## 5 Conclusions  
Analysis of the obtained results showed that there is a dependence on meteorological parameters for the following values: the altitude of the HLC center; elements m\({}_{22}\) and m\({}_{44}\) of BSPM (with m\({}_{11}\) always equal to 1); and the m\({}_{33}\) element of BSPM requires further study and expansion of the analyzed dataset. For the rest of the values, a sufficiently large error value is observed, and at the moment, it is impossible to give an unambiguous answer. At the same time, the result is not affected by the choice of data compression method to reduce their dimensionality.  
In almost all cases, the random forest method gave better results than the simple multilayer perceptron. This is most likely caused by two factors: preprocessing of input data and a small amount of experimental data suitable for training. As for preprocessing, the usual normalization (zero mean and variance 1) was chosen, which may not be sufficient. As further steps, it is necessary to consider transformations that bring the histogram distribution of the input data to a symmetric form and more similar to a normal distribution.  
The size of the data also affected the performance of the neural network. As the neural network becomes more complex, it is able to approximate more sophisticated functions, but a larger amount of data must be used. Using small amounts of data leads to overtraining of the network and hence deterioration in the results obtained. To improve the results and to establish additional possible dependencies between meteorological parameters and HLC characteristics, we plan to conduct research in the preprocessing of meteorological parameters, namely taking into account the dynamics of change over time, the gradient in the area of the experiment, and the anthropogenic factor. It is also necessary to increase the volume of the experimental dataset (performing new experiments on laser sensing of the atmosphere).  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **RF (PCA)** & **NN (PCA)** & **RF (AE)** & **NN(AE)** \\ \hline Fold 1 & 0.24 & 0.25 & 0.18 & 0.20 \\ Fold 2 & 0.25 & 0.28 & 0.21 & 0.22 \\ \hline \end{tabular}
\end{table}
Table 6: The value of standard deviation in estimating the m\({}_{44}\) BSPM element for random forest method and neural network with different data compression methods.  
**Author Contributions:** [PERSON], [PERSON], [PERSON] ([PERSON]) and [PERSON] developed a prototype software product based on artificial neural networks for meteorological observation data analysis and prediction of optical and geometric characteristics of HLC. They also analyzed the results obtained and partially investigated the applicability feature of neural networks to small datasets. In addition, these participants analyzed the effect of data preprocessing on the efficiency of neural network training. [PERSON]. ([PERSON]), E.N., [PERSON], [PERSON] and [PERSON] developed the methodology of the experiments, built the HAMPL of NR TSU, and performed lidar measurements. [PERSON]. ([PERSON]) and E.N. processed lidar data. [PERSON]. ([PERSON]) together with [PERSON] processed the meteorological data. [PERSON] supervised the experiments on the HAMPL of NR TSU and the processing of lidar and meteorological data. [PERSON], [PERSON], [PERSON] ([PERSON]), [PERSON], [PERSON] ([PERSON]), E.N., [PERSON], [PERSON], [PERSON] and [PERSON] discussed the results obtained and wrote and edited the text of this paper. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the Russian Science Foundation, Grant No 21-72-10089.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data are contained within the article.  
**Conflicts of Interest:** The authors declare no conflict of interest.