## 4 Discussion  
### How Spatial Information Contributes to Field-Scale \(V_{cmax,0}^{25}\) Estimation  
This study assessed different forms of texture information for field-scale \(V_{cmax,0}^{25}\) estimation and revealed significant differences in the ability of different texture features to describe field-scale \(V_{cmax,0}^{25}\). We further elucidated the contribution of differing texture information using the SHAP method. Figure 7 shows the mean of the absolute SHAP (mean(1 SHAP1)) for the six deep neural network-based models. Due to the high dimensionality of input data, only the top five most important features were presented. In the \(\mu_{\textit{ref}}\)-driven \(V_{cmax,0}^{25}\) model (Figure 7a), the nir and red bands contributed most. This result is consistent with the current understanding of the relationship between \(V_{cmax,0}^{25}\) and the spectrum. These two bands indicate the vegetation growth information and are the components of some classical vegetation indices, such as NDVI and EVI. In the GLCM-based texture-feature-driven-\(V_{cmax,0}^{25}\) model (Figure 7c), the top 5 most important features were entropy in the green and red bands, dissimilarity in the blue band, contrast in the RGB band, and homogeneity in the green band. The five features exhibited nearly equal importance. In the LBPH-driven \(V_{cmax,0}^{25}\) model (Figure 7e), the top five most important features were the histogram bars from subregions 1, 5, 1, 2, 3. In the \(\mu_{\textit{ref}}\)-\(\sigma_{\textit{ref}}\) joint-driven model (Figure 7b), the top 5 most important features included mean value in red, green, and red-edge bands, and the standard deviation value in the green and nir bands. Here, the mean value information played a dominant role, and the standard deviation information played a subordinate one. Adding the standard deviation information diminished the importance of the nir band, which contributed most in the \(\mu_{\textit{ref}}\) -driven model. In the \(\mu_{\textit{ref}}\)-GLCM-based texture feature joint-driven model, the GLCM-based texture features contributed more than the mean reflectance. There were four GLCM textures in the top five most important features, including entropy in the blue, green and red-edge bands, and homogeneity. Conversely, the mean reflectance played a dominant role in the \(\mu_{\textit{ref}}\)-LBPH joint-driven model. The mean values of reflectance in the red, nir, green and blue bands were the top four most important features in this model. The most important LBPH feature was the histogram bar in subregion 8. The SHAP-based feature importance analysis suggests that entropy is a valuable feature for \(V_{cmax,0}^{25}\) estimation, with dissimilarity and homogeneity also showing potential. The entropy, dissimilarity, and homogeneity describe the uncertainty of, local variation in, and smoothness of the image texture, respectively [56]. There perhaps exists some inherent link between \(V_{cmax,0}^{25}\) and these GLCM-based texture features. While standard deviation is a simple and intuitive indicator of spatial heterogeneity, it offered limited information for \(V_{cmax,0}^{25}\) estimation. The LBPH also failed to indicate the dynamics of \(V_{cmax,0}^{25}\). Although this method is regarded as a powerful tool for describing local information and has achieved success in classification issues such as face recognition and weed detection, the  
Figure 6: The accuracy of \(GPP\) estimation based on the 8 field-scale \(V_{cmax,0}^{25}\) models. The blue bar represents the accuracy metrics on the training dataset, and the orange bar represents the accuracy metrics on the testing dataset. histogram-format texture descriptor may be unsuitable for regression issues. LBPH failed to provide stable features for quantifying \(V^{25}_{cmax,0}\). Despite this, the combination creating the \(\mu_{n\!f}\)-LBPH joint-driven model outperforms the other two \(\mu_{n\!f}\)-texture joint-driven model. A possible reason is that LBPH is a high-dimensional feature and contains more potential information.