## 5 Conclusions  
Accurate and timely crop distribution access is important to food production management. This study proposed a new method for crop identification by using multi-temporal MODIS remote sensing images in North China. Firstly, the time series were combined as inputs to the PB-Con1D and PB-BiLSTM models for producing the original classification results. Then, the Snapshot and SWA strategies were introduced in the deep learning models to gradually improve crop classification accuracy and obtain the best-performing PB-CDST (OA: 81.36%) and PB-BMST (OA: 79.37%) models. They were compared with the PB-TRSTSA (OA: 77.79%) model to show the advantages of our proposed models for multiple-crop classification. Subsequently, the better-performing PB-Conv1D and PB-BiLSTM were combined with ensemble learning to obtain the PB-CB model. The proposed PB-CB (OA: 83.43%) algorithm combines the temporal features learned from the PB-Conv1D and PB-BiLSTM models to classify multiple-crop areas, ensuring classification accuracy. Additionally, the results of the correlation of multiple-crop cultivated areas generated by MODIS combined with the PB-CB method to statistical data showed that the R\({}^{2}\) of wheat, corn, and rice exceeded 0.7 and 0.6 at the municipal and county levels, respectively. Therefore, the newly presented PB-CB model is an effective method for multiple-crop area \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Reference Classes**} & \multicolumn{8}{c}{**Classified**} \\ \cline{2-10}  & **SU** & **RI** & **SP** & **OT** & **WT-OT** & **WT-RI** & **WT-SP** & **WT-SU** & **Total** \\ \hline
**SU** & 5 & 0 & 1 & \(-2\) & 0 & \(-1\) & 0 & \(-3\) & 10 \\
**RI** & \(-1\) & 3 & \(-2\) & 0 & 0 & 0 & 0 & 0 & 6 \\
**SP** & 2 & 0 & 0 & 2 & \(-2\) & 0 & \(-2\) & 0 & 0 \\
**OT** & 1 & 0 & 0 & \(-2\) & 1 & 0 & 0 & 0 \\
**WT-OT** & 0 & 0 & 2 & 0 & \(-3\) & 1 & \(-1\) & 1 & \(-6\) \\
**WT-RI** & \(-2\) & 0 & 0 & 0 & \(-1\) & 6 & \(-2\) & \(-1\) & 12 \\
**WT-SP** & 0 & 0 & \(-1\) & 1 & 1 & 0 & 4 & \(-5\) & 8 \\
**WT-SU** & 1 & \(-1\) & 0 & 0 & 1 & \(-18\) & 2 & 15 & 30 \\
**Total** & 4 & 4 & 0 & \(-1\) & 0 & 23 & 7 & 23 & 60 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Difference between the confusion matrix of the PB-CB classifier and that of the PB-BV classifier. Values are calculated as Figure 0(a) minus Figure 0(a). identification from time series MODIS remotely sensed imagery. Meanwhile, the PB-CB model is available for other crops (e.g., soybean and cotton) and consequently has strong prospects for application. Future work can investigate the method's feasibility for the mapping of other crops and the production of higher-spatial-resolution images. X.W. ([PERSON]): Methodology, Investigation, Software, Data curation, Validation, Writing--original draft. J.Z. : Conceptualization, Investigation, Validation, Resources, Supervision, Project administration, Funding acquisition, Writing--review &editing. X.W. ([PERSON]): Software, Investigation, Data curation, Visualization, Writing--review &editing. Z.W. : Software, Investigation, Data curation, Visualization, Writing-review &editing. F.A.P. : Investigation, Visualization, Writing--review &editing. All authors have read and agreed to the published version of the manuscript. This work was jointly supported by the Open Fund of Key Laboratory of Urban Land Resources Monitoring and Simulation, Ministry of Natural Resources (No. KF-2021-06-081), the Finance Science and Technology Project of Hainan Province (No. ZDY2021 SHFZ063), the Shandong Key Research and Development Project (No. 2018 GNC110025, ZR2017 ZB0422), The 2023 Zhonglou District of Changzhou City Science and Technology Research Project (No. JBGS2023011), and the Science and Technology Support Plan for Youth Innovation of Colleges and Universities of Shandong Province of China (No. 20235 KJ232). **Informed Consent Statement:** Not applicable. **Data Availability Statement:** All data generated or analyzed during this study are included in this published article.