## 2 Materials and Methods
### Additional Variables for Model  
Building on the data merging process, it became necessary to derive additional variables to enhance the predictive modeling process. The consolidated dataset exhibits a sequential structure, where each flight is represented as a sequence of variables (see Figure 3 for an overview of the data structure). In total, the dataset comprises 122,159 observations, derived from 1730 filtered flight arrivals, with 45 features and two dependent variables: \(\delta_{LT}\) (difference between estimated landing time and actual landing time in minutes) and \(\delta_{IBT}\) (difference between scheduled in-block time and actual in-block time in minutes). Not all features were suitable for inclusion in the model, particularly those containing information unavailable at the departure phase. For example, details related to actual flight execution (e.g., CTFM profiles) had to be excluded to ensure the model could make predictions solely based on information known at departure. Additionally, the presence of constant features--those that remain unchanged throughout a flight sequence, such as the Airport of Departure (ADEP)--introduced unique challenges. These challenges included limited information gain, as constant features do not vary across the sequence and provide minimal value for sequential models that rely on dynamic patterns over time steps. Including such features also introduces redundancy, repeating the same information at all time steps, and increases the risk of overfitting by causing the model to memorize patterns specific to these constants, reducing its ability to generalize. Furthermore, constant features can increase computational overhead during training without a proportional improvement in model performance. It is important to note that, given the sequential nature of the dataset, a sequence-to-one predictive approach was adopted, where a single predicted value (the delay) is generated for each flight sequence. The Bidirectional Long Short-Term Memory (BiLSTM) network, a type of recurrent neural network, was chosen for this task due to its capability to capture temporal dependencies and dynamic patterns [38]. Compared to the time series characterizing flight information and weather conditions along the route at the time of departure--such as latitude (_LAT_), longitude (_LON_), altitude (_ALT_), ground speed (_FS_), distance of the waypoint from the departing airport (\(POINT\_DIST\)), wind speed (_windspd_), wind direction (_winddir_), and wind component (_WindComponent_)--it was necessary to adjust the constant terms in a way that retained the required information while ensuring they were represented as a time series. A schematic representation of this process is provided in Figure 3.  
The dataset contains two types of constants: constant time terms (scheduled in-block time/off-block time \(SIBT/SOBT\), the actual take-off time \(ATOT\), and the actual off-block time \(AOBT\)) and constant terms associated with the categorical nature of the data, i.e., aerodrome of departure or aircraft type. In the first case, the constant time terms were transformed into time series as follows. Let \(F\) represent the data matrix for a specific flight included in the dataset. The defined  
Figure 3: A schematic representation of the data processing flow, starting with the preprocessed dataset that includes slot coordination data, movement data, trajectory data, and meteorological (velocity) data, through redefining constant time terms into time series, and culminating in the implementation of historical data into the training, validation, and testing datasets.