## 3 Results
### Estimation of HLC Detection Altitude  
One of the important characteristics of HLCs, in addition to the BSPM elements, are the altitudes of their lower and upper boundaries. It is of interest to determine whether there is a relationship between meteorological parameters and HLC detection altitudes. For this purpose, it was decided to move from the determination of the upper and lower boundary to the determination of the altitude of the cloud center and the deviation of the boundaries from this center. To counterbalance the scale of the center altitude variation, normalization was performed: 8 km was subtracted and divided by two (average HLC altitude is about 6-10 km, thickness--4 km. We take the center of this interval and divide by half of the thickness). This allows us to further obtain a more stable process of neural network training. The normalization parameters were taken from the general distribution of altitudes. Due to \begin{table}
\begin{tabular}{c c c c c} \hline  & **Temperature** & **Relative Humidity** & **Absolute** & **Wind Speed** \\  & (\({}^{\circ}\)C) & (kg\({}^{\circ}\)kg\({}^{-1}\)) & Humidity (\%) & **(m/s\({}^{2}\))** \\ \hline PCA & 2.36 & 60.7 & \(0.57\times 0^{-7}\) & 1.61 \\ AE & 1.66 & 42.54 & \(0.51\times 10^{-7}\) & 1.58 \\ \hline \end{tabular}
\end{table} 
Table 1: RMS deviation of meteorological parameters reconstructed from compressed vertical profile data. the fact that there are data from lidar experiments from 2009, in which the HLC altitudes were also determined, the set of available values increases to 779 observations. To determine the quality of neural network performance, we used the cross-validation approach, which is convenient to apply in conditions with a small amount of data. In this approach, the data are randomly divided into K equal parts, so-called folds. Then, the same steps are performed for each part:  
* The current part forms the test sample;
* The remaining parts form the training sample;
* Training of the neural network on the training sample and calculation of the standard deviation on the test sample. As a result, we obtain K different values of standard deviations and K trained neural networks. In the case of normal training and the absence of data heterogeneity, these values will be commensurable in values. Otherwise, we will obtain quite different values. In addition, the random forest (RF) method with the number of trees equal to 100 was used as a reference. This method is convenient because it is robust to different scales of input data changes and is not prone to overtraining. Thus, if the neural network obtains a result worse than the random forest method, it becomes a sign that the network architecture is chosen incorrectly. It is also a benefit that the random forest method allows us to identify those input parameters that give the greatest contribution to the determination of the output value, which can also provide additional information for analysis. Thus, it is interesting to study the behavior of the random forest method on full data and on compressed ones. At the same time, it is important to understand that, in some cases, the set of parameters obtained in this way may lead to misinterpretation of the data. This information can only be used for auxiliary purposes. In addition, point diagrams are a convenient study tool to evaluate the relationship of one value to another. Figure 11 shows the scatter plots for each fold using the random forest method and compression with PCA. In the case of perfect altitude determination, we should see a straight line as the estimate will coincide with the true value. Due to the presence of noise or weak dependence on the input data, the estimate will differ from the true value. In the figure, we can see  
Figure 11: Scatter plot of HLC center altitude determination using random forest and PCA compression method. a linear relationship between the estimate and the true value. In addition, there are point deviations that give a very large error.