## 3 Results
### Implementation of Data Dimensionality Reduction  
A total of 124,512 altitude profiles of meteorological parameters with hourly resolution were obtained using the ERA5 reanalysis for the period from 2009 to 2023. Each profile corresponds to the lidar coordinates and consists of more than 30 points on a heterogeneous pressure grid. For standardization, all profiles were transformed by interpolation to a single 31-point elevation grid. Feeding all of these values to the input of a neural network will result in the number of parameters of this network increasing significantly, which creates the need for data compression with maximum information preservation. The classical method of dimensionality reduction is principal component analysis (PCA). This method uses a singular value decomposition of the covariance matrix of the data. The spectrum of this decomposition characterizes the components that carry the most information. An alternative approach is the use of so-called autoencoders, which are special neural networks. Such a tool can be represented as an ordinary multilayer perceptron. Its specific feature is that during training, they are required to obtain the same values at the output as at the input. In this case, each layer of the neural network is an encoder that translates the  
Figure 10: Atmosphere meteorological characteristics scatter plot depending on m\({}_{34}\) BSPM element. Figure 9: Atmosphere meteorological characteristics scatter plot depending on m\({}_{43}\) BSPM element. vector of input values into a new linear space of a different dimension. If there is a layer with a small number of neurons inside the autoencoder, it leads to data compression. The outputs of this layer can be used as new components containing maximum information from the point of view of this autoencoder. In some cases, such neural networks obtain better data compression than PCA, as they take into account nonlinear dependencies between input data. In addition, the choice of the activation function allows for customization of the mapping scale of the input data to the compressed representation. We will use the hyperbolic tangent as such a function: this will allow us to obtain components in the range from -1 to 1. The activation function of the output layer will be linear, which will allow us to obtain arbitrary values at the output of the neural network. In addition, we need to take into account the fact that the input data have different scales of change. This complicates the use of a hyperbolic tangent, which may contribute to the frozen state of some neurons. This in turn results in values that are too large or too small, forcing the neuron to keep its state at -1 or 1, which disturbs the training of the network. To eliminate this problem, all input data are normalized by subtracting the mean from them and dividing by the standard deviation. This produces input values with a mean of 0 and a standard deviation of 1. To determine the dimensionality of the inner compressive layer of the autoencoder, as well as the constraint on the singular spectrum in PCA, we considered the standard deviation between the original altitude profiles and those reconstructed from the compressed components, determined according to the following formula:  
\[MSE=\sqrt{\frac{1}{N}\sum\Bigl{(}y_{predict}-y_{data}\Bigr{)}^{2}} \tag{1}\]  
If increasing the number of compressed components did not significantly improve this metric, the increase in components was stopped. During training, the data were divided randomly into two samples: training and test. The test sample represents 33% of the total data. Table 1 shows the standard deviation values for PCA and autoencoder (AE) obtained on the test sample. In most cases, AE gives better compression than PCA. The exception is absolute humidity, for which these approaches give comparable results.