## 4 Discussion
### Limitations and Future Studies  
Although our study demonstrated the effectiveness of PLSR models based on low-order FOD spectra and appropriate feature selection in capturing the variation of ChIP parameters, it is crucial to acknowledge the potential risk of overfitting when using hyperspectral data for PLSR modeling. For example, while the LASSO-based PLSR model using 1.2-order spectra achieved higher R\({}^{2}\) and RPD values in estimating \(\Phi\)F, its AICc value was higher due to the inclusion of more spectral bands (Figure 5). This may limit model transferability and broader application. Similarly, a previous study on PLSR models for estimating leaf photosynthetic capacity in temperate deciduous forests also highlighted this risk, suggesting that data-driven PLSR models may be prone to overfitting when applied across different growth stages [23]. In addition to the FOD transform used in this study to enhance the spectral data, the continuous wavelet transform may serve as an alternative method to reduce the dependence of the sample on specific data, thereby minimizing the risk of overfitting. For example, a study by [PERSON] et al. [59] demonstrated that continuous wavelet transform improved the prediction performance of potato chlorophyll content. Furthermore, an appropriate dimensionality reduction algorithm can ensure the retention of sufficient valid information while minimizing model complexity. A previous study showed that the PLSR model, relying on principal component analysis, effectively reduces collinearity and mitigates overfitting [60]. Therefore, careful consideration is required when employing data-driven PLSR models, and appropriate feature selection remains essential.  
The optimal PLSR model was developed using a composite dataset that integrates data collected across different species, canopy positions, and seasonal periods. This approach inherently accounts for spatiotemporal variation, allowing the model to generalize across  
Figure 10: The number of wavelengths selected by the LASSO algorithm for estimating ChIP parameters varies across spectral regions and different FOD orders. Each region is represented by a distinct color. The black dashed line indicates the optimal FOD order, and the total number of bands selected for estimating PSIImax (49), NPQ (74), qL (77), \(\Phi\)P (105), \(\Phi\)N (25), and \(\Phi\)F (73) are shown.  
diverse conditions. However, while the model captures overall patterns, it does not explicitly assess the effects of spatiotemporal heterogeneity on the estimation of ChIF parameters. The current sample size may limit the feasibility of such an approach. Future studies should aim to expand data collection across multiple growing seasons and environmental conditions to enhance model robustness and validate its ability to mitigate the effects of spatiotemporal heterogeneity.  
In addition, while the contribution of selected bands in the optimal PLSR model used to track ChIF parameters was analyzed, data-driven PLSR models may not fully match the known absorption features. For example, the contribution rates of selected wavelengths to the estimation of NPQ, qL, and \(\Phi\)F were relatively low (Figure 7). This is an inherent characteristic of data-driven PLSR models, where multiple wavelengths collectively contribute to the prediction, rather than relying on a few dominant features. As a result, a mechanistic evaluation of the selected bands remains challenging. Future studies will need to explore a broader range of species and establish more comprehensive datasets to enhance the generalizability and scalability of the model. Furthermore, given the complex nonlinear relationships among the variables in the model, future research may benefit from integrating PLSR models with traditional mechanistic models to improve both interpretability and prediction accuracy.