## 3 Results
### Preliminary Analysis  
As a first step in the analysis, the change in BSPM elements with altitude within the HLC thickness was investigated. Figure 2 shows an example of one BSPM element measurement made on 19 May 2016, starting at 14:07. The m\({}_{11}\) element is always equal to one because all BSPM elements are normalized to it. The remaining plots show the behavior of the values of all BSPM elements within the HLC altitude range. The element values in both channels of the lidar receiving system are consistent with each other and correspond to some constant value with some noise added. Similar behavior is present in the other dimensions. Thus, altitude dependence within the HLC is not observed, and for one observation, it is sufficient to take the median value of the BSPM element for the channel with the best signal-to-noise ratio, which is more resistant to the presence of outliers.  
The next step was to study the distributions of values of the BSPM elements as functions of meteorological parameters. Figure 3 presents histograms of median values of BSPM elements in the range of HLC altitudes. Since the measurements were performed under different meteorological conditions and for different altitudes of HLC formation, we can assume that we should obtain histograms \"smeared\" in some interval, since their construction did not consider the presence of dependencies on meteorological parameters. Figure 3 shows that this is fulfilled only for the following BSPM elements: m\({}_{22}\), m\({}_{33}\), and m\({}_{44}\). For the remaining elements, no variability is observed. For elements m\({}_{12}\), m\({}_{21}\), m\({}_{13}\), m\({}_{31}\), m\({}_{14}\), and m\({}_{41}\), a distribution like a normal distribution is observed, with a mean of 0 and some small variance at the noise level. The background lidar signal value is used as a noise. This value is calculated as the average lidar signal for the upper 3 km of the lidar operation altitude range (12-15 km) for each receiving channel. For elements m\({}_{Figure 3: Distribution of BSPM element values.  
Figure 2: An example of the BSPM values of the elements’ dependence on the altitude within the HLC thickness obtained in measurements with the first (parallel) and second (parallel) channels of the lidar receiving system, respectively.  
The last step is to make sure that there is some dependence between the meteorological parameters and the values of the HLC BSPM elements. To investigate this question, instead of the altitude profile, the value of the meteorological parameter in the central height region of the HLC was taken. Figures 4-6 show the scatter plot for the m\({}_{22}\), m\({}_{33}\), and m\({}_{44}\) BSPM elements. In pressure and temperature diagrams, there is no distribution of elongated points along one of the axes, which indicates that there is some dependence between the values. This was implemented as a proof of concept to test for any dependency on the experimental environment. So, if we  
Thus, the following HLC BSPM elements are subject to analysis using machine learning methods: m\({}_{22}\), m\({}_{33}\), and m\({}_{44}\). This is probably due to the fact that the element m\({}_{44}\) and the sum m\({}_{22}\) + m\({}_{33}\) are invariant with respect to the rotation of the lidar basis (or the cloud itself) relative to the vertical axis [23]. The rest of the elements do not reveal dependences with meteorological parameters or require much more data.