## 4 Discussion
### Uncertainty Quantification  
Given that deep learning models are inherently black-box in nature and subject to uncertainty, their outputs may be influenced by factors such as model parameters, training procedures, and inputs. Predictive uncertainty refers to the spatial variability in the difference between predicted and true SOM values across the study area, and its distribution is used to assess the model's generalization stability. To quantify the predictive uncertainty of the model, this study adopted the Monte Carlo Dropout method [55]. During the testing phase, the Dropout mechanism is kept active, and forward propagation is performed 100 times, each time generating a set of prediction results. The prediction error is calculated by subtracting the actual values from the predicted values across all 100 iterations. The standard deviation of these errors for each sample is then computed and used as a quantitative indicator of uncertainty. This uncertainty metric is subsequently applied to the entire cultivated area to produce a spatial uncertainty map, as shown in Figure 9. In the map, color intensity represents the magnitude of predictive uncertainty at different spatial locations, with darker colors indicating higher uncertainty. This metric effectively captures the spatial variation in predictive uncertainty and serves as a basis for evaluating the robustness and reliability of the model across different regions.  
As shown in Figure 9, the predictive uncertainty of GPTransformer exhibits relatively large fluctuations, indicating a certain degree of instability. The 1D-CNN model shows a more stable spatial distribution of predictive uncertainty, with smaller variation. Among the three models, GPTransCNN demonstrates the least spatial fluctuation in uncertainty, reflecting the most stable overall performance. To further investigate the spatial distribution of predictive uncertainty, this study introduced the Terrain Ruggedness Index (TRI) for auxiliary analysis. The TRI is an important indicator used to measure terrain heterogeneity and complexity. It quantifies the elevation differences between a grid cell and its neighboring cells, thereby reflecting the structural complexity and heterogeneity of the terrain. Higher TRI values indicate rougher surfaces and more complex terrain structures [56].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **R2** & **RMSE** & **MAE** \\ \hline Transformer & 0.2963 & 6.7240 & 5.0769 \\ NPTransformer & 0.3096 & 6.6560 & 4.9973 \\ GPTransformer & 0.3227 & 6.5835 & 5.0062 \\
1D-CNN & 0.3998 & 6.2091 & 4.4844 \\ TransCNN & 0.4151 & 6.1289 & 4.4499 \\ NPTransCNN & 0.4135 & 6.1249 & 4.4925 \\ GPTransCNN & 0.4260 & 6.0631 & 4.4334 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Results of ten-fold cross-validated ablation analysis.  
As shown in Figure 10, the spatial distribution of predictive uncertainty for the three models, along with the TRI distribution, is presented. For ease of comparison, a representative spatial region was selected and uniformly applied across all maps. This region was enlarged and displayed in the upper-right corner of each subfigure to provide a clearer visual comparison of both the differences in predictive uncertainty among the models and the correspondence between model uncertainty and TRI distribution. In areas with high TRI values, the predictive uncertainty of GPTransformer increases, indicating its limited capacity to model local features under complex terrain conditions. The 1D-CNN model shows relatively low uncertainty in these areas, indicating its ability to extract local features and adapt to terrain variation. GPTransCNN shows the lowest predictive uncertainty in high-TRI regions, further confirming that its hybrid structure effectively balances global trend modeling and local detail extraction. This enables GPTransCNN to achieve greater stability and robustness under complex terrain conditions.