## 3 Proposed Framework
### Pa Structure  
This study introduced a Pa structure at the data level. This means that, unlike previous studies, each prepared FC in Table 3 was fed to an ML model. This approach allows for the utilization of the strengths of different datasets simultaneously. Additionally, since there is a specific FC in each branch, the Pa structure can achieve higher accuracies compared to the conventional image stacking approach, which introduces unnecessary redundancy and reduces computational efficiency during the classification process. There is a total of five different FCs, resulting in five branches within the Pa structure. In this study, four widely used ML models in crop classification, including CART, SVM, RF, and GBT, were assessed to find the optimal models in each branch of Pa structure. The CART algorithm is a statistical method which identifies target classes by finding the common characteristics of each class [68]. This method has been widely used in land cover classification due to its simple design and computational efficiency [69]. The tree Maximum Nodes (MN) and Minimum Leaf Population (MLP) are two of the main parameters of this method that must be set. SVM is another ML method that determines the best possible hyperplane to classify different samples into specific classes based on the input features [70]. This approach offers remarkable advantages in dealing with complex problems, limited sample sizes, and high-dimensional data. When using SVM, the main parameters that need to be modified are the Gamma (G) value and the Cost (C) parameter. Based on the proven performance in the previous articles, the kernel function was set to 'Radial Basis Function' (RBF) [71]. RF is an ensemble method that creates multiple decision trees to make predictions. RF has a bagging approach, meaning each tree is built using a random subset of training samples. During prediction, each tree in the forest independently makes a prediction, and the final output is determined by majority voting. The Number of Trees (NT), the Maximum Nodes (MN), and the Variables Per Split (VPS) are the parameters that must be set in this method [72]. GBT is an ensemble algorithm that combines gradient boosting with decision trees. It builds trees sequentially to correct errors made by previous trees. GBT captures complex relationships, processes data sets, and handles missing values automatically [73]. The parameters needing to be set in this classifier are the Number of Trees (NT), the Shrinkage (SH), and the Maximum Nodes (MN). To select the best model in each branch of the Pa structure, each of the aforementioned ML models is separately evaluated in each branch. The model that achieves the highest accuracy is chosen as the base model for that particular branch. This approach is adopted because some ML models exhibit poorer performance compared to others. Consequently, their simultaneous use alongside other ML models can negatively impact the results. To this end, the hyperparameters of each ML model in each branch were first determined using a five-fold cross-validation approach with the aid of a grid search technique. This involves randomly dividing the training data into five folds. During each iteration, one-fold is held out for validation, while the remaining k-1 folds are used to train the algorithms in each branch using the hyperparameters from the search space. This process is repeated \begin{table}
\begin{tabular}{c c c} \hline \hline
**FC** & **Branch Number** & **Description** \\ \hline FC\({}_{1}\) & 1 & Only S2 spectral bands, B2 to B12 (Table 1) \\ FC\({}_{2}\) & 2 & Only S2-derived SIs: NDVI, NDBI, NDWI, SAVI, EVI (Table A1) \\ FC\({}_{3}\) & 3 & Only L8/9 spectral bands, B2 to B7 (Table 1) \\  & & Only L8/9-derived SIs: NDVI, NDBI, NDWI, SAVI, \\  & & EVI (Table A1) \\ FC\({}_{5}\) & 5 & Only VV and VH bands \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Five different FCs used in the branches of the Pa structure. k times, and the best hyperparameters are selected based on the average classification accuracy.