## 4 Results  
### Classification Accuracy  
The RF classification achieved an overall accuracy of 97.35% with a Kappa coefficient of 0.95 in 2023. Similarly, both the overall accuracy and Kappa coefficient exceeded 0.90 in 2021 and 2022, highlighting the model's robust and reliable performance across years (Table 3). The scatter plots comparing mapped and statistical areas from 2019 to 2022 show R2 values ranging from 0.85 to 0.88 and RMSE values between 0.42 and 0.58 ha  
Figure 5: **(a)** Schematic of separability time windows based on vegetation index time series in 2023, with vertical lines showing maximum and minimum values of vegetation index statistical features. **(b)** Boxplots of vegetation index separability for four crop types within time windows. (Figure 6a-d), demonstrating strong agreement between predictions and statistical data. Crop-specific regression analysis yielded R\({}^{2}\) of 0.86, 0.79, 0.94, and 0.61 for maize, oats, potato, and sesame, respectively (Figure 6e-h), with potato exhibiting the highest prediction accuracy and sesame showing a slightly lower fit, likely due to its smaller cultivation areas and fragmented planting patterns. Overall, RF demonstrated strong predictive capability, proving the effectiveness and accuracy of this model for crop distribution monitoring. The spatiotemporal analysis of crop distribution patterns (2019-2023) revealed distinct agricultural zoning in Zhangjiakou (Figure 7). Aside from \"other crops\", maize was the most widely planted crop, followed by oats, potato, and sesame. Maize was primarily \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Year** & **Crops** & **Maize** & **Oats** & **Potato** & **Sesame** & **Other** & **Producer’s** & **F1** & **Overall** & **Kappa** \\ \hline \multirow{4}{*}{2023} & Maize & 218 & 1 & 0 & 0 & 3 & 98.19 & 99.09 & \multirow{4}{*}{97.35} & \multirow{4}{*}{0.95} \\  & Oats & 0 & 164 & 2 & 0 & 8 & 94.25 & 94.25 & & \\  & Potato & 0 & 3 & 131 & 0 & 6 & 93.57 & 95.97 & \multirow{4}{*}{0.95} \\  & Sesame & 0 & 6 & 0 & 19 & 2 & 70.37 & 82.60 & & \\  & Other crops & 0 & 0 & 0 & 0 & 611 & 1 & 98.46 & & \\  & User’s Acc. & 1 & 94.25 & 98.49 & 1 & 96.98 & & & \\ \hline \multirow{4}{*}{2022} & Maize & 222 & 2 & 0 & 0 & 0 & 99.11 & 99.11 & \multirow{4}{*}{96.44} & \multirow{4}{*}{94.51} \\  & Oats & 0 & 230 & 0 & 1 & 15 & 93.49 & 94.26 & & \\  & Potato & 0 & 0 & 6 & 0 & 2 & 75 & 85.71 & \multirow{4}{*}{96.44} & \multirow{4}{*}{94.51} \\  & Sesame & 0 & 1 & 0 & 5 & 0 & 83.33 & 83.33 & & \\  & Other crops & 2 & 9 & 0 & 0 & 404 & 97.35 & 96.65 & & \\  & User’s Acc. & 99.11 & 95.04 & 100 & 83.33 & 95.96 & & & \\ \hline \multirow{4}{*}{2021} & Maize & 213 & 6 & 0 & 0 & 0 & 97.26 & 97.04 & \multirow{4}{*}{95.75} & \multirow{4}{*}{93.18} \\  & Oats & 4 & 72 & 0 & 0 & 10 & 83.72 & 87.80 & & \\ \cline{1-1}  & Potato & 1 & 0 & 3 & 0 & 0 & 75 & 85.71 & \multirow{4}{*}{95.75} & \multirow{4}{*}{93.18} \\ \cline{1-1}  & Sesame & 0 & 0 & 0 & 1 & 0 & 100 & 100 & \\ \cline{1-1}  & Other crops & 2 & 0 & 0 & 0 & 229 & 99.13 & 97.45 & & \\ \cline{1-1}  & User’s Acc. & 96.82 & 92.31 & 100 & 100 & 95.81 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Random Forest classification accuracy assessment (confusion matrix) of the crop area from 2021 to 2023. Figure 6: Regression validation of crop mapping accuracy for 2019–2022. (**a–d**) Regression analysis of mapped versus statistical areas for four crop types (maize, oats, potato, and sesame) across counties from 2019 to 2022. (**e–h**) Crop-specific regression analysis of area estimates for maize, oats, potato, and sesame over 2019–2022. RMSE is reported in hectares (ha). distributed in the southern districts of Zhangjiakou, such as Zhuolu, Yuxian, Yangyuan, Xuanhua, Wanquan, Qiaoxi, and Huaian, and its proportion was 31% in 2019, peaked at 35.6% in 2020, and then decreased to 30% in 2023.