## 3 Method
### Classification Schemes and Accuracy Assessment  
Although the addition of multi-temporal features can improve crop identification accuracy to a certain extent, not all features play a positive role in recognition [54]. Therefore, the feature optimization method is essentially used to obtain the effective recognition \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline
**Date** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** & **14** & **15** \\ \hline
7 & 15 & 105 & 455 & 1365 & 3003 & 5005 & 6435 & 6435 & 5005 & 3003 & 1365 & 455 & 105 & 15 & 1 \\ \hline
12 & 10 & 45 & 120 & 210 & 252 & 210 & 120 & 45 & 10 & 1 & & & & \\ \hline
28 & 6 & 15 & 20 & 15 & 6 & 1 & & & & & & & \\ May & 3 & 3 & 1 & & & & & & & & & & \\ \hline
8 & 1 & & & & & & & & & & & & & \\ May & & & & & & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: All possible combination types at each stage and the number of images contained in each type. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Letter** & \(\mathbf{T_{2}}\)**Date** & \(\mathbf{T_{1}}\)**Date** \\ \hline A & 8 May & 28 April \\ B & 13 May & 8 May \\ C & 28 May & 13 May \\ D & 12 June & 28 May \\ E & 7 July & 12 June \\ F & 13 May & 28 April \\ G & 28 May & 8 May \\ H & 28 May & 28 April \\ I & 12 June & 13 May \\ J & 12 June & 8 May \\ K & 12 June & 28 April \\ L & 7 July & 28 May \\ M & 7 July & 13 May \\ N & 7 July & 8 May \\ O & 7 July & 28 April \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Definition of each letter in Figure 4 in 2020 different time phases. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Date** & **Available Difference Time Phase** & \(\mathbf{n}\) & **Number of Images after Band Combination (\(C_{all}\))** \\ \hline
8 May & A & 1 & 1 \\
13 May & A, B, F & 3 & 7 \\
28 May & A, B, F, C, G, H & 6 & 63 \\
12 June & A, B, F, C, G, H, D, I, J, K & 10 & 1023 \\
7 July & A, B, C, D, E, F, G, H, I, J, K, L, M, N, O & 15 & 32,767 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Available difference images and total images after band combination for each period in 2020.  
feature set. Finally, different classifiers are modeled to explore the impact of different features on crop recognition accuracy in different periods, as follows:  
(2) Classification model  
In this study, each image's optimal recognition feature set was used as the input of RF, GBDT, Cart, and SVM classifiers to achieve crop recognition of all images in different periods. RF classification is composed of multiple decision trees, which have the advantages of strong noise immunity, fast speed, and high accuracy and has been widely used in various classification scenarios [56; 57; 58]. Its principle is to use bootstrap resampling to extract multiple samples from the original sample, model the decision tree for each bootstrap sample and run it in parallel, and combine the predictions of multiple decision trees to obtain the final prediction according to a voting process. The key parameters are the number of decision tree classifiers (ntree) and the maximum number of features (mtry). The optimal values for ntree are 100, and mtry is 10. The GBDT classifiers have the advantages of high robustness, high accuracy, and fast speed [59; 60]. Its basic principle is to generate a weak Cart regression tree learner, obtain the residuals of the input after training, and then iteratively train the next learner based on the residuals generated by the previous round of learners. During each iteration, each learner aims to minimize the loss function. The final prediction is obtained by accumulating the weak learners' results. There are some parameters that need to be optimized: learning_rate (the step size when learning), max_features (the number of features to consider when finding the best split) and n_estimators (the number of boosting stages to perform).