This chapter presents a comprehensive study on the application of optimization methods for forecasting satellite meteorological data, with a focus on ecological and energy-related purposes. Paper explores the significant role of mathematical models and heuristic methods in addressing deviations in satellite data and improving forecast accuracy. A detailed analysis of regression models, including conventional and ridge regression, highlights their utility in forecasting meteorological indicators. Additionally, statistical and machine learning approaches, such as autoregressive models and neural networks, are examined for their ability to capture complex dependencies and forecast time series data effectively. The research introduces a modified method of group argumentation for constructing and selecting optimal models, emphasizing its computational efficiency and accuracy. Furthermore, the paper outlines the use of Kolmogorov-Gabor polynomials and the classical least squares method to estimate model coefficients. A multi-resolution approach is employed to build complex nonlinear models, ensuring minimal data loss and enhanced predictive performance. Empirical validation using three years of temperature data demonstrates the high correlation and accuracy of the proposed models, achieving an average forecasting accuracy of 93–95%. The results underscore the potential of these optimization techniques in providing reliable forecasts for meteorological indicators, thereby aiding in the assessment of environmental changes and their impacts on agriculture and renewable energy generation. This study significantly contributes to the field of meteorological forecasting by showcasing advanced mathematical and computational methods that enhance the precision and reliability of satellite data interpretation.