Employing Discrete Wavelet Transform Methods and Python Libraries to Derive Mathematical Models Of Environmental Data

The article addresses the urgent problem of computer modeling of large-scale environmental monitoring datasets using discrete wavelet transforms. The research object consists of time series of harmful pollutant concentrations in the atmosphere, including nitrogen oxides, benzene, and sulfur dioxide, collected from automated stations in Central and Eastern Europe. The input data are characterized by high stochasticity, noise, missing values, and temporal shifts, which significantly com- plicate the extraction of trends and patterns required for forecasting. An efficient processing approach is proposed, combining multilevel wavelet decomposition with adaptive filtering based on soft-thre- sholding and an automatic decomposition-level selection mechanism grounded in energy-based coef- ficient analysis.

For modeling, the Python ecosystem was employed: PyWavelets for wavelet modeling, Matplotlib for dynamics visualization, and Pandas for structuring large input datasets. A series of computational experiments was conducted on data from Polish, Czech, and German cities, confirming the effectiveness of the proposed method. It is demonstrated that the integration of Daubechies (db4) wavelet transforms with ensemble learning methods (Random Forest, XGBoost) and LSTM neural networks enables highly accurate forecasting, even under non-stationary emissions and meteorological fluctuations. The proposed approach can serve as the basis for developing next-generation adaptive environmental monitoring systems, particularly in industrially intensive urban areas.