Fig. 5

Validation at the county level. The subgraphs are arranged in descending order based on crop harvest area. The X-axis represents the county-level aggregation of allocated results, while the Y-axis represents the actual values from county-level statistical data. To enhance the clarity of the validation, a logarithmic transformation is performed for both axes. The validation metrics are displayed in the upper left corner of each subgraph, including the sample size \(\left(N\right)\), correlation coefficient \((r)\), coefficient of determination (\({R}^{2}\)), and root mean square error \(({RMSE})\). The count of legend represents the number of validation samples in one square block in the figure. The unit of legend (Count) represents the number of validation samples within each square block in the figure.