## 3 Methodology and Materials
### Data Sample  
The dataset utilized in this paper was sourced from the Jena Climate dataset, available through Kaggle. This dataset was collected at the Weather Station of the Max Planck Institute for Biogeochemistry in Jena, Germany, and is intended for climate and environmental research. It provides a comprehensive and detailed long-term record of various meteorological conditions. The data span a period of over eight years, from 1 January 2009 to 31 December 2016, offering a robust foundation for the time series analysis in this study. Data introduction was adapted from [PERSON]; [PERSON] Enhancing Data Preprocessing using Positional Self-Attention Autoencoders. In Proceedings of the 2024 16 th International Conference on Intelligent Human Machine Systems and Cybernetics (IHMSC 2024), Hangzhou, China, 24-25 August 2024 [2]. Table 2 provides a comprehensive summary of the range and mean values for each feature, reflecting distinct aspects of the atmospheric state. Atmospheric pressure, ranging from 913.60 to 1015.35 mbar, indicates the weight of the air and is crucial in shaping weather patterns. Temperature data, ranging from \(-\)23.01 \({}^{\circ}\)C to 37.28 \({}^{\circ}\)C, offer insights into atmospheric stability, including the dew point temperature, a key indicator of atmospheric moisture. Relative humidity, spanning from 12.95% to 100%, impacts weather conditions and ecological systems. Water vapor metrics, including the maximum water vapor pressure, actual vapor pressure, vapor pressure deficit, specific humidity, and water vapor concentration, collectively delineate the moisture level of the air, influencing precipitation, cloud formation, and overall atmospheric processes. Air density, affected by temperature, Version 7 August 2024, submitted to Journal Not Specified 4 of 24 pressures and humidity, has implications across various fields, from aviation to engineering. Despite some data anomalies, the wind speed and direction are fundamental in understanding air movement, weather systems, and pollutant dispersion. The range and mean of these variables illustrate the dynamic and complex nature of the climate at the Jena station, offering deep insights into weather patterns and providing a robust foundation for extensive climatic research and applications in forecasting, environmental planning, and beyond. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Feature** & **Mean** & **Minimum** & **Maximum** \\ \hline p (mbar) & 989.21 & 913.60 & 1015.35 \\ T (degC) & 9.45 & \(-\)23.01 & 37.28 \\ Tpot (K) & 283.49 & 250.60 & 311.34 \\ Tdev (degC) & 4.96 & \(-\)25.01 & 23.11 \\ rh (\%) & 76.01 & 12.95 & 100.00 \\ VPmax (mbar) & 13.58 & 0.95 & 63.77 \\ VPact (mbar) & 9.53 & 0.79 & 28.32 \\ VPdef (mbar) & 4.04 & 0.00 & 46.01 \\ sh (g/kg) & 6.02 & 0.50 & 18.13 \\ H2 OC (mmol/mol) & 9.64 & 0.80 & 28.82 \\ rho (g/m\({}^{3}\)) & 1216.06 & 1059.45 & 1393.54 \\ wv (m/s) & 1.70 & \(-\)9999.00 & 28.49 \\ max. wv (m/s) & 3.06 & \(-\)9999.00 & 23.50 \\ wd (deg) & 174.74 & 0.00 & 360.00 \\ \hline \hline \end{tabular} Note: data anomalies exist in wind speed measurements.  
\end{table} 
Table 2: The overall range and mean for each feature reflecting distinct aspects of data features. Figure 4 illustrates the relationships between various features within the dataset. Temperature T (degC) demonstrates a strong positive correlation with both potential temperature Tpot (K) and dew point temperature Tdew (degC), suggesting a cohesive relationship among different measures of atmospheric heat. The specific humidity sh (g/kg), water vapor concentration H2 Ocmmol/mol, and actual vapor pressure VPact (mbar) exhibit close interrelationships, reflecting the interconnected nature of moisture variables. Conversely, relative humidity rh% shows an inverse correlation with temperature, highlighting the dynamic balance between temperature and the air's moisture-carrying capacity. Atmospheric pressure p (mbar) negatively correlates with temperature, consistent with the principles of thermal expansion.