on 8 December 2015. The aerosols are homogeneously mixed under this condition. Therefore, the distribution of the sample points is tight, as shown in Fig. 4(a). The Fig. 4(b) shows that the clustering results are clear, and no cross occurs. Fig. 4(c) shows that the sequence of category changes with altitude. Fig. 4(d) shows the result of BLH is about 982.5 m. Aerosol concentration is relatively uniform in the vertical direction under this case. As shown in Fig. 4(b), the sample points in cluster 2 are tightly gathered. The clustering algorithm can direct calculate the BLH under this distribution. The result of clustering algorithm

indicates that only a junction exists in the sequence of category, as shown in Fig.4(c), and the junction is in the altitude of 982.5 m. Therefore, the result of BLH is approximately 982.5 m. Fig. 5 shows the case detection of the PDM algorithm at 04:00 (LT) on 26 December 2015. This is a complex case where a cloud layer exists. Fig. 5(a) shows that the distribution of the sample points is discrete. The clustering results show that the sample points in the cloud are assigned to cluster 2, as seen in Fig. 5(b). Fig. 5(c) shows the sequence of category that changes with altitude. As shown in Fig. 5(d), the aerosol concentration changed drastically in the altitude from 0 km to 1 km, and a cloud layer exists at the altitude of 2.2 km. Under this situation, the distribution of particles is very confusing. Nevertheless, the results of the sample points clustering are still clear. The clustering algorithm can effectively detect the junctions. The result indicates that three junctions in the sequence of category, as shown in Fig. 4(c), and the junctions are in the altitude of 877.5 m, 2220 m and 2422.5 m, respectively. Fig. 5(d) shows the result of BLH retrieved by proposed algorithm, and the BLH is about 877.5 m. In addition, the altitude of 2220 m and 2422.5 m correspond to the base and top of the cloud, respectively. In general, the PDM algorithm is tested with three different real cases. The result shows that the proposed algorithm can effective identify the BLH under the complex case. The PDM algorithm transforms the gradient solution into a particle clustering solution. Based on the particle clustering, the atmospheric aerosols are clustered into one class, and the atmospheric molecules are clustered into another class. According to this particle distribution to obtain the boundary layer height, the PDM algorithm can effectively avoid the influence of changes in aerosol concentration. Moreover, this algorithm can determine the base and top of the cloud (if there is).

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Fig. 4. The case study under the strong convection condition at 03:00 (LT) on 8 December 2015. (a) Scatter plots of color ratio and depolarization ratio. The color bar shows the altitude of sample point. (b) The classification results. The red and blue point represent the cluster 1 and 2, respectively. The black fork represents the centroid of the cluster. (c) The sequence of category. (d) The result of the case analysis. The red line and blue line represent the boundary layer and backscatter signal, respectively. The orange circle represents the result of BLH. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

Fig. 5. The case study with cloud at 04:00 (LT) on 26 December 2015. (a) Scatter plots of color ratio and depolarization ratio. The color bar shows the altitude of sample point. (b) The classification results. The red and blue point represent the cluster 1 and 2, respectively. The black fork represents the centroid of the cluster. (c) The sequence of category. (d) The result of the case analysis. The red line and blue line represent the boundary layer and backscatter signal, respectively. The orange circle represents the result of BLH. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

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Fig. 6. Comparison between results from different methods under different convection states. (a) At 4:00 on 8 December 2015 under the strong convective state, (b) At 20:00 on 7 December 2015 under the weak convective state. The blue line indicates the backscatter signal. The orange, red, black and green lines represent the boundary layer results obtained with the proposed algorithm, the ideal profiling fitting method, the wavelet covariance transform method and the manual method, respectively. The average time is five minutes for a profile. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

4.2. Compare with other algorithms To assess the performance of the PDM algorithm, the calculated results of BLH from proposed algorithm under different convective case are compared with those of WCT method and ideal profile fitting method. In addition, the BLH determined by manual method [4] will be the reference BLH to assess the performance of the new method. Fig. 6 shows the results of the three algorithms under different convection states: weak convection and strong convection. The blue line indicates the backscatter signal. The orange, red, black and green lines represent the boundary layer results obtained with the PDM algorithm, the ideal profiling fitting method, the WCT method and the manual method, respectively. Fig. 6(a) shows a comparison of the results under strong convection conditions; the BLH calculated by the PDM algorithm, the ideal profiling fitting method, and the WCT method are 892 m, 930 m and 858 m, respectively. The reference BLH is about 900 m. It indicates that the calculated results of the three algorithms are consistent under the strong convection state. Fig. 6(b) shows the comparison results under weak convection conditions. The values of BLH calculated by the different methods are 1175 m, 889 m and 1043 m, respectively. The reference BLH is about 1200 m. In this case, the result of the proposed algorithm is closer to the reference values than those of the classical algorithms. The reason is that the concentration of aerosol is nonuniform in the vertical direction under weak convection conditions. The classical algorithms rely on the gradient of aerosol concentration to calculate the BLH. Therefore, when the aerosol concentration changes drastically or is low in the vertical direction. The traditional algorithms either could not detect the results for the boundary layer, or yielded low detection results. However, the low aerosol concentration does not affect the PDM algorithm that identifies the boundary layer based on the particles clustering. It can accurately find the BLH under the complex cases.

Fig. 7 shows the scatter plots of the BLH obtained by the PDM algorithm and the other algorithms. The experimental data are collected from June 2015 to December 2015. The average time is 30 min for a sample point. The gray line represents a 1:1 reference line; the red line represents the regression line, and the dots represent sample points. Fig. 7(a) shows a comparison of the BLH obtained by the PDM algorithm with the results obtained by the manual method. The results are in good agreement with one another, and the correlation coefficient is R2 = 0.89 with a RMSE of 131 m and a mean bias of 49 m. Fig. 7(b) shows a comparison of the BLH obtained by the ideal profile fitting method with the results obtained by the manual method. The correlation between the results is R2 = 0.64, with a RMSE of 270 m and a mean bias of 165 m, which indicates that the results are relatively consistent between these two methods. Fig. 7(c) shows a comparison of the results of the WCT method with the results of the manual method. The correlation coefficient is R2 = 0.76, with a RMSE of 196 m and a mean bias of 23 m, which indicates that the performance of the proposed algorithm is similar to the WCT in most cases. According to the above analysis, the performance of the PDM algorithm is same as the performance of the traditional algorithms under strong convection conditions. The reason is that the aerosol concentration is relatively uniform in the vertical direction, the gradient of aerosol concentration is evident. Consequently, all the retrieved algorithms can detect the boundary layer accurately. Moreover, when aerosol concentration is nouniform in the vertical direction, there is a considerable difference in the performance of the different algorithms. Once the aerosol concentration changes drastically or lowers in the vertical direction, there will be multiple gradient values, or no gradient values at all. It is difficult for the traditional algorithms to detect the true BLH from the multiple aerosols layer. However, the PDM algorithm can still detect the BLH under the weak convection conditions. The proposed algorithm detected the top of the boundary layer based on the particles

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Fig. 7. Correlation and data-density plots for the BLH retrieved using the proposed algorithm and the other algorithms. (a) Correlation between the results of the proposed algorithm and the manual method. (b) Correlation between the results of the ideal profile fitting method and manual method. (c) Correlation between the results of the wavelet covariance transform method and manual method. The average time is 30 min for a sample point.

clustering. The drastic gradient changes in the aerosol concentration can be understood as the extremely dispersed distribution of the particles. The PDM algorithm can overcome this problem and identify the BLH accurately. Consequently, the proposed algorithm can better deal with the weak convection conditions. Finally, the results of long-time experiment indicate that the reliability of the PDM algorithm is acceptable under all weather conditions.

better reliability and stability than the traditional algorithms. Furthermore, the algorithm has not been tested in airborne and satellite equipment, the advantages of this algorithm will be extended to the space-borne data in future studies. Conflicts of interest The authors declare no conflicts of interest.

5. Conclusions A two-wavelength Lidar inversion algorithm is proposed based on the particle distribution to determine the top of the boundary layer. The color ratio and the depolarization ratio are used to analyze the particle distribution, based on which the PDM algorithm can overcome the effects of complex aerosol layers to calculate the BLH. Then, the proposed algorithm is tested with three real cases. The result shows that the propose algorithm can effective identify the BLH under the complex case. The PDM algorithm transforms the gradient solution into particle clustering solution. Based on the particle clustering, the PDM algorithm can effectively determine BLH, the base and top of the cloud (if any). Moreover, the performance of the PDM algorithm is compared with other algorithms under different convection conditions. The result shows that the proposed algorithm can better deal with the weak convection conditions. Finally, long-term data from June 2015 to December 2015 were used to verify the reliability of the PDM algorithm. The correlation between the results of the proposed algorithm and the manual method is R2 = 0.89 with a RMSE of 131 m and mean bias of 49 m; the correlation between the results of the ideal profile fitting method and manual method is R2 = 0.64, with a RMSE of 270 m and mean bias of 165 m; and the correlation between the results of the wavelet covariance transform method and manual method is R2 = 0.76, with a RMSE of 196 m and mean bias of 23 m. These findings indicate that the PDM algorithm has the

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