## 2 Materials and Methods
### Meteorological Data  
Meteorological data constitute an essential dataset acquired from the Czech Hydrome-teorological Institute (CHMU), encompassing a comprehensive array of metrics pertinent to wind direction and speed. The CHMU meteorological data were provided as gridded reanalysis datasets (representation of past atmospheric conditions generated by combining actual observations (e.g., weather station data, satellite measurements, radiosondes) with numerical weather prediction models ). These datasets cover the temporal span from 1 June 2019 to 31 August 2019 and incorporate a spatial domain extending longitudinally from 120\({}^{\circ}\) W to 120\({}^{\circ}\) E and latitudinally from 80\({}^{\circ}\) N to 20\({}^{\circ}\) S. The spatial grid delineates this area into increments of 1.25 degrees, adhering to the standards outlined in ICAO Annex 3. The dataset comprises 17 distinct flight levels, ranging from 050 to 530. Predictions for wind direction and speed are provided at 3 h intervals, with a predictive time horizon spanning from 6 to 36 h. Data updates occur four times daily at 00:00, 06:00, 12:00, and 18:00. The structure and visualization of this dataset are presented in Figure 2.  
These meteorological data were utilized to characterize the weather conditions at specific points along the FTFM and CTFM profiles. The first step involved selecting key meteorological parameters--wind speed and direction--corresponding to each waypoint along the specified flight trajectory. The construction of these profiles is detailed in the preceding chapter. However, to clarify the data preprocessing approach, a flight profile was defined as follows:  
\[FP_{i}=\left[ \begin{array}{cccc}lat_{1}&lon_{1}&alt_{1}\\ lat_{2}&lon_{2}&alt_{2}\\ \vdots&\vdots&\vdots\\ lat_{w-1}&lon_{w-1}&alt_{w-1}\\ lat_{w}&lon_{w}&alt_{w}\\ \end{array} \right], \tag{1}\]  
where \(FP_{i}\) represents a specific flight profile selected from the set of all profiles based on a unique flight identifier \(i\), where \(i=1\ldots 1730\). This simplified notation contains information about the geographical longitude, latitude, and flight altitude at a specific point along the route. The number of route points varies, and it is therefore defined by the total count of route points, denoted as \(w\). In the context of air traffic management and machine learning applications for predictive modeling, the procedure for correlating meteorological data consists of identifying the closest data point from the meteorological dataset to a particular flight trajectory coordinate. Hence, when considering a designated flight trajectory point \(P_{p}\) (located at \(P_{p}\in FP_{i}\)) along with a collection of meteorological points \(Q\), this can be expressed as  
\[Q_{nearest}=\underset{q\in Q}{\text{arg min}}||P_{p}-q||, \tag{2}\]where \(||P_{p}-q||\) represents the Euclidean distance between point \(P_{p}\) (\(p=1\ldots w\)) and each point \(q\) in the set \(Q\), and \(\underset{q\in Q}{\arg\min}\) finds the point in \(Q\) that minimizes this distance. Meteorological data were effectively divided into batches based on geographical latitude, longitude, and time, considering their size, as shown in Figure 2. This process led to the selection of data subset(s) that covered the geographical latitude and longitude of the flight trajectory at a specific time. For this purpose, i.e., batch processing, a software solution was created in the Matlab2024a environment. The mentioned process preceded the actual selection of meteorological data concerning the flight trajectory. Within the data processing methodology, a two-step process was employed to ascertain the nearest meteorological data point concerning a specific target point. This approach accommodates both horizontal position (latitude and longitude) and altitude (in feet). This process was iterative and chosen because calculating the Euclidean distance between two points in 3D space would be complicated due to the different units of measurement for altitude (in feet) and coordinates (in degrees).